INFLUENCE OF SUBMERGED CHANNEL OBSTRUCTIONS ON FLOW
PATTERNS, TURBULENCE, AND BED MORPHOLOGY UNDER ICE COVER EXPERIMENTAL STUDY AND NUMERICAL SIMULATION

by

Guowei Li
B.Eng., Chang’an University, China, 2019
M.L.W.S., University of British Columbia, 2020

DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
IN
NATURAL RESOURCES AND ENVIRONMENTAL STUDIES

UNIVERSITY OF NORTHERN BRITISH COLUMBIA
October 2024
© Guowei Li, 2024

Abstract
This dissertation explores the complex interactions between submerged angled spur dikes,
rigid leafless vegetation, and ice cover in cold-region rivers, focusing on understanding their
effects on flow dynamics, sediment transport, and scour formation. The research addresses a
significant gap in existing knowledge by examining these interactions under various flow
conditions, including open channel and ice-covered scenarios, through large-scale flume
experiments and advanced numerical simulations.

The study first investigates the influence of spur dike orientation, submergence level, and
ice cover roughness on local scour depth and flow patterns. Results reveal that larger dike
alignment angles (greater than 90°) reduce scour depth, while rough ice cover exacerbates
scouring compared to smooth ice conditions. The research highlights the critical role of dike
orientation and ice roughness in designing hydraulic structures to minimize erosion and protect
riverbanks. Building on these findings, the second part of the study focuses on the turbulent
flow structures around submerged angled spur dikes under ice cover. Quadrant analysis
indicates that ice cover intensifies turbulence, mainly through increased ejection and sweep
events near the dike tip, leading to more significant sediment mobilization and scour. The
research emphasizes the importance of considering ice-covered flow dynamics in river
engineering, especially in cold regions where ice significantly alters flow behavior. The final
component of the dissertation examines the hydrodynamic characteristics within vegetated
pools under ice cover representing regional obstruction to the flow field, emphasizing the role
of vegetation configuration on flow modification. The study demonstrates that vegetation,
particularly in staggered configurations, effectively reduces flow velocity and enhances

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sediment deposition, creating favorable conditions for aquatic habitats. However, ice cover
introduces additional complexity by altering the velocity profiles and turbulence distribution,
with implications for river management and restoration efforts.

The findings of this research provide valuable insights into the design and implementation
of river management strategies in cold climates. The study’s outcomes have practical
applications in optimizing spur dike configurations, enhancing the effectiveness of vegetated
riverbank stabilization, and improving the resilience of river ecosystems to ice-related
challenges. Future research should further explore the synergistic effects of spur dikes and
vegetation, integrate more diverse vegetation models, and validate these findings in natural
river systems under varying climatic conditions.

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Preface
I served as the primary investigator in this research, responsible for designing the
experimental plan, collecting and processing data, and interpreting the results. I also led the
manuscript writing process and integrated the reviewers’ feedback into the final versions of the
dissertation. However, I recognize the assistance from my lab partner, Sanaz Sediqi, for her
help in flume preparation, and my supervisory committee members, such as Dr. Jueyi Sui and
Prof. Mauricio Dziedzic, for their role in finalizing the manuscripts, supervising the
experimental design and assisting with data analysis. Due to their considerable contributions,
they have been included as co-authors in some related publications.
This Ph.D. dissertation has resulted in one published manuscript for Chapter 3, with the
manuscript for Chapter 4 accepted and the manuscript for Chapter 5 currently under review.
This dissertation’s publication status and authorships are as follows.

1)

Li, G., Sui, J., Sediqi, S., & Dziedzic, M. (2023). Local scour around submerged
angled spur dikes under ice cover. International Journal of Sediment Research, 38(6),
781–793. https://doi.org/10.1016/j.ijsrc.2023.08.003

2) Li, G., Sui, J., Sediqi, S. (2024). Turbulent flow structure around submerged angled
spur dikes under ice cover. Manuscript submitted to Journal of Hydrology and
Hydromechanics (accepted, forwarded to the publisher for copy editing and
typesetting).
3) Li, G., Sui, J., Sediqi, S. (2024). Hydrodynamic characteristics in pools with leafless
vegetation under ice-covered flow conditions - an experimental study and numerical
simulation. Manuscript submitted to Journal of Hydrology (under review).
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TABLE OF CONTENTS

Abstract .......................................................................................................................................... ii
Preface ........................................................................................................................................... iv
TABLE OF CONTENTS .............................................................................................................. v
List of Tables ................................................................................................................................ vii
List of Figures ............................................................................................................................. viii
Acknowledgment ......................................................................................................................... xii
1.

CHAPTER ONE: INTRODUCTION AND LITERATURE REVIEW ............................ 1
1.1 Channel Bed Deformation and Navigation Regulation ....................................................... 1
1.2 Local Scour Around Hydraulic Structures ...........................................................................8
1.3 Submerged Aquatic Vegetation Patches ..............................................................................20
1.4 Pool-Riffle Sequences............................................................................................................32
1.5 Formation of Ice Cover in Natural Rivers ..........................................................................38
1.6 Hypothesis..............................................................................................................................44
1.7 Objectives ..............................................................................................................................48
1.8 Thesis Structure ....................................................................................................................51

2.

CHAPTER TWO: MATERIALS, METHODS AND EXPERIMENTAL DESIGN ...... 56
2.1 Experimental Flume and Apparatus ...................................................................................57
2.2 Submerged Spur Dike and Vegetated Pool Setup ..............................................................62
2.3 Sediments and Gravel ...........................................................................................................68
2.4 Synthetic Ice Cover ...............................................................................................................69
2.5 Numerical Simulation Setup ................................................................................................72
2.6 Research Innovation .............................................................................................................77

3.

CHAPTER THREE: LOCAL SCOUR AROUND SUBMERGED ANGLED SPUR

DIKES UNDER ICE COVER .................................................................................................... 79
3.1 Introduction ...........................................................................................................................79
3.2 Materials and Methods .........................................................................................................83
3.3 Results and Discussions ........................................................................................................90
3.4 Chapter Summary............................................................................................................... 105

4.

CHAPTER FOUR: TURBULENT FLOW STRUCTURE AROUND SUBMERGED

ANGLED SPUR DIKES UNDER ICE COVER .................................................................... 108
4.1 Introduction ......................................................................................................................... 108
4.2 Material and Methods ........................................................................................................ 111
4.3 Results and Discussions ...................................................................................................... 119
4.4 Limitations and Recommendations ................................................................................... 139
4.5 Chapter Summary............................................................................................................... 140
v

5.

CHAPTER FIVE: HYDRODYNAMIC CHARACTERISTICS IN POOLS WITH

LEAFLESS VEGETATION UNDER ICE COVER .............................................................. 144
5.1 Introduction ......................................................................................................................... 144
5.2 Laboratory Experiments ....................................................................................................149
5.3 Numerical Model................................................................................................................. 155
5.4 Results and Discussions ......................................................................................................160
5.5 Chapter Summary............................................................................................................... 188

6.

CHAPTER SIX: GENERAL CONCLUSIONS .............................................................. 192
6.1 Synthesis .............................................................................................................................. 192
6.2 Conclusions of Chapter Three ........................................................................................... 194
6.3 Conclusions of Chapter Four ............................................................................................. 195
6.4 Conclusions of Chapter Five .............................................................................................. 196
6.5 Significance of This Study ..................................................................................................198
6.6 Limitation of the Current Study ........................................................................................ 200
6.7 Future Directions ................................................................................................................. 202

BIBLIOGRAPHY ..................................................................................................................... 206
APPENDIX I. TERRAIN ELEVATION SHANGE CONTOURS ........................................ 227
APPENDIX II. LINEAR REGRESSION DATA WORKSHEET ......................................... 253
APPENDIX III. NUMERICAL SIMULATION RUNNING TIME OPTIMIZATION ...... 257
APPENDIX IV. SEDIMENT SIZE DISTRIBUTION IN NECHOKO RIVER................... 259

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List of Tables
Table 1.1 Equilibrium Scour Predictive Equations .............................................................................................. 16
Table 3.1 Summary of working parameter setups under the smooth ice cover .................................................... 89
Table 3.2 Type III sum of squares analysis results ............................................................................................. 104
Table 4.1 Summary of experimental conditions and features of the flume and spur dikes under the open channel
condition. ............................................................................................................................................................ 115
Table 4.2 Examples of curve-fitting constants in the logarithmic law equation for L = 50 cm spur dike. ......... 127
Table 4.3 Comparison of the RSS-increasing, RSS-damping, and RSS-decreasing zones under open, smooth,
and rough ice-covered flow conditions. .............................................................................................................. 133
Table 5.1 Parameters in the Pool Section and Model Setups ............................................................................. 161
Table A.II.1 Linear regression data worksheet for the derivation of the empirical equation of local scour around
the submerged spur dike (upstream sandbox) ..................................................................................................... 253
Table A.II.2 Validation worksheet of the derived local scour around submerged angled spur dikes using data
collected from the downstream sandbox. ........................................................................................................... 255

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List of Figures
Figure 1.1. Illustration depicting the critical coherent structures and physical phenomena occurring in the flow
around a solitary spur dike (source: Koken & Constantinescu, 2008a). ................................................................. 6
Figure 1.2 Damages to a spur dike from tidal bores include several critical impacts: (a) the upstream
propagation of a tidal bore, (b) the destruction of the spur dike structure, and (c) the overturning of concrete
armor, with the inset showing how the tidal bore dislodges concrete armor placed against the seawall. (source:
Pan & Li, 2022) .................................................................................................................................................... 10
Figure 1.3 Progression of scour over time in clear-water and live-bed conditions (source: Chabert &
Engelrndinger, 1956). ........................................................................................................................................... 11
Figure 1.4 Interactive effects of wave-dominated flows over submerged canopies (A) KH-vortices generated by
velocity gradients at the canopy top and (B) asymmetrical particle motion leading to a strong mean drift above
the canopy (Abdolahpour et al., 2020). ................................................................................................................ 21
Figure 1.5 Schematic of a riffle-pool sequence at low flow, illustrating 1. flow acceleration, 2. deceleration
above pools, 3. regressive run erosion, 4. pool refilling, 5. coarse grain accumulation from bank erosion, and 6.
pool scouring with riffle deposition during high flows (source: Fuller, 2018). .................................................... 33
Figure 1.6 Flow characteristics in ice-covered river channels: (a) cross-sectional geometry, (b) partial crosssection view, and (c) vertical profiles of velocity and shear stress (source: J. Pan et al., 2023). .......................... 39
Figure 2.1 The layout of the experimental flume. ................................................................................................ 59
Figure 2.2 Flow-3D simulation results of the cross-sectional velocity contour. Contour lines are distributed
evenly in the flume cross-section, indicating that the impacts of secondary currents and side walls are negligible.
.............................................................................................................................................................................. 60
Figure 2.3 The submerged angled spur dike model was built with marine plywood (120° alignment with flume
wall, water flowing from left to right). ................................................................................................................. 64
Figure 2.4 (a) Picture of the non-vegetated pool; (b) Pool section and the cartesian coordinate system for the
experimental setup. ............................................................................................................................................... 65
Figure 2.5 Top view of a vegetation zone and ADV measurement positions within the pool area. ..................... 67
Figure 2.6 Sieve analysis results of the bed sediments used in this study. ........................................................... 69
Figure 2.7 Styrofoam cubes are attached to the Styrofoam panel to simulate the rough ice cover. ..................... 71
Figure 2.8 The vegetated pool's simulation model and boundary conditions under ice-covered flow conditions.
.............................................................................................................................................................................. 76
Figure 3.1 Schematic diagram of the experimental flume setup for local scour around submerged angled spur
dikes...................................................................................................................................................................... 85
Figure 3.2 Field photo of the Quesnel River Research Center (QRRC) experimental flume. ............................. 86
Figure 3.3 Channel bed elevation contours around a spur dike: (a) Open channel flow; (b) Smooth ice-covered
flow; and (c) Rough ice-covered flow (units: mm)............................................................................................... 92
Figure 3.4 Variations of ds/(Lsin α) values for different cover conditions under different submergence levels. .. 93
Figure 3.5 Dependence of ds/(Lsin α) values on submergence ratio (S). ............................................................. 94
Figure 3.6 Variation of ds/L against α (minor submergence)................................................................................ 95
Figure 3.7 Variation of ds/L against α (moderate submergence). ......................................................................... 96
Figure 3.8 Dependence of the dimensionless maximum scour depth ds/(Lsin α) on Froude number (Fr)........... 97
Figure 3.9 Comparison of dependence of ds/(Lsin α) on Frd for different submergence levels under different

viii

cover conditions.................................................................................................................................................... 99
Figure 3.10 Dependence of ds/(Lsin α) on Frd under different cover conditions for different submergence levels.
............................................................................................................................................................................ 100
Figure 3.11 Comparison between measured and calculated (using Equation (10)) values of maximum relative
scour.................................................................................................................................................................... 103
Figure 4.1 Schematic diagram of the experimental flume: (a) Side view; (b) Cartesian coordinate system. ..... 112
Figure 4.2 Schematic plot of measuring positions (dike length = 50cm). .......................................................... 115
Figure 4.3 The non-dimensional streamwise velocities (u/uavg.) in front of the spur dike tip (minor submergence
of spur dikes, T = 25 cm). ................................................................................................................................... 120
Figure 4.4 Flow velocity vectors generated from measured data in the X-Y plane close to the dike tip for
different alignment angles (z/h = 0.45). Note: The origin (0,0) is located at the center of the spur dike surface
attached to the sidewall, and the flow direction is from left to right................................................................... 121
Figure 4.5 Time-averaged streamwise velocity contours at the rear side of the spur dike (x = 0.025 m, α = 90°).
The outline of the spur dike is denoted in dash lines, and the flow is oriented towards the viewer and
perpendicular to the paper’s plane. ..................................................................................................................... 122
Figure 4.6 Time-averaged lateral velocity contours at the rear side of the spur dike (x = 0.025 m, α = 90°). The
outline of the spur dike is denoted in dash lines, and the flow is oriented towards the viewer and perpendicular to
the paper's plane. ................................................................................................................................................ 123
Figure 4.7 Time-averaged vertical velocity contours at the rear side of the spur dike (x = 0.025 m, α = 90°). The
outline of the spur dike is denoted in dash lines, and the flow is oriented towards the viewer and perpendicular to
the paper's plane. ................................................................................................................................................ 124
Figure 4.8 Flow vectors in the X-Z plane at the dike tip (y = 60 cm, T = 25 cm, α = 90°). (a) Open channel, (b)
Smooth ice cover, (c) Rough ice cover. The spur dike outline is shaded in light grey, and the flow direction is
from left to right. ................................................................................................................................................ 125
Figure 4.9 Fitting logarithmic law distribution on measured data under the open channel flow condition. ...... 127
Figure 4.10 Comparison of the measured (Obs.) and equation-estimated (Est.) velocities. .............................. 129
Figure 4.11 Vertical RSS profiles in the X-Z plane (−‫ݑ‬′‫ݓ‬′/‫ ∗ ݑ‬2) for the minor submergence case of the spur
dike. .................................................................................................................................................................... 130
Figure 4.12 Vertical RSS profiles in the X-Z plane (−‫ݑ‬′‫ݓ‬′/‫ ∗ ݑ‬2) for moderate submergence case of the spur
dike. .................................................................................................................................................................... 131
Figure 4.13 Reynolds shear stress distribution in the RSS-increasing, RSS-damping, and RSS-decreasing zones
............................................................................................................................................................................ 133
Figure 4.14 Percentage of the dominating turbulent events at the dike tip across the measured flow depth with
different hole size values (Ht) (α = 90°, L = 50 cm, T = 25 cm). ........................................................................ 135
Figure 4.15 Variation of the absolute contributions values |Si| along the measured results around spur dikes for
the case of Ht = 0. ............................................................................................................................................... 137
Figure 4.16 Probability distributions of u’/u* and w’/u* at z/H = 0.04 when Ht = 0 (α = 90°, L = 50cm, T = H).
............................................................................................................................................................................ 139
Figure 5.1 (a) Front view and (b) plan view of the experimental flume. ........................................................... 151
Figure 5.2 (a). Picture of the non-vegetated pool; (b) Pool section and the cartesian coordinate system for the
experimental setup. ............................................................................................................................................. 151
Figure 5.3 Top view of a vegetation zone and ADV measurement positions within the pool area. ................... 154

ix

Figure 5.4 Styrofoam cubes are attached to the Styrofoam panel to simulate the rough ice cover. ................... 155
Figure 5.5 The vegetated pool's simulation model and boundary conditions under ice-covered flow conditions.
............................................................................................................................................................................ 160
Figure 5.6 Simulated streamwise velocity profiles using Flow-3D for non-vegetated flume under open channel
conditions for pools with entrance and exit slopes of (a) 5°, (b) 7°, and (c) 10°. Simulation results for the pool
with an entrance and exit slope of 10° show optimal conditions for fully developed flow, consistent with ADV
measurements. .................................................................................................................................................... 162
Figure 5.7 Validation of numerical results against those of experiments. Red lines indicate the slope. However,
the figures indicate the velocity variation with depth, and thus velocity measurements were all conducted above
the channel bed and slope. (a) ADV measurement locations along the centerline; (b) Averaged streamwise
velocity profiles in the pool without vegetation under open flow conditions; (c) Averaged streamwise velocity
profiles in the pool with vegetation under open flow conditions. ....................................................................... 165
Figure 5.8 Simulated cross-sectional velocity contours in the pool (a) without the presence of vegetation in the
pool (open channel flow); (b) with vegetation in the pool (vegetation height =15 cm, open channel flow); (c)
with vegetation in the pool (vegetation height =15 cm, smooth ice-covered flow); (d) with vegetation in the pool
(vegetation height =15 cm, rough ice-covered flow) (unit: m/s). ....................................................................... 168
Figure 5.9 Secondary flow velocity vector diagram in the presence of vegetation in the pool bed under different
water surface cover conditions (vegetation height = 15cm; unit: m/s). .............................................................. 169
Figure 5.10 Streamwise velocity contour diagram near the vegetation zone in the pool (unit: m/s): (a) open flow,
vegetation height = 15 cm, (b) smooth ice-covered flow, vegetation height = 15 cm, (c) open channel flow,
vegetation height = 10 cm .................................................................................................................................. 172
Figure 5.11 Time-averaged velocity fields along the central axis (X-Z plane) of the pool channel: (a) Nonvegetated open channel flow; (b) vegetated open channel flow (vegetation height =10 cm); (c) vegetated open
channel flow (vegetation height =15 cm); (d) vegetated smooth ice-covered flow (vegetation height =15 cm); (d)
vegetated rough ice-covered flow (vegetation height =15 cm) ........................................................................... 174
Figure 5.12 Profiling positions for the streamwise velocity in the numerical model (staggered vegetation
arrangement). ...................................................................................................................................................... 175
Figure 5.13 Comparison of streamwise velocity at various positions with different submerged vegetation
heights (staggered vegetation arrangement). ...................................................................................................... 176
Figure 5.14 Streamwise velocity under different surface cover conditions behind vegetation elements
(vegetation height = 10 cm, staggered vegetation arrangement). ....................................................................... 178
Figure 5.15 The numerical model simulated the TKE contour in the X-Z plane (staggered vegetation
arrangement). ...................................................................................................................................................... 179
Figure 5.16 Comparison of turbulent kinetic energy across various positions in the vegetated pool zone (y = 0,
staggered vegetation arrangement). .................................................................................................................... 180
Figure 5.17 Streamwise turbulent kinetic energy distribution along the vegetated deep pool. .......................... 182
Figure 5.18 Comparison of turbulent kinetic energy (TKE) behind vegetation elements arranged in a staggered
configuration under different water surface cover conditions. ........................................................................... 183
Figure 5.19 Comparison of the simulated turbulent kinetic energy (TKE) under different inflow conditions
under open channel flow. .................................................................................................................................... 184
Figure 5.20 Comparison of measured velocity values (u/U0) to calculation using Equation (5.22). ................. 188
Figure A.I Terrain elevation change countours .................................................................................................. 257
Figure A.III.1 FLOW-3D simulation log for running at the same time as experimental vegetated pool conditions

x

(118 days, not realistic for multiple simulations)................................................................................................ 257
Figure A.III.2 FLOW-3D tips on steady solution time (approximately 800 seconds). The simulation duration
was set as 1000 seconds for each case to save computational time. ................................................................... 258

xi

Acknowledgment
I want to express my deepest gratitude to my supervisor, Dr. Jueyi Sui, for his unwavering
support, patience, and guidance throughout my Ph.D. journey. His extensive knowledge and
insightful feedback have been instrumental in refining my research and shaping the quality of
this dissertation. I am truly fortunate to have had his mentorship, which extended beyond
academics and helped me grow professionally and personally.
I am also sincerely grateful to my committee members, Prof. Mauricio Dziedzic, Dr. Faran
Ali, and Dr. Liang Chen, for their valuable contributions. Their insightful comments and
suggestions have been crucial in shaping the direction and outcome of my research. I want to
express my special thanks to Prof. Mauricio Dziedzic for helping me acquire the license for the
Flow-3D software and all the assistance from Dr. Nikhil P. Aravindakshan at UNBC HPC
Center and Cristine Webb from Flow Science Inc.
My heartfelt thanks go to Dr. Ellen Petticrew and Dr. Phil Owens for providing the
resources and facilities at the Quesnel River Research Center (QRRC), which significantly
enhanced the depth and quality of my work. I am also profoundly thankful to Dr. Jason Raine
and Jordan Lindgren for their kindness, support, and the time they dedicated to assisting me. I
also want to acknowledge the assistance of my dear friend Sanaz Sediqi, whose continuous
collaboration has been a great source of strength during my studies.
I also greatly appreciate the support from my parents and grandparents, who always
comforted me during my lowest time, especially my mom. Lastly, I want to acknowledge the
spiritual guidance and encouragement from God, whose presence has provided me with the
strength, clarity, and perseverance needed to complete this journey.

xii

1.

CHAPTER ONE: INTRODUCTION AND LITERATURE REVIEW

This research was driven by recognizing the significant role that river restoration
structures, such as spur dikes in channels and rigid leafless vegetation patches in pools and ice
cover, influence flow dynamics within fluvial systems. While the effects of spur dikes in
channels, vegetation patches in pools and ice cover, have been studied independently, a lack of
research has explored their combined impact on flow resistance and channel bed deformation.
This study aimed to fill that gap by thoroughly investigating the interplay between various
structures and ice cover, such as spur dikes and rigid leafless vegetation patches. This research
critically evaluates how these structures influence flow resistance and channel bed deformation
by examining various configurations and arrangements of spur dikes in sandboxes and
vegetation patches in an artificially constructed pool and the effects of ice cover roughness.
Understanding these combined effects is essential for the sustainable management and
restoration of river systems, particularly in cold-weather environments. The insights gained
from this study can guide decisions related to vegetation restoration, channel regulation, and
the revitalization of river ecosystems. Furthermore, the findings contribute to developing
precise assessment methods that can be applied in future restoration projects, helping to
mitigate flood risks and ensure the long-term stability of river channels.

1.1 Channel Bed Deformation and Navigation Regulation
Riverbed deformation results from the interaction between water flow and the riverbed. A
particular riverbed morphology and sediment composition correspond to specific flow
conditions, and in turn, such flow conditions contribute to different extent of riverbed
1

deformations. The factors influencing riverbed deformation are highly complex, some of which
include (1) tectonic movements and the Earth’s rotational dynamics, (2) changes in water
volume and the process of runoff variation, (3) the river’s sediment load, leading to significant
changes in sediment composition, (4) riverbed morphology and geological conditions, (5)
anthropogenic activities (van Denderen et al., 2022; Wang & Xu, 2018; Zheng et al., 2022).
The equilibrium state of a river is temporary and relative; riverbed deformation is an ongoing
process.
The slope is often steep, with complex topography in the upstream sections of large rivers,
while downstream sections frequently flow through broad plains. Mountainous rivers feature
steep bed slopes and turbulent flow, whereas rivers on plains often have unstable beds and
shallow, meandering channels (Van Appledorn et al., 2019). Given the complexity of riverbed
deformation and sediment transport, some of the primary objectives of river regulation are to
prevent further bed deterioration, mitigate floods and droughts, and still meet ecological and
societal needs by establishing reasonable flow standards and implementing appropriate
regulatory structures (Boulange et al., 2021; Chen & Olden, 2017; Xu et al., 2021). Long-term
river regulation generally focuses on flood prevention and runoff navigation under the joint
impacts of climate change and urbanization (Li et al., 2024). In contrast, short-term and
localized regulation aims to prevent bank erosion, stabilize hydraulic structures, and ensure
transportation facility safety (e.g., canals and bridges) (Duró et al., 2020).
Flood management is the primary objective in managing major Canadian rivers. The
persistent flooding challenges across the country in the 1970s highlighted the need for a shift
from traditional methods focused solely on structural solutions and disaster aid. This shift was

2

driven by dissatisfaction with the limitations of structural approaches, concerns over the
redistribution of resources from the public to floodplain residents, evolving social values,
increasing urbanization, and the continuous rise in flood damage costs despite existing control
measures. In response, the federal government undertook a comprehensive evaluation of its
flood management programs and policies, aiming to develop a new national strategy to address
flood-related issues. This assessment incorporated input from provincial agencies, insights
from joint basin study reports, and lessons from the U.S. experience managing flood losses. As
a result, the Flood Damage Reduction Program was launched in 1975 (Watt, 2013, pp. 1976–
1995). Regardless of the objectives of river regulation, such activities should not cause
significant ecological impacts or damage to the river sections or neighboring areas. All river
regulation projects must adhere to this principle to satisfy the Sustainable Development Goals
(SDGs) (Widén et al., 2022).

1.1.1 Spur Dikes for River Regulation
Spur dikes, or groins, are hydraulic structures extending from riverbanks into the flow,
designed to alter water currents and stabilize river channels. Primarily used in river engineering
and navigation, these structures serve multiple purposes, including bank protection, sediment
management, and flow direction. By deflecting strong currents away from the banks, spur dikes
reduce erosion, promote sediment deposition in targeted areas, and create favorable conditions
for navigation (Kumar & Ojha, 2021). The effectiveness of spur dikes depends on their length,
orientation, spacing, and river flow conditions (Patel & Kumar, 2024). As integral to river
regulation strategies, spur dikes are crucial for maintaining channel stability and mitigating
3

flood risks, particularly in regions with complex hydraulic dynamics. The design and
implementation of spur dikes require careful consideration of the interplay between hydraulic
forces, sediment transport, and environmental impacts, making them a critical focus in the
study of river engineering.
Spur dikes can be designed in various plan view shapes, including straight, L-head, Thead, hockey, inverted hockey, and curved (Alasadi et al., 2023). Among these, the straight
rectangular shape is the most researched. Depending on their orientation angle relative to the
flow direction, spur dikes can also be classified as attracting (oriented towards downstream),
deflecting (90° alignment with the bank), or repelling (oriented towards upstream). Structurally,
they can be either impermeable or permeable. A submerged spur dike is entirely underwater,
while a non-submerged spur dike remains partially above the water's surface (Patel et al., 2022).
The head of the spur dike can also take on different shapes, including rectangular, chamfered,
and oblong (Masjedi & Foroushani, 2012). Spur dikes can be arranged individually or in groups
for different design purposes (Ulu et al., 2023). However, if two spur dikes are placed at
significant distances from each other along a river, they should also be referred to as individual
spur dikes.
This study focuses mainly on submerged repelling spur dikes. These spur dikes are
typically used in river regulation projects to improve navigability, especially in rivers with
shallow channels where navigation difficulties frequently arise. In such cases, spur dikes are
employed to straighten the river channel, stabilize navigation routes, and increase channel
depth, thereby facilitating sedimentation (Liu et al., 2024). Given the complexities associated
with sediment transport and channel morphology in regulated rivers, the orientation angle of

4

spur dikes is particularly critical. Spur dikes oriented at angles greater than 90° (repelling) are
particularly effective for bank protection, as they promote sediment deposition between them,
resulting in a highly stable riverbank (Patel et al., 2022).

1.1.2 Major Hydraulic Issues of Spur Dikes
Spur dikes are widely applied in river regulation projects, making the study of their
hydraulic characteristics and associated channel deformation critical for engineering purposes.
The main issues include the water surface profile near the spur dike, the flow field, and the
potential for scouring around the dike head (Huang et al., 2019; Li et al., 2024).
The primary effects of spur dikes under submerged conditions are to scour the riverbed,
increase flow velocity to erode shallow areas or block and redirect the flow to raise water levels
upstream, slowing down the flow (Huang et al., 2019). After a spur dike is constructed, the
upstream flow is obstructed when water flows towards it, reducing flow velocity and lowering
the water surface as water reaches the spur dike. Due to the narrowing of the channel, both
flow velocity and turbulence increase. When the water flows past the spur dike, the flow
gradually recovers, with velocity and turbulence decreasing and the water surface rising,
eventually merging with the natural river section and returning to normal conditions (Qi et al.,
2024).
Spur dikes influence the main flow in two primary ways: by affecting the overall
movement of the main flow and by expanding the recirculation zones around the dike head and
wake region (Huang et al., 2019). Studies have shown that spur dikes create a distinct shear
layer and high-energy turbulent zone downstream (Koken & Constantinescu, 2008a). The
5

vortex formed by the dike head is the leading cause of local scouring. This study focuses on
the scouring effects and flow field alterations around spur dikes.

Figure 1.1. Illustration depicting the critical coherent structures and physical phenomena occurring in the flow
around a solitary spur dike (source: Koken & Constantinescu, 2008a).

The study of water surface and near-field flow regions generally employs theoretical
calculations, physical model experiments, and field observations (Zhang & Liu, 2023).
Physical models are utilized in scientific research to study fundamental processes and their
interactions under controlled conditions, in hydraulic engineering for planning and design
purposes, and to assist in public decision-making by providing clear explanations and
demonstrations (Mosselman, 2018). However, physical models have limitations, including
scaling issues and lengthy research periods, which restrict their flexibility, adjustment, and
optimization (Schweiger et al., 2020). Therefore, leveraging the latest advancements in
computational fluid dynamics (CFD) and numerical simulation technologies, alongside
developments in hydraulics research, offers significant academic and engineering potential for
advancing river and port regulation projects.
In river regulation, numerical models are valuable in scientific research, but their field

6

applications often cannot be fully verified or validated by strict scientific standards
(Mosselman, 2018). Over the past decade, considerable effort has been dedicated to developing
various CFD simulations of flow fields obstructed by spur dikes (e.g., Mulahasan et al., 2023).
The reliability of simulation results has gained increasing acceptance, and the application of
numerical methods in engineering projects has expanded. Incorporating these advancements,
substantial researchers have conducted investigations on Canada’s natural river and navigation
regulation, achieving significant outcomes (e.g., Seo & Wang, 2021). Physical modeling has
become increasingly vital in hydraulic engineering, particularly in understanding hydraulic
structures like spillways, energy dissipation systems, and river channels. These models are
essential for ensuring the accuracy and reliability of engineering designs, which directly
contribute to the success of projects and the development of new techniques in related fields
(Peña & Anta, 2021).
Traditional hydraulic mass, momentum, and energy equations commonly serve as the
basis for open-channel calculations (Gray & Miller, 2023). However, for natural flows in
complex topographies, accurately determining parameters such as channel slope, energy loss
coefficients, and adequate water surface area is challenging, often leading to significant errors
in computational results (Xue et al., 2023). Due to the three-dimensional complexity of natural
flows, using more refined analytical models to simulate these profiles has become a focal point
in river regulation practice.
In fluid mechanics studies, physical modeling experiments face limitations due to the scale
of the models, making it difficult to measure flow velocities accurately in many scenarios,
especially in downstream regions (Pfister & Chanson, 2014). As a result, numerical modeling

7

has become an essential development trend. In recent years, three-dimensional flow
simulations of gas-liquid-solid multiphase flow modeling methods have been successfully
applied in various fields, including hydraulic engineering, chemical engineering, structural
engineering, and environmental engineering (Sun & Sakai, 2015). These methods have
successfully replicated complex physical processes that are difficult to capture through physical
model experiments and have provided crucial physical parameters that are challenging to
measure. Such data is essential for understanding the mechanisms of physical changes and
informing engineering design. Thus, numerical modeling methods have become vital in
scientific research and engineering applications.
Spur dikes designed for partial submergence (non-submerged conditions) and installed in
the field typically have irregular shapes. During flood events, these non-submerged spur dikes
become submerged, functioning as fully submerged dikes, particularly considering the impact
of increasing climate change (Gul et al., 2024; Lodhi et al., 2015). Therefore, submerged spur
dike configuration is the focus of this research.

1.2 Local Scour Around Hydraulic Structures
Local scour is a natural phenomenon caused by the action of water flow on riverbeds,
often leading to structure foundation erosion, such as pier and abutment scour, which can result
in structure failure. The mechanisms of local scour around spur dikes resemble the bridge
abutments (Kothyari & Ranga Raju, 2001). For hydraulic structures such as spur dikes and
bridges, damage caused by local scour is severe. In Europe, the 2002 flood in Germany resulted
in bridge and road infrastructure repair costs of €577 million, while Austria’s ÖBB suffered
8

approximately €100 million in economic losses due to the same event. In the U.K., flood events
in 2009 caused the partial or complete destruction of 20 road bridges, leading to estimated
financial losses of around £2 million per week. Scour risk mitigation in Europe is projected to
cost €541 million annually between 2040 and 2070. In the U.S., major floods in 1964 and 1972
caused bridge and highway damages amounting to $100 million per event, and the Federal
Highway Administration (FHWA) estimates that 50 to 60 bridges collapse annually due to such
events. In New Zealand, scour damage costs are estimated at 36 million NZD annually. In Iran,
bridge collapse financial losses totaled $562.5 million in the first decade of the 21st century,
while South Africa’s annual scour damage costs are around 22 million ZAR. Additionally, the
2007 floods in Bangladesh and Indonesia damaged transport infrastructure, accounting for 34%
and 25% of total infrastructure costs, respectively, amounting to $363 million and $35 million
(Pizarro et al., 2020).
If the design of a spur dike is not considered adequately concerning flow conditions, the
shallow foundation can lead to scouring, resulting in structural instability and posing a hazard
to structure safety (Patel et al., 2022). The primary locations of spur dike failure are
concentrated at the dike head and foundation, where continuous water erosion weakens the
structural integrity, causing the dike to lose support and eventually collapse under its weight.
Additionally, the stones and materials composing the dike may become dislodged under the
force of upstream water flow, leading to further structural deterioration. In the section from the
confluence of the Puyang River to the Changshan sluice, over 180 spur dikes are employed for
riverbank protection in China. However, strong tidal bores and turbulent flows near the dike
head often result in significant sediment and rubble erosion, forming deep scour holes. This

9

process can lead to the collapse of the dike head, hollowing and fragmentation of the protective
covering, and subsequent damage to the entire structure (Pan & Li, 2022).

Figure 1.2 Damages to a spur dike from tidal bores include several critical impacts: (a) the upstream
propagation of a tidal bore, (b) the destruction of the spur dike structure, and (c) the overturning of concrete
armor, with the inset showing how the tidal bore dislodges concrete armor placed against the seawall. (source:
Pan & Li, 2022)

1.2.1 Classification of Local Scour
Based on sediment transport dynamics, local scour at bridge piers can be classified into
two primary types: clear-water scour and live-bed scour (Pandey et al., 2018). Clear-water
scour occurs when the flow approaching the pier is devoid of sediment, typically when the flow
velocity is insufficient to mobilize bed material upstream. In this scenario, the scour hole
develops as the sediment is eroded from around the hydraulic structure, but no additional
sediment is carried into the hole by the flow. This results in a scour depth that is generally
deeper than that found in live-bed conditions, as the absence of incoming sediment allows the
erosion process to continue unimpeded.

10

On the other hand, live-bed scour occurs when the flow carries sediment and actively
transports the sediments across the riverbed. In this case, sediment is continuously supplied to
the scour hole, partially filling it and limiting the maximum depth of the scour. The dynamic
interaction between sediment transport and erosion in live-bed conditions often leads to a more
complex and fluctuating scour profile.
Research has shown that the maximum scour depth under clear-water conditions can be
approximately 10% greater than that under live-bed conditions due to the absence of sediment
inflow to counteract the erosive forces (Chabert & Engelrndinger, 1956). Understanding these
distinctions is critical for accurately predicting scour depth and ensuring the structural integrity
of bridge piers under various hydraulic conditions.

Figure 1.3 Progression of scour over time in clear-water and live-bed conditions (source: Chabert &
Engelrndinger, 1956).

1.2.2 Mechanisms of Local Scour Around Hydraulic Structures
Current research on the flow structure around hydraulic structures generally focuses on
downflow in front of the structure, horseshoe vortices around the foundation, flow separation
11

at the sides, and wake vortices behind the structure. Apsilidis et al. (2010) conducted
experiments using Time-Resolved Digital Particle Image Velocimetry (TR-DPIV) to measure
the flow fields around cylindrical piers. The results indicated that developing three-dimensional
boundary layer separation generates well-defined horseshoe vortices closely linked to the
Reynolds number. Namaee et al. (2023) used flow measurements in flume experiments and
numerical simulation to confirm that flow separation at the sides of bridge piers forms two
counter-rotating symmetric vortices, which are then shed into the downstream flow as wake
vortices. Zhang et al. (2020) applied unstructured finite-volume modeling to simulate the flow
and local scour around a vertical cylinder, finding that the upstream horseshoe vortex reached
maximum velocity near the pier base while wake vortices formed at the rear exhibited flow
separation, aligning well with experimental observations.
The mechanisms behind local scour near the riverbed around spur dikes are complex, and
experts have differing opinions. The main perspectives on the mechanisms of local scour near
the riverbed around spur dikes are listed below.
1) Horseshoe Vortex Theory: This theory posits that the presence of the spur dike creates
horseshoe vortices near the riverbed around the dike head. These vortices intensify the scouring
effect by directing sediment and material downstream, deepening the scour holes (Koken &
Gogus, 2015).
2) Increased Downstream Flow Velocity Theory: This theory suggests that the scour at
the spur dike head is due to the flow obstruction by the dike, which accelerates the flow velocity
around the dike head. This increase in velocity causes more sediment to be transported
downstream, leading to local scour (Huang et al., 2019).

12

3) Downflow Theory: According to this theory, downflow generated by the obstruction
of the spur dike creates a pressure difference around the dike head. This pressure difference
forces water downwards, moving sediment away from the dike base and contributing to scour
(Zhuang et al., 2023).
4) Composite Theory: This perspective combines elements of the previous theories,
proposing that both downflow and horseshoe vortices, along with their interaction, contribute
to the local scour near the spur dike (Li et al., 2024).
Based on theoretical stress analysis and experimental studies, it can be concluded that
when water flows around the spur dike, the obstruction caused by the dike generates a
downflow, which creates pressure differences around the dike head. Consequently, a lowpressure zone forms behind the dike. The flow undergoes deflection, creating spiral vortices
that move downward, contributing to the scouring process. This downflow, interacting with the
velocity gradient near the riverbed, intensifies the erosion and deepens the scour hole. As the
downflow progresses, the scour hole elongates and deepens while the sediment transport rate
increases, preventing material deposition within the scour hole. This process continues until
the flow velocity at the strongest point of erosion decreases and the scour hole stabilizes (Koken
& Constantinescu, 2008a, 2008b; Li et al., 2024; Qi et al., 2024).

1.2.3 Factors Influencing Local Scour Around Spur Dikes
The factors influencing local scour near the riverbed around spur dikes can be broadly
categorized into hydrodynamic factors, sediment factors, and geometric conditions (Qi et al.,
2024). Hydrodynamic factors include flow discharge Q (m³/s), average flow velocity upstream

13

of the scour hole Uup, average flow velocity at the dike head Ud, and local gravitational
acceleration g (m/s²). Sediment factors involve the median particle size d50 (mm), sediment
density ρs, and non-uniformity coefficient. Geometric conditions encompass channel width B
(m), dike length Ld (m), dike width Bd (m), bed slope s0, and the dike orientation angle α (°).
Early research from the 1960s indicates that sediment size affects the equilibrium depth
of clear-water scour but does not influence the maximum depth of live-bed scour because,
under live-bed conditions, sediment transport maintains equilibrium, with upstream sediment
replenishing the material removed from the scour hole (National Academies of Sciences, 2021).
Studies conducted in the 2000s found that the influence of sediment size becomes negligible
when the structure size to median sediment diameter ratio exceeds 50 (Melville & Coleman,
2000). As the ratio increases, scour depth generally decreases. However, once the ratio
surpasses 100, further increases in sediment size have minimal impact on reducing scour depth
due to scaling effects (Lee & Sturm, 2009). The flow velocity and sediment transport dynamics
near the dike also influence this relationship (Li et al., 2013). Further studies have shown that
factors such as the length of the dike, its alignment with the flow, and the slope of the upstream
bank all affect scour depth (Han et al., 2022; Patel & Kumar, 2024).

1.2.4 Calculation of Maximum Local Scour Depth Around Spur Dikes
Due to the complexity of local scour near spur dike heads, most calculation methods for
maximum scour depth are based on empirical or semi-theoretical methods. Some researchers
have begun approaching this from a numerical perspective, using CFD software or HEC-RAS
to predict scour depth. However, these predictions require experimental or field data for

14

validation.
1) ys = f(...)Hup Type Calculation Equations
In this expression, ys represents the maximum local scour depth at the spur dike head, and
Hup is the average water depth upstream of the dike. The function f(...) represents the correction
factor, which depends on various parameters such as channel width B, dike length Ld, average
water depth H0, average flow velocity U0, sediment settling velocity Us, local gravitational
acceleration g, water density ρ, dynamic viscosity μ, sediment median particle diameter d50 ,
standard deviation of sediment size distribution σ, specific weight difference of sediment Δγ,
dike orientation angle α, Froude number Fr, channel slope s0, among others. Typical formulas
of this type include those by Laursen (1963), Cunha & Veiga (1970), and Froehlich (1989).
2) Calculation Equations for Local Scour around Spur Dikes under Special Conditions
When calculating local scour around spur dikes under special conditions, various
equations have been developed to address the complexity of these scenarios. Melville (1997)
proposed specific calculation methods for compound channels that account for the unique flow
dynamics present in these environments. In curved channels, the scour characteristics differ
significantly, and the equation by Ahmad (1953) is typically employed to predict scour depth
accurately. Permeable spur dikes, which allow water to pass through their structures, require a
different approach, and Nasrollahi et al. (2008) equation can be used in these cases. For nonsubmerged spur dikes, where the structure remains above the water level during flow events,
almost all equations for bridge abutments are applicable (Kothyari & Ranga Raju, 2001). When
dealing with maximum scour depth under submerged conditions, a standard method involves
calculating the equivalent clear-water scour depth for non-submerged case hn and applying a

15

correction factor k to account for the effects of submergence, yielding the maximum scour
depth hs = khn (Hao et al., 2013).
3) Hydraulic Engineering Circular No. 18 (HEC-18) Framework
The HEC-18 framework, developed by the Federal Highway Administration (FHWA), is
a widely recognized guideline for evaluating scour at hydraulic structures (Federal Highway
Administration, 2001). The Colorado State University (CSU) equation is crucial for estimating
local scour depth within this framework. The CSU equation integrates multiple factors
influencing scour, including flow velocity, flow depth, sediment size, and hydraulic structures’
geometry. Specifically, it accounts for the effects of flow intensity and the structure's shape,
providing a detailed approach to predict the maximum scour depth around spur dikes. The
equation is particularly valuable for its ability to adjust for varying hydraulic conditions and
sediment characteristics. It is a robust method for engineers and researchers on bridge and river
training projects. Applying the CSU equation within the HEC-18 framework helps ensure that
spur dike designs are resilient against potential scour-induced failures, thereby enhancing the
safety and longevity of hydraulic structures.
Table 1.1 Equilibrium Scour Predictive Equations
Reference
Equation

Notes
ys = equilibrium scour depth
y1 = approach flow depth

Ahmad (1953)

ଶ/ଷ

‫ݕ‬௦ + ‫ݕ‬ଵ = 0.45‫ܭ‬௦ ‫ݍ‬ଶ

Ks = empirical constant
q2 = local discharge intensity in
contracted channel (ft2/s)

Laursen (1963)

଻/଺
⎡൬ ‫ݕ‬௦ + 1൰
⎤
ܽ
‫ݕ‬௦ 11.5‫ݕ‬ଵ
= 5.5 ⎢
− 1⎥
଴.ହ
߬
‫ݕ‬ଵ
‫ݕ‬ଵ ⎢
⎥
ቀ ଵቁ
߬௖
⎣
⎦

16

Applies to clear-water scour.
a = characteristic width
τ1 = grain roughness component of the

bed shear
τc = critical shear stress at the threshold
of motion
Froehlich (1989)

ܽ௣ ଴.଺ଶ ܽ ଴.଴଼
‫ݕ‬௦
= 0.32‫ܭ‬௦ ‫ ݎܨ‬଴.ଶ ቀ ቁ
൬ ൰
+1
ܽ
ܽ
݀ହ଴

ap = projected width of pier

‫ݕ‬௦ = ‫ܭ‬௬௔ ‫ܭ‬ଵ ‫ܭ‬஽ ‫ܭ‬௦ ‫ܭ‬ఏ
2.4 ܽ for ܽ/‫ݕ‬ଵ < 0.7
‫ܭ‬௬௔ = ቐ2(‫ݕ‬ଵ ܽ)଴.ହ for 0.7 < ܽ/‫ݕ‬ଵ < 5
4.5‫ݕ‬ଵ for ܽ/‫ݕ‬ଵ > 5
Melville (1997)

ܸଵ − ൫ܸ௟௣ − ܸ௖ ൯
‫ܭ‬ଵ = ቐ
ܸ௖
1

V1 = approaching velocity
Vlp = flow velocity at the structure

for ‫ܭ‬ଵ < 1.0

location under live-bed conditions

for ‫ܭ‬ଵ ≥ 1.0

ܽ
ܽ
0.57݈‫݃݋‬ଵ଴ ൬2.24
൰ for
≤ 25
݀ହ଴
݀ହ଴
‫ܭ‬஽ = ൞
ܽ
1
for
> 25
݀ହ଴

Vc = critical velocity

K1 = correction factor for shape
K2 = correction factor for the attack of
the flow
FHWA (2001)

‫ݕ‬௦ = 2.0‫ܭ‬ଵ ‫ܭ‬ଶ ‫ܭ‬ଷ ‫ܭ‬ସ ܽ଴.଺ହ ‫ݕ‬ଵ଴.ଷହ ‫ݎܨ‬ଵ଴.ଷହ

K3 = correction factor for bed condition
K4 = correction factor for armoring of
bed material
Fr1 = Fr directly upstream of the
structure
m = empirical constant
Kf = correction factor for Fr
KyL = correction factor for a/y1

Nasrollahi et al.
(2008)

‫ݕ‬௦
= ݉‫ܭ‬௙ ‫ܭ‬௬௅ ‫ܭ‬ௗ ‫ܭ‬ோ ‫ܭ‬௡
ܽ

Kd = correction factor for d50
KR = correction factor for permeability
Kn = correction factor for a/B, where B =
channel width.

17

1.2.5 Numerical Modelling of Spur Dike in a Channel
Local scour around in-stream structures has long been a predominant cause of structural
damage, attracting considerable attention from scholars and engineers. Research has been
conducted on the equilibrium scour depth and the extent of scour holes around spur dikes under
open-flow conditions using flume experiments (e.g., Xu et al., 2023), field measurements (e.g.,
Pan & Li, 2022), and numerical simulations (e.g., Kuhnle et al., 2008). For one-dimensional
scour analysis such as the HEC-RAS 1D model, the HEC-18 report recommends using the
Colorado State University (CSU) equation (Richardson et al., 1990) for calculating scour under
both live-bed and clear-water conditions. This equation is the default in HEC-RAS software.
An alternative equation developed by Froehlich (1991) has also been incorporated into the local
scour estimation in many applications. Although the Froehlich equation is not recommended
in the HEC-18 report, it has demonstrated good agreement with observed data.
Two-dimensional (2D) scour around spur dikes with various alignment angles has also
been extensively studied. In these studies, the flow and local scour patterns are assumed to be
uniform across the dike’s span. Research has focused on the relationship between the
development of scour depth and bed shear stress under different flow conditions. Koken and
Constantinescu (2008a) found that in the scour initiation stage, the highest bed shear stress in
the mean flow occurs in the region of strong acceleration near the tip of the spur dike. However,
elevated shear stress values are also found beneath the upstream portion of the detached shear
layer. Additionally, Liao et al. (2021) used a 2D mobile-bed model incorporating a repose angle
formula and a bed geometry adjustment mechanism to enhance the accuracy of simulating local
scour holes around structures. Experimental studies have shown that the alignment angle

18

influences the shape and depth of the scour hole, with a right angle (90°) leading to a more
pronounced scour due to the interaction between the flow and the riverbed (Li et al., 2023).
Modified or new two-dimensional numerical models have also been developed to simulate
local scour around submerged spur dikes, considering factors such as sediment transport and
flow turbulence. For instance, Liao et al. (2014) developed the EFA2D model, a 2D mobilebed simulation incorporating non-equilibrium suspended sediment concentration and bedrock
erosion for natural rivers. Horvat et al. (2015) introduced a 2D model coupling active layer and
multiple size-class sediment transport with an improved advection algorithm, proposing a
scheme that permits larger time steps. The model was validated with field data from the Danube
River. These models have been validated against experimental data, demonstrating their
accuracy in predicting scour patterns. The results of these studies are crucial for designing spur
dikes that minimize scour risk, ensuring their stability and effectiveness in river engineering
applications.
Realistically, local scour around a submerged angled spur dike occurs in a complex threedimensional (3D) manner, where the scour process is non-uniform in any given dimension. The
initiation of scour typically begins at the leading edge of the dike and propagates downstream
along the dike’s length, altering the local flow patterns and sediment transport dynamics
(Farshad et al., 2022). Researchers have conducted physical experiments and developed 3D
models to predict scour progression around spur dikes. For instance, Han et al. (2019)
developed a three-dimensional numerical model. They utilized it to investigate flow dynamics
and local scour in fields of grouped spur dikes with varying layout angles. Implementing the
porous medium method (PMM) simplifies the process of numerical discretization and

19

differentiation. The fully three-dimensional features are evident in the spur dikes angled at 90°
and those angled downstream. The primary flow follows an S-shaped trajectory, with largescale vortices forming a recirculation zone behind the spur dikes. This flow pattern leads to a
complex distribution of suspended sediment and uneven erosion and deposition on the sandbed.

1.3 Submerged Aquatic Vegetation Patches
The evolution of river morphology is a fundamental issue in river dynamics research.
Traditional research on river channel changes typically focuses only on the interactions
between the channel and water flow without considering the influence of vegetation, which is
widely present in river systems. With its above-ground structures like stems, vegetation acts as
a resistance boundary that disturbs water flow and alters hydraulic conditions (Cui et al., 2023).
This disturbance can affect bank erosion processes, riverbank stability, and changes in river
morphology. Moreover, the root systems of vegetation intertwine with the soil, increasing its
cohesion, particularly in the case of riparian vegetation, which plays a significant role in
stabilizing riverbanks (Finotello et al., 2024). Therefore, vegetation can alter river morphology
through feedback mechanisms between river hydrodynamics and bank stabilization processes,
creating dynamic response mechanisms that exert significant influence.
The flow characteristics in vegetated channels are highly complex, influenced by the everchanging river morphology, inflow conditions, and vegetation traits such as diameter, height,
flexibility, submergence, and arrangement (Barahimi & Sui, 2024b; Li et al., 2018).
Understanding the interactions between vegetation characteristics, channel morphology, and
hydraulic properties is essential for revealing universal patterns and understanding turbulent
20

structures in rivers, thereby enriching the emerging subject of eco-hydraulics. Research on the
impact of vegetation on flow characteristics, coupled with studies on the soil stabilization
effects of vegetation roots and extending to the influence of vegetation on bank stability and
morphological evolution, can provide a comprehensive understanding of the role of vegetation
in river system evolution.

Figure 1.4 Interactive effects of wave-dominated flows over submerged canopies (A) KH-vortices generated by
velocity gradients at the canopy top and (B) asymmetrical particle motion leading to a strong mean drift above
the canopy (Abdolahpour et al., 2020).

1.3.1 Impact of Vegetation on Flow Resistance
Vegetation is a crucial biological factor in river ecosystems, but its presence can lead to
increased water levels, greater flow resistance, and reduced flow velocity. Therefore,
understanding the impact of vegetation on flow resistance is essential for ensuring the safety
of flood conveyance and making reliable flood forecasts. Flow resistance in river channels is
typically described by roughness coefficients, such as the Manning coefficient n and or the
Darcy-Weisbach friction factor f, which are comprehensive coefficients accounting for the
irregularities and roughness of the riverbed and banks (Yochum, 2018). A hydrodynamic model
with a resistance term is first established to determine these roughness coefficients. Then,
measured parameters such as water depth and flow velocity are substituted into the resistance
21

equation to obtain roughness coefficients under different hydraulic conditions. However, when
vegetation is present in the channel, factors such as the shape, flexibility, submergence, and
distribution of vegetation complicate the determination of the roughness coefficient.
To determine the variations in roughness coefficients under different vegetative flow
conditions, researchers attempted to relate the Manning coefficient n with parameters that
describe flow conditions, establishing an n-vR curve, where vR is the product of average
velocity and hydraulic radius (Chen et al., 2009). However, the n-vR curve primarily reflects
the relationship between the Manning coefficient and the Reynolds number without capturing
the essential interaction between vegetation and flow. It does not consider the influence of
vegetation characteristics such as height and arrangement. Consequently, focus has also been
given to the relationship between roughness coefficients and vegetation parameters, such as
vegetation density, stiffness, submergence, and the proportion of the river's surface area
covered by vegetation.
Since the structural characteristics of vegetation, such as stems and trunks, resemble
cylindrical shapes in their interaction with water flow, when water flows past these cylindrical
structures, it creates flow patterns similar to those observed in classical fluid dynamics studies
of flow around a cylinder (Le Minor et al., 2021). Therefore, in addition to using roughness
coefficients to reveal the impact of vegetation on flow resistance in rivers, the drag coefficient
CD can also be employed to describe the resistance effect of vegetation on water flow. Zhang
et al. (2020) examined the drag coefficient Cd associated with an array of emergent flexible
vegetation in a steady, nonuniform flow. Their investigation highlighted two key effects within
the vegetated patch: the blockage effect, which increases the drag coefficient, and the sheltering

22

effect, which reduces drag, particularly at the leading edge and tail of the vegetation. These
opposing influences are crucial in determining the overall drag dynamics within the vegetated
patch.

1.3.2 Impact of Vegetation on Bed Shear Stress
Recent studies indicate that sediment transport rates in vegetated channels are linked to
bed shear stress (Conde-Frias et al., 2023; Xu et al., 2022). Therefore, understanding the
distribution of bed shear stress in vegetated channels is crucial for comprehending sediment
transport patterns. While there are various methods to estimate bed shear stress in nonvegetated channels, these approaches often need to be more suitable for vegetated channels due
to the influence of vegetation on velocity profiles and turbulence.
In vegetated channels, the downslope force of the water due to gravity balances bed shear
stress and vegetation drag. Jordanova and James (2003) attempted to estimate bed shear stress
by subtracting vegetation drag from the downslope force. However, this method introduces
significant uncertainty since vegetation drag and downslope force are larger than bed shear
stress. In non-vegetated channels, near-bed turbulent kinetic energy (TKE) can be used to
estimate bed shear stress, as turbulence is primarily generated by bed shear, establishing a
relationship between the two. In vegetated channels, however, vegetation-generated turbulence
constitutes most of the total turbulent energy, complicating the correlation between bed shear
stress and TKE (Zhao & Nepf, 2021).
Kumar et al. (2024) used computational fluid dynamics (CFD) models to simulate bed
shear stress in vegetated channels, revealing that streamwise velocity is more remarkable in

23

non-vegetated and gap regions between vegetation stems than in areas near the vegetation. The
lowest streamwise velocity and significant negative transverse velocity are observed directly
behind the vegetation stems. Turbulent kinetic energy is higher behind the vegetation than the
front, and turbulent kinetic energy and intensity increase as the flow moves through vegetated
regions. A Reynolds stress model was used to study bed shear stress in compound channels
with floodplain vegetation (Koftis & Prinos, 2018). Results indicate that shear stress at the
floodplain bottom decreases while shear stress at the interface between the floodplain and the
main channel increases as vegetation density increases. Their simulation results closely
matched flume experimental data. Bed shear stress in vegetated experimental channels under
uniform flow conditions can be estimated with existing equations, but non-uniform flow
conditions are more common in actual river channels. Zhang et al. (2016) pointed out a generic
pattern: bed shear stress decreases along the flow direction in decelerating flows, while bed
shear stress increases along the flow direction in accelerating flows. However, the detailed
variation trend of bed shear stress in vegetated channels under non-uniform flow conditions
remains an area for further research.

1.3.3 Impact of Vegetation on Velocity Distribution
There is a significant difference in the vertical streamwise velocity distribution between
submerged and emergent vegetation regions. In channels with emergent vegetation, the vertical
velocity distribution resembles traditional open channels, with notable variations near the
riverbed due to bed resistance (Maji et al., 2017). However, in channels with submerged
vegetation, the velocity distribution no longer follows traditional patterns, especially near the

24

vegetated boundary, leading to uneven velocity distribution in the vertical direction (Barahimi
& Sui, 2024b). Two main views exist regarding the velocity distribution in submerged
vegetated regions: the two-layer and three-layer models.

1.3.3.1 Two-Layer Model
The two-layer model divides the vertical velocity profile into vegetated and free-stream
regions above the vegetation. Researchers have conducted flume experiments focusing on
various lengths and velocity gradients in vegetated conditions, deriving multiple forms of
velocity distribution equations. Kouwen et al. (1969) used the vegetation height Hv as the length
scale and the shear velocity u∗ as the velocity scale, yielding the following equation:
‫ݑ‬
‫ݑ‬௛௩ 1
‫ݕ‬
=
+ ݈݊ ൬ ൰
‫∗ݑ‬
‫ߢ ∗ݑ‬
ℎ௩

(1.1)

where κ is the von Kármán constant, and y is the height above the riverbed. Stephan and
Gutknecht (2002) used the average height of the deflected flexible vegetation hp as the
characteristic length scale for the velocity distribution above the flexible vegetation and u∗ as
the characteristic velocity scale. The equation for velocity distribution in the vegetated region
is given as:
‫ ݕ‬− ℎ௣
‫ݑ‬
1
= ݈݊ ቆ
ቇ + 8.5
‫ߢ ∗ݑ‬
ℎ௣

(1.2)

Zhang et al. (2021) used an enhanced momentum equation to derive the velocity within the
vegetation layer, while the velocity in the free-surface layer incorporates both the momentum
equation and the influence of wake effects. It can be observed that different characteristic length
scales yield different velocity distribution equations. This variation arises from differences in

25

vegetation type, density, flexibility, morphology, and flow conditions, which result in different
flow parameter distributions. However, the trends are consistent overall, and the equations
follow the expected distribution patterns.

1.3.3.2 Three-Layer Model
Compared to the two-layer model, the three-layer model is more complex, with
inconsistent standards across regions and varying velocity distribution equations. The threelayer model generally divides the flow into the lower section near the bed and vegetation
bottom, the middle section within the vegetation stern, and the upper section of free flow above
the vegetation. El‐Hakim and Salama (1992) conducted plastic model vegetation experiments,
dividing the vertical flow into sections based on the average height of the deflected flexible
vegetation Hiv and Hv1 slightly above the vegetation. In the region of 0 < z < Hiv, velocity
follows a logarithmic distribution, following the first region, when Hiv < z < Hv1, the velocity
distribution is almost linear. Lastly, various dimensionless parameters describe the velocity
distributions for Hv1 < z < H, where H is the approach water depth. Carollo et al. (2002)
introduced Y1 and Y2 as dividing points for a three-layer model, where Y is defined as z/H, i.e.,
the ratio of vertical position to flow depth. Y1 and Y2 correspond to positions slightly above and
below the vegetation and are used to separate the velocity profile into three distinct zones.
Selecting different dividing positions and using different dimensionless parameters to
describe the velocity distribution ultimately leads to varying velocity distribution models and
highlights the importance of using appropriate dimensionless parameters that account for
vegetation characteristics and flow properties to derive consistent velocity distribution
26

equations. With advances in computational fluid dynamics (CFD), numerical simulations align
well with experimental results, revealing a mirrored “S” shape for velocity profiles near the top
of the vegetation (Abid, 2020).

1.3.4 Impact of Vegetation on Turbulence Characteristics
In vegetated channels, the interface between the flow and the vegetated layer creates
strong shear forces, leading to intense turbulence and complex three-dimensional flow
variations. Researchers have conducted flume experiments and numerical simulations to
explore the turbulence characteristics in vegetated channels.

1.3.4.1 Experimental Research
Nepf and Vivoni (2000) applied the tracing method to observe turbulence structure
changes in arrays of cylindrical vegetation and discovered that turbulence scales are influenced
by vegetation density and morphology. Sanjou (2016) used dye injection to study turbulent
diffusion in submerged vegetated canopy open‐channel flows. He concluded that sweep motion
contributes more significantly to dye concentration transport near the vegetation edge than
ejection motions. Nosrati et al. (2024), Okamoto et al. (2012), and Nezu and Onitsuka (2001)
conducted flume experiments using model vegetation resembling cylinders and strips,
measuring flow fields with ADV, LDV, LIF, and PIV. The results consistently showed that
turbulence intensity peaks near the top of the vegetation canopy. Xu and Nepf (2020) studied
plastic Typha latifolia in their experiments, focusing on the interaction between flexible
vegetation and flow dynamics. Although the vegetation was arranged as emergent, it has been
27

found that turbulent kinetic energy also reaches its maximum at the top of the vegetation layer
and is vertically transferred to the riverbed, indicating that the flexibility and density of
submerged vegetation significantly affect turbulence. As the canopy density increases,
turbulence intensity and kinetic energy increase, with peak values occurring in this region
(Barahimi & Sui, 2023). Caroppi et al. (2021) compared the flow between rigid and flexible
vegetation under similar conditions. On average, the normalized shear penetration was 6–10
times higher for flexible vegetation than that observed for rigid cylinders, which leads to
broader zones where significant momentum exchange occurred with the adjacent open water.
Regarding the influence of vegetation density, Souliotis and Prinos (2011) conducted
flume experiments on submerged flexible vegetation, revealing that increasing vegetation
density accelerates the development of flow velocity and turbulence characteristics within the
vegetated patch, extending the downstream reach where these effects remain significant. Lou
et al. (2022) analyzed the relationship between vertical vegetation density and turbulence
intensity. They found that in unidirectional flow, a vertically varying vegetation density
enhances the vertical gradient of the mean streamwise velocity, leading to increased
stratification of flow velocities across different heights within the water column. Errico et al.
(2019) conducted experiments using natural common reeds (Phragmites australis). They found
similar patterns: as vegetation density increased, turbulence intensity increased, with the
distribution showing greater variability at lower densities.
Additionally, other scholars have conducted experimental studies on different types of
vegetation. Han et al. (2021) focused on submerged and emergent vegetation, finding that in
scenarios with submerged vegetation, the gravitational current interacts with the top of the

28

vegetation layer, effectively creating a new “wall boundary” that does not exist in emergent
vegetation patches and inducing a region of negative vorticity above the vegetation canopy.
Meng et al. (2021) simulated flow with various materials, such as reed, plastic sticks, grass,
and chlorella, and observed that the impacts of vegetation types on the flow field cannot be
ignored. Across both horizontal and vertical directions, turbulence intensity showed an “S”
shape distribution pattern (Tang et al., 2023). In channels with complex flow conditions, such
as meandering rivers with dense vegetation, variations in turbulence were particularly
pronounced (Finotello et al., 2024). Turbulence intensity significantly increased at the
intersection of the non-vegetated and vegetated zones. Still, the changes were less evident with
emergent vegetation, as the vegetation obstructs the whole water depth (Han et al., 2021).

1.3.4.2 Numerical Simulation
While conducting experimental research on vegetated flows, many scholars also attempt
to use numerical modeling methods to study the impact of vegetation on flow characteristics.
Numerical simulations can accurately capture the flow dynamics across the entire
computational domain compared to physical model tests. Based on their calculation principles,
standard numerical models are classified into two main categories: Reynolds-Averaged NavierStokes (RANS) and Large Eddy Simulation (LES) methods (Chipongo et al., 2020). The RANS
approach involves establishing Reynolds-averaged equations for specific flow conditions and
then closing these equations using turbulence models such as the k−ϵ model, k−ω model, or
Reynolds Stress Model (RSM). The LES method, on the other hand, solves the filtered NavierStokes equations directly by resolving large-scale eddies and modeling smaller ones using
29

subgrid-scale models.
(1) Reynolds-Averaged Navier-Stokes (RANS): Two consideration levels can be
incorporated when studying vegetated flows using RANS. The first is determining the
momentum source terms in the dynamic equations through additional forces or momentum
transfer processes, which reflect the impact of vegetation on the flow. The second approach
directly models the vegetation as a series of cylindrical obstacles (Li & Yu, 2010). In terms of
modifying the dynamic equations to account for the impact of vegetation, Wu et al. (2005)
incorporated the drag force exerted by the vegetation into the momentum equations. They also
developed a k−ϵ turbulence model that includes terms for turbulence generated by the
vegetation, aiming to establish a depth-averaged turbulence model. Since the governing
equations in the model include vegetation density, the model is particularly suitable for
conditions with higher vegetation density. Zhang et al. (2013) incorporated the drag force of
vegetation into the momentum and k−ϵ models, constructing a two-dimensional numerical
model that accounts for the impact of vegetation and applying the Volume of Fluid (VOF)
method to simulate the surface flow in vegetated channels. Hsieh and Shiu (2006) used a multiporosity model, not analyzing individual vegetation elements but considering the entire
vegetation patch as a porous medium. Given the complex three-dimensional flow variations in
vegetated channels, three-dimensional modeling is crucial. Considering vegetation as a
continuous porous medium, Lima et al. (2015) utilized the momentum and k−ϵ models to study
the flow around square cylinder arrays under different spacing conditions. They found that as
vegetation density increased, the flow dynamics in the gaps between vegetation changed
significantly. Existing models need further refinement to account for the complex interactions

30

between flow, vegetation stiffness, and morphological changes within densely vegetated
channels. In summary, using the RANS method to simulate vegetated channel flow allows a
macro-level understanding of the flow characteristics within vegetated channels. However,
simulating the fine-scale turbulence structures in these complex flow environments presents
certain challenges. Therefore, some researchers suggest applying the Large Eddy Simulation
(LES) method to study vegetated flows, as it can capture more detailed turbulence
characteristics within the vegetated flow (Stoesser et al., 2009).
(2) Large Eddy Simulation (LES) Method: Nadaoka and Yagi (1998) developed a twodimensional shallow water model using LES techniques, introducing the concept of sub-depth
scale turbulence. The model successfully simulated the hierarchical structure of turbulence and
its effects on flow distribution, aligning well with experimental results. However, it is
challenging for the model to capture changes in flow and turbulence characteristics in the
horizontal direction across different depths. Su et al. (2003) also applied the three-dimensional
LES model to study flow structures and eddy development in vegetated channels, finding that
the LES model effectively simulated complex interactions between vegetation and turbulence.
LES models can also capture the expansion and contraction of flow around vegetation and its
impact on eddy formation. Yan et al. (2017) introduced an additional diffusion term into the
LES model to account for the dispersion effect caused by the presence of vegetation,
demonstrating its influence on turbulence. Cui and Neary (2008) used LES to capture the flow
patterns around submerged vegetation, showing that the model could accurately replicate the
exchange of momentum and turbulence between the vegetation and the surrounding flow.
Overall, applying the Large Eddy Simulation (LES) method to the study of vegetated flow can

31

significantly enhance the exchange of momentum and turbulence, making it a valuable tool in
these studies. This method excels in simulating detailed turbulence characteristics and related
interactions. However, when dealing with large computational domains or regions where finescale turbulent structures occupy only a small portion, LES may not be the most efficient choice
for simulating overall flow characteristics in channels because LES requires finer
computational grids, which increases the number of grid cells and, consequently, computational
demands, leading to reduced computational efficiency (Sarkar, 2020).

1.4 Pool-Riffle Sequences
Pool-riffle sequences are among the most common geomorphic features in fluvial systems,
playing a critical role in the structure and function of river channels. These alternating deep
and shallow reaches are fundamental to river dynamics, sediment transport, habitat diversity,
and ecological processes (Lei et al., 2023). The concept of pool-riffle sequences was first
systematically studied in the early 20th century, with seminal work by Leopold and Wolman
(1957), who identified these sequences as integral components of alluvial rivers. Their research
established the basis for understanding the formation and maintenance of pools and riffles
through balancing sediment transport and hydraulic forces. Subsequent studies expanded on
this foundation, exploring these features' geomorphological and ecological significance. Pools,
the deeper sections of these sequences, are especially significant due to their influence on
hydraulic conditions, sediment storage, and aquatic habitats. Riffles are less likely to contain
many fine sediments than pools because, during low flow periods, pools tend to collect finer
materials. Consequently, riffles develop a protective layer known as armoring that is

32

challenging for vegetation roots to penetrate (de Almeida & Rodríguez, 2011). This thesis will
focus on the intricate structure of pools within pool-riffle sequences, particularly emphasizing
their interaction with submerged vegetation. Submerged vegetation can significantly alter a
pool’s hydraulic dynamics, sediment distribution, and ecological functions. By exploring these
interactions, the research aims to deepen the understanding of how vegetation influences pool
formation, stability, and habitat provision within fluvial systems. This focus is essential for
advancing river restoration efforts and improving the management of aquatic habitats in
vegetated stream environments.

Figure 1.5 Schematic of a riffle-pool sequence at low flow, illustrating 1. flow acceleration, 2. deceleration
above pools, 3. regressive run erosion, 4. pool refilling, 5. coarse grain accumulation from bank erosion, and 6.
pool scouring with riffle deposition during high flows (source: Fuller, 2018).

1.4.1 Formation Mechanisms of Pools
A combination of hydraulic, sedimentary, and geomorphic factors influences the
formation of pools in pool-riffle sequences. Pools are typically formed in areas of reduced flow
velocity, where finer sediments are deposited. One of the primary mechanisms is flow
convergence and divergence, where the convergence of flow at riffles accelerates the water,
which then diverges and slows down in pools. This flow pattern contributes to the scouring of
pools and the deposition of sediments in riffles (Lisle, 1986). Another significant factor is

33

sediment sorting and transport, where the lower energy environment in pools allows for the
deposition of finer particles. At the same time, riffles, with higher flow velocities, tend to
winnow out finer sediments, leaving behind coarser materials (Buffington et al., 2004).
Additionally, the interaction between channel geometry and bedform also plays a critical role
in pool formation, with variations in channel width and curvature leading to the development
of secondary currents that enhance pool scour (Thompson, 2006). Lastly, reduced turbulence
and flow resistance in pools allow for settling sediments, contributing to the deepening of the
pool (Dietrich & Whiting, 1989).

1.4.2 Hydraulic Dynamics of Pools
The hydraulic dynamics within pools are distinct from those in riffles, with significant
implications for sediment transport, channel stability, and aquatic habitats. Flow velocities in
pools are typically lower than in riffles, reducing shear stress and sediment transport capacity.
The transition from riffle to pool often involves flow separation, creating zones of recirculating
flow within the pool. These recirculation zones can trap sediments and organic matter,
contributing to the pool’s stability and ecological function (Wilcox & Wohl, 2006). Shear stress
in pools is unevenly distributed, with the highest values usually found near the pool exit, where
flow accelerates towards the downstream riffle. This shear stress distribution influences
sediment erosion and deposition patterns within the pool. Additionally, pools often exhibit
lower hydraulic roughness than riffles due to the finer sediment composition and smoother bed
surface. This reduced roughness affects the flow structure and energy dissipation within the
pool (Montgomery et al., 1995).

34

1.4.3 Sediment Dynamics in Pools
Pool sediment dynamics are closely linked to the hydraulic conditions and channel
morphology. Pools act as temporary storage areas for sediments, playing a crucial role in the
sediment budget of a river system. The lower flow velocities in pools favor the deposition of
fine sediments, which can accumulate over time. The rate and extent of sediment deposition
are influenced by factors such as flow regime, sediment supply, and channel morphology (Lisle
& Hilton, 1992).
While pools are sites of sediment deposition, they also experience sediment scour,
particularly during high-flow events. The balance between sediment deposition and scour
determines the long-term stability of the pool (Carling, 1991). Furthermore, pools exhibit
distinct sediment sorting patterns, with finer materials accumulating in the deepest parts and
coarser materials deposited near the pool margins. Bedload transport through pools is typically
reduced compared to riffles due to the lower shear stress and flow velocities. However, during
high-flow events, pools can act as conduits for bedload transport, contributing to downstream
sediment redistribution.

1.4.4 Morphological Characteristics of Pools
Pools are characterized by their depth, width, and sediment composition, which differ
markedly from adjacent riffles. The depth of a pool is typically much greater than that of a
riffle, with pools often being several times deeper. This depth is influenced by factors such as
channel slope, sediment supply, and flow regime. Pools also tend to be wider than riffles,

35

reflecting the lower flow velocities and the associated lateral expansion of the channel (Allan
et al., 2021).
The sediment composition of pools is generally finer and more cohesive than that found
in riffles due to the lower energy environment that favors the deposition of silts, clays, and fine
sands. The longitudinal profile of pools often exhibits a concave shape, with the deepest point
located downstream of the riffle crest (de Almeida & Rodríguez, 2011). These characteristics
indicate the hydraulic conditions and reflect the geomorphic processes at play.

1.4.5 Human Impacts on Pool Dynamics
Human activities, such as river regulation, channelization, and land use changes, all
impact pool dynamics, altering pool formation, maintenance, and ecological function. Flow
regulation through dams and weirs can disrupt the natural processes that maintain pool-riffle
sequences. Reduced flow variability can lead to the infilling of pools with sediments, while
altered flow regimes can prevent the scour necessary for pool maintenance (Kondolf, 1997).
River channelization, involving the straightening and deepening of channels, can eliminate
pool-riffle sequences. The loss of these features reduces habitat diversity and alters sediment
transport dynamics, leading to channel instability and ecological degradation (Brookes, 1987).
Additionally, changes in land use, such as deforestation, agriculture, and urbanization, can alter
the sediment supply to rivers. Increased sediment loads can lead to the rapid infilling of pools,
while reduced sediment supply can prevent the formation of new pools (Trimble, 1997).
Human activities that degrade water quality, such as pollution and nutrient loading, can impact
the ecological function of pools. Poor water quality can reduce the suitability of pools as

36

habitats for sensitive species and disrupt the natural processes that maintain pool structure
(Allan, 2004).

1.4.6 Ecological Significance and Restoration of Pools
Pools are essential to the ecosystem, providing critical habitats for many aquatic
organisms. Pools' physical and hydraulic characteristics create unique environmental
conditions that support diverse biological communities. Pools contribute to habitat diversity
within river systems by offering deep, slow-flowing environments that contrast with the
shallow, fast-flowing conditions of riffles, thereby supporting a wide range of species, from
benthic invertebrates to fish (Bisson et al., 1988). In addition to serving as diverse habitats,
pools act as refuges for aquatic organisms during periods of low or high flow, offering
protection from adverse hydraulic conditions. Pools’ depth and flow structure provide stable
environments where organisms can avoid predators and extreme flow velocities. Many fish
species, particularly salmonids, utilize pools for spawning and rearing due to the fine sediments
and stable flow conditions that provide suitable substrates for egg deposition and juvenile
development (Beechie et al., 2005). Pools often exhibit lower water temperatures than riffles
due to their depth and reduced exposure to solar radiation, creating thermal refugia for
temperature-sensitive species, particularly during warm seasons (Ebersole et al., 2003).
Moreover, pools are sites of organic matter accumulation, which provides essential food
resources for aquatic organisms. The recirculating flow within pools can trap leaf litter, woody
debris, and other organic materials, contributing to the overall productivity of the river system
(Nakajima et al., 2006).

37

The restoration of pool-riffle sequences has become a key focus of river restoration efforts,
particularly in systems impacted by human activities. Restoration strategies aim to recreate the
natural processes that form and maintain pools, enhancing habitat diversity and ecological
function. Restoring the natural flow regime, including reintroducing flow variability, is crucial
for assembling and maintaining pool-riffle sequences (Schwartz et al., 2015). Managed flow
releases from dams can help re-establish the dynamic processes that create and sustain pools.
In addition to flow regime restoration, other strategies include reconfiguring channel
morphology to promote the development of pool-riffle sequences, restoring sediment supply
to balance deposition and scour processes, and improving water quality to support healthy
aquatic habitats (Halket & Snelgrove, 2012; Harrison et al., 2011; Lei et al., 2023). These
restoration efforts require a comprehensive understanding of the natural processes that govern
pool-riffle dynamics and the specific conditions of the river system.

1.5 Formation of Ice Cover in Natural Rivers
In cold regions, rivers often form ice covers during winter. These ice formations alter the
river’s surface boundary conditions, flow dynamics, and sediment transport, leading to an
elevated upstream water level and potentially causing severe ice-related flooding (Sahu et al.,
2024). Any obstruction in the channel, either point obstructions such as spur dikes and bridge
piers or regional obstructions such as vegetation patches, will alter the river's original boundary
conditions and flow conditions, including water level, average flow velocity across sections,
ice transport, and sediment transport (Figure 1.6).

38

Figure 1.6 Flow characteristics in ice-covered river channels: (a) cross-sectional geometry, (b) partial crosssection view, and (c) vertical profiles of velocity and shear stress (source: J. Pan et al., 2023).

These changes significantly affect the flow fields under ice coves. The construction of
hydraulic structures in cold regions must consider the impact of ice cover. In April 1987, the
collapse of the Schoharie Creek Bridge on the New York State Thruway resulted in ten (10)
deaths and five (5) vehicles falling into the river. The primary cause of the accident was the
scouring of the bridge pier base by water flow beneath the ice cover (Hains & Zabilansky,
2012). A significant scour hole was observed upstream of the Melvin Price Lock and Dam
foundation on the Mississippi River, which reappeared within a year after repairs. Researchers
found through model testing that even a 100-year flood would not produce such a large scour
39

hole. However, small flows under the ice cover were to blame for the incident, negatively
impacting in-stream structures’ functionality (Carr & Tuthill, 2012).

1.5.1 Local Scour Around Hydraulic Structures Under Ice Cover
Ice cover alters the flow velocity distribution, resulting in differences in local scour at
hydraulic structures compared to open water conditions, such as changes in maximum scour
depth and extent. Wang et al. (2008) conducted flume experiments to study the critical flow
velocity for sediment movement under ice cover. They discovered that sediment transportation
is more easily initiated under ice cover, indicating that local scour is more intense under ice
cover conditions than in open flow. Ackermann et al. (2002) studied the effects of ice cover on
local scour around cylindrical bridge piers using clear-water scour and live-bed scour. Their
experimental data indicated that the maximum scour depth under ice cover increased by 25%
to 35% compared to open-water conditions. Munteanu (2004) conducted experimental studies
under various ice-cover conditions, including open water, complete ice cover, and partially icecovered channel conditions. The most intense local scour around the bridge piers occurred
under the partial ice cover, with the maximum local scour depth near the piers being
approximately 55% greater than under open-water conditions. Hains and Zabilansky (2005)
investigated the changes in local scour around cylindrical bridge piers under open-channel,
fixed ice cover, and floating ice cover conditions. Their results showed that the maximum local
scour depth under ice cover conditions was 21% greater than under open-water conditions.
Additionally, the local scour processes under fixed and floating ice covers were similar, with
an increase in ice cover roughness leading to greater local scour depths around the bridge piers.

40

Wu et al. (2014) conducted experimental studies on local scour around semi-circular
abutments under ice cover, finding that the point of maximum scour depth occurs
approximately 15 degrees upstream from the top of the abutment. Further investigation by Wu
et al. (2015) was conducted on local scour around rectangular and semi-circular abutments
under ice cover conditions, including the impact of protective layers formed during the scour
process on local scour. They also developed an empirical relationship for predicting the
maximum local scour depth:
ఈ

‫ݕ‬௠
ܷ
݀ହ଴ ఉ ݊௜ ఊ
= ‫ܣ‬ቆ
ቇ ൬ ൰ ൬ ൰
‫ܪ‬
‫ܪ‬
݊௕
ඥ݃‫ܪ‬

(1.3)

in which ym represents the maximum local scour depth, U denotes the approaching flow
velocity, H indicates the approaching water depth, d50 is the median grain size of the sediment,
ni is the ice cover roughness, and nb represents the riverbed Manning roughness.
Namaee and Sui (2020) conducted experimental studies on local scour around bridge piers
placed side by side under ice cover in a flume at the same cross-section. The study found that
the degree of scour under ice cover is related to the strength of the horseshoe vortex and is
influenced by the size of the piers and the spacing between them. Namaee and Sui (2019) also
analyzed the impact of armor layers on the local scour depth of side-by-side bridge piers under
ice cover conditions and the sedimentation initiation mechanism near the piers. They proposed
a regression equation for side-by-side bridge piers’ maximum local scour depth:
‫ݕ‬௠
݀ହ଴ ఈ ‫ ܩ‬ఉ ݊௜ ఊ
= ‫ ܣ‬൬ ൰ ൬ ൰ ൬ ൰ ‫ ݎܨ‬ఎ
‫ݕ‬଴
‫ݕ‬଴
‫ܦ‬
݊௕

(1.4)

in which Fr represents the Froude number in the pier upstream, y0 denotes the pier upstream
water depth, D indicates the diameter of the piers, and G is the distance between two side-by-

41

side piers.
The flow fields around in-stream structures are highly complex and have numerous
influencing factors. Most experimental research on local scour around abutments, piers, or spur
dikes under ice cover primarily involves dimensional analysis, examining factors such as
spatial arrangement, hydraulic conditions, ice cover roughness, and sediment grain size.
Through regression analysis, these studies have developed relationships for predicting local
scour depth under ice cover within the specific range of experimental conditions. However, the
resulting equations vary in form, and inputs depend on the experimental conditions. Due to
limitations in flume experiments, factors considered, and the number of trials, most of these
equations fit their experimental data well but do not align as closely with data from other
experimental conditions.

1.5.2 Flow Fields Around Vegetation Patches Under Ice Cover
Understanding the flow fields around vegetation patches under ice cover is critical for
advancing knowledge in riverine hydraulics and ecology, particularly in cold regions where ice
cover significantly influences hydrodynamic processes. The interaction between flow,
vegetation, and ice cover affects sediment transport, nutrient cycling, and habitat availability,
essential for maintaining the ecological balance in cold-water river systems. Recent studies
have focused on unraveling the complexities of these interactions, providing insights into how
ice cover modifies flow patterns around vegetation patches, which in turn affects the physical
and biological processes in these environments.
Flow fields around vegetation patches are inherently complex, influenced by vegetation

42

density, morphology, and spatial arrangement. In open-channel conditions, vegetation patches
act as roughness elements, altering the flow structure by creating zones of flow deceleration
and acceleration, inducing turbulence, and affecting sediment deposition patterns (H. M. Nepf,
2012). The flow resistance vegetation offers is typically quantified using parameters such as
drag coefficient and vegetation density (Nepf, 1999). The interaction between flow and
vegetation can result in the formation of coherent structures, such as vortices and wakes, which
play a significant role in sediment transport and nutrient distribution within river systems
(Nikora, 2010). Ice cover introduces additional complexity to flow fields around vegetation
patches. The presence of ice alters the flow structure by imposing a rigid boundary at the water
surface, reducing vertical mixing and modifying the velocity profile within the water column.
Under ice cover, the flow velocity near the ice-water interface is typically lower than in openchannel conditions, redistributing shear stress and turbulence within the flow (Barahimi & Sui,
2024b; Smith & Ettema, 1997). This change in flow dynamics can significantly impact the
interactions between flow and vegetation, influencing sediment transport, nutrient exchange,
and habitat formation.
Barahimi and Sui (2023) conducted flume experiments to investigate the flow structure
around submerged flexible vegetation patches under ice-covered conditions. Their results
showed that ice cover reduced the flow velocity within the vegetation patch, particularly near
the bed, leading to increased sediment deposition. A field study investigated the interactions
between flow, ice, and adjacent riparian floodplains in northern Canadian rivers (Prowse &
Culp, 2011). The observations highlighted how seasonal ice affects the distribution of flow
velocities and shear stress around vegetation patches. They addressed that river ice has been

43

identified as a significant and often primary cause of flooding in cold-region rivers, influencing
a wide range of abiotic and biotic processes within the river channel and nearby riparian
floodplains.
Modifying flow fields around vegetation patches under ice cover has valuable ecological
implications. Vegetation patches play a critical role in providing habitat for aquatic organisms,
stabilizing riverbanks, and promoting biodiversity. The altered flow conditions under ice cover
can impact the availability of these habitats, particularly during winter when flow velocities
are reduced and sediment deposition increases. For instance, Prowse and Culp (2011)
emphasized that ice can create microhabitats with distinct thermal and flow conditions, crucial
for overwintering fish and invertebrates. Additionally, the changes in sediment transport
dynamics caused by ice cover can lead to the formation of new geomorphic features, such as
point bars and mid-channel islands, which further contribute to habitat diversity within river
systems (Gurnell et al., 2012). However, the increased scour around vegetation patches during
ice melt events can also threaten the stability of these patches, particularly in regions where ice
cover is subject to frequent fluctuations.

1.6 Hypothesis
The present study hypothesizes that the interaction between obstructions, such as spur
dikes and submerged vegetated patches, under ice cover leads to changes in bed deformation
and flow field characteristics. The complexity of these interactions under ice-covered
conditions is expected to exceed the effects observed under open-water conditions due to the
additional influence of ice cover on flow dynamics and sediment transport. This study

44

specifically focuses on the local scour around submerged angled spur dikes, flow field changes
around submerged spur dikes, and the interactions with submerged vegetated patches in pools
under ice cover.
1. Local Scour Around Spur Dikes Under Ice Cover: It is well-established that ice
cover increases the severity of local scour around hydraulic structures due to the altered
flow regime and reduced turbulence near the ice-water interface. The hypothesis is that
the local scour depth around submerged spur dikes under ice cover will be greater than
open channel conditions, primarily due to the enhanced flow constriction and ice cover,
which shifts the velocity profile closer to the bed. Additionally, the geometry and
orientation of the spur dike relative to the flow direction will play a critical role in
determining the extent of scour, with more pronounced effects expected for spur dikes
positioned at sharper angles to the flow. The presence of ice cover is hypothesized to
amplify the downstream extension of the scour hole, as the restricted vertical mixing
and increased flow velocity near the bed will lead to more aggressive sediment
entrainment.
2. Flow Field Changes Around Submerged Spur Dikes Under Ice Cover: The
interaction between flow and submerged spur dikes under ice cover is hypothesized to
be more complex than under open channel conditions. Ice cover suppresses turbulence
and reduces vertical velocity gradients, affecting the wake and vortex formation around
submerged structures. The hypothesis is that ice cover will lead to a more stable and
elongated wake region downstream of the submerged spur dike, with reduced
turbulence intensity and altered shear stress distribution. This modification of the flow

45

field is expected to influence sediment transport processes, potentially leading to
increased sediment deposition in the wake region and altering the scour patterns around
the spur dike. Additionally, the ice cover is expected to enhance the lateral spreading of
the flow around the submerged structure, potentially leading to broader zones of
sediment mobilization and deposition.
3. Influence of Ice Cover Roughness and Thickness on Scour and Deposition Patterns:
Ice cover roughness is a critical factor influencing flow dynamics under ice-covered
conditions. The hypothesis is that increased ice cover roughness will enhance the
redistribution of shear stress and turbulence intensity within the flow field, leading to
more irregular scour and deposition patterns around spur dikes. The effect of ice cover
roughness is hypothesized to create highly variable and site-specific scour and
deposition patterns, with valuable implications for river management and infrastructure
design in cold regions.
4. Interaction Between Submerged Vegetated Patches in Pools Under Ice Cover: The
presence of submerged vegetated patches in pools under ice cover adds complexity to
the flow field. Vegetation is known to introduce flow resistance and create zones of
reduced velocity and turbulence, which can influence sediment transport and deposition
patterns. The hypothesis is that the interaction between submerged vegetated patches
under ice cover will result in a more heterogeneous flow field, with localized zones of
high-velocity zones and turbulent kinetic energy near the boundary between vegetation
and flow, and reduced flow velocities and enhanced deposition within the vegetated
patches. The presence of ice cover is expected to further complicate this interaction by

46

suppressing vertical mixing and enhancing the lateral flow components, leading to more
pronounced secondary currents. The combined effect of the vegetated patches and ice
cover is hypothesized to create complex flow fields highly susceptible to ice cover
roughness and thickness variations.
5. Combined Effect of Ice Cover and Vegetation Height on Flow: The hypothesis
extends to the combined effects of ice cover and vegetation height on the overall flow
structure and bed deformation. Higher vegetation is anticipated to lead to greater flow
resistance and more substantial alterations to the velocity profile under ice cover, with
the most significant effects observed near the bed. This increased flow resistance is
expected to result in a more pronounced flow field change, with a high-velocity core
forming closer to the water surface and more consistent variations within the vegetated
patches. Additionally, the hypothesis suggests that the interaction between high
vegetation and rough ice cover will lead to the most significant deviations from open
channel flow conditions, with complex flow structures emerging that are difficult to
predict using existing models.
This study hypothesizes that the interaction between local and regional obstructions under
ice cover leads to complex and highly variable flow field changes and bed deformation patterns.
The presence of ice cover, combined with the effects of vegetation patches and spur dike
geometry, introduces significant challenges in predicting flow structure and scour processes.
The study aims to comprehensively understand these interactions, with implications for
designing and managing hydraulic structures in cold regions.

47

1.7 Objectives
The primary objective of this PhD study is to investigate the complex interactions between
bed deformation and flow field changes caused by obstructions under ice cover. Specifically,
the study focuses on two distinct areas: (1) the local scour and flow field changes around spur
dikes under ice cover, and (2) the flow field changes around submerged vegetation patches in
pools under ice cover. By understanding these interactions, this research aims to provide
valuable insights into the underlying mechanisms that govern flow and sediment dynamics in
ice-covered rivers, contributing to the broader knowledge required for effective river
management and infrastructure design in cold regions.

1.7.1 Local Scour and Flow Field Changes Around Spur Dikes Under Ice Cover
Spur dikes are hydraulic structures designed to protect riverbanks and control flow direction.
However, the local scour processes around these structures can be significantly altered under
ice cover. The first objective of this study is to analyze the extent and characteristics of local
scour around spur dikes under ice-covered conditions, which will involve:
1. Evaluating the impact of ice cover on the local scour depth and pattern around
spur dikes: The study assesses how ice cover modifies the scour depth and pattern
compared to open-water conditions, which includes understanding the influence of ice
roughness and the positioning of the spur dike relative to the flow direction.
2. Investigating the flow field changes induced by spur dikes under ice cover: By
analyzing the flow velocity, turbulence, and shear stress distribution around spur dikes,
the study will identify the key factors that influence flow field changes under ice cover,

48

which includes the effect of ice-induced flow constriction and how it alters the flow
structure near the spur dike.
3. Developing predictive models for scour around spur dikes under ice cover: The
study aims to develop and validate predictive models that accurately estimate the local
scour depth around spur dikes under varying ice-covered conditions. These models will
consider factors including ice cover characteristics, flow conditions, and spur dike
geometry.

1.7.2 Flow Field Changes Around Submerged Vegetation Patches in Pools Under Ice
Cover
Submerged vegetation patches are critical in stabilizing riverbeds, enhancing habitat diversity,
and influencing sediment transport. Under ice cover, the interaction between flow and
vegetation becomes more complex due to the altered hydraulic conditions. The second
objective of this study is to explore the flow field changes around submerged vegetation patches
in pools under ice cover, which will involve:
1. Analyzing the impact of ice cover on flow velocity and turbulence within and
around submerged vegetation patches: The study will focus on how ice cover affects
the flow velocity distribution, turbulence intensity, and the formation of vortices within
and around submerged vegetation patches.
2. Evaluating the combined effects of ice cover and vegetation on the flow structure
in pools: The objective is to explore the synergistic effects of ice cover and submerged
vegetation on the overall flow structure in pools, which includes analyzing how

49

different ice cover conditions (e.g., smooth and rough ice) interact with vegetation to
create complex flow patterns that impact sediment transport and bed morphology.

1.7.3. Comparative Analysis of Open-Channel Flow, Smooth Ice-Covered, and Rough IceCovered Conditions
Given the distinct differences in flow behavior under open-channel, smooth ice-covered, and
rough ice-covered conditions, an essential objective of this study is to conduct a comparative
analysis of these scenarios:
1. Comparing velocity profile distributions under different cover conditions: The
study will compare the distributions observed under open-channel flow, smooth icecovered, and rough ice-covered conditions, which will provide insights into how each
condition influences flow structure and the implications for sediment transport and
scour around hydraulic structures and vegetation patches.
2. Assessing the implications of different cover conditions on river management: The
findings from the comparative analysis will be used to conclude the practical
implications of these flow conditions for river management, flood control, and the
design of hydraulic structures in cold regions.
This PhD study aims to comprehensively understand the interactions between bed
deformation and flow field changes caused by local and regional obstructions under ice cover.
By focusing on the specific challenges posed by local scour around spur dikes and flow field
changes around submerged vegetation patches in pools under ice cover, this research will
contribute valuable knowledge to the field of cold-region hydraulics and inform the design and

50

management of river systems in such environments.

1.8 Thesis Structure
This thesis is organized into six chapters, each building on the previous one to
comprehensively understand the bed deformation and flow field changes caused by
obstructions under ice cover. The chapters are structured to guide the reader from the
foundational materials and methods through detailed experimental investigations and analyses,
concluding with the implications and contributions of the study to the field of cold-region
hydraulics.
Chapters 3 through 5 are structured to follow the chronological order of experimental
dates, enabling a cohesive progression of research insights. Chapter 3 focuses on local scour
around submerged angled spur dikes, investigating how design parameters, such as height,
length, and alignment angle, affect scour depth and morphology. This chapter addresses
structural impacts, providing foundational insights into the influence of submerged
obstructions on sediment dynamics. Chapter 4 builds upon these findings by analyzing
turbulent flow structures around the spur dike to elucidate the causes of observed scour patterns
from Chapter 3. This analysis focuses on turbulence characteristics, including sweeps and
ejections, which are critical in sediment transport processes. Together, Chapters 3 and 4 provide
a comprehensive understanding of local scour mechanisms in ice-covered channels.
Chapter 5 transitions into eco-hydraulics, expanding the research from structural
obstructions to vegetative impacts. Influenced by insights from cold region engineering and
collaboration with Dr. Sediqi, this chapter investigates how submerged vegetation in ice-

51

covered pools affects flow resistance, turbulent kinetic energy, and velocity profiles. This
chapter reflects an integration of eco-hydraulic principles, aligning with emerging trends that
emphasize sustainable and resilient river management strategies. Note that the scour pattern
differed between simulated and measured results, with the simulation showing a more
symmetrical pattern than observed in the field. This discrepancy may stem from minor errors
in field scour measurement, such as slight inaccuracies in measuring equipment alignment or
natural variability in sediment placement during tests (such as initial leveling). Due to these
differences, the terrain elevation changes were not symmetrically analyzed here as they were
for the localized obstruction analysis in previous chapters.
The progression across these chapters highlights a systematic exploration from structural
to vegetative impacts on flow dynamics, presenting a holistic approach to understanding and
managing cold-region channels.
Chapter Two: Materials, Equipment, and Experimental Design
Chapter Two serves as the foundation for the experimental work presented in this thesis.
This chapter provides a detailed overview of the materials, equipment, and methodologies used
throughout the study. The chapter begins by describing the characteristics of the experimental
flume, including its dimensions and flow capabilities, which are critical for replicating riverine
conditions under controlled laboratory settings.
Following this, the chapter elaborates on the various apparatuses used in the experiments,
such as the models of submerged spur dikes and vegetated patches. The design and construction
of these models are described in detail, ensuring that their relevance to real-world conditions
is clearly understood. The chapter also discusses the ice cover simulation, including how

52

different ice cover conditions (smooth and rough) were replicated within the flume. The sand
used for simulating the riverbed is another critical component, and its composition, grain size
distribution, and packing methods are thoroughly explained to highlight their impact on scour
and sediment transport processes.
The experimental design section of this chapter outlines the procedures followed in
conducting the experiments, including the setup configurations, flow conditions, and
measurement techniques. The design rationale is provided to ensure that the experiments
accurately reflect the dynamic interactions between flow, bed deformation, and obstruction
under ice cover. This chapter is critical as it lays the groundwork for the experimental results
and analyses discussed in the subsequent chapters.
Chapter Three: Local Scour Around Submerged Spur Dikes Under Ice Cover
Chapter Three delves into the investigation of local scour around submerged spur dikes
with varying orientation angles under ice cover. This chapter is focused on understanding how
ice cover influences the scour depth and pattern compared to open-water conditions. The study
examines different orientation angles of the submerged spur dikes to assess their impact on the
scour process.
The chapter begins by reviewing the existing literature on local scour around hydraulic
structures, particularly under ice-covered conditions, to provide context for the experiments.
The results of the experiments are then presented, highlighting the differences in scour depth
and pattern due to the presence of ice cover. The findings demonstrate that ice cover
significantly alters the flow velocity profile, leading to more pronounced and extensive scour
around the spur dikes.

53

This chapter also discusses the implications of these findings for the design and placement
of spur dikes in cold-region rivers. By understanding the relationship between spur dike
orientation, ice cover, and local scour, this chapter provides valuable insights into mitigating
scour risks and enhancing the stability of hydraulic structures in ice-affected environments.
Chapter Four: Flow Field Changes Around Submerged Spur Dikes Under Ice Cover
Building on the findings of Chapter Three, Chapter Four shifts the focus to the flow field
changes induced by submerged spur dikes under ice cover. This chapter explores the flow
velocity, turbulence, and shear stress distribution modifications caused by submerged spur
dikes in ice-covered conditions.
The chapter begins by discussing the theoretical background of flow structures around
submerged obstructions, emphasizing how ice cover alters these flow structures. The
experimental results are then presented, showing how ice cover affects the wake region
downstream of the spur dikes, leading to flow stability and turbulence intensity changes.
The findings reveal that ice cover increases the flow resistance and alters the flow path,
which could lead to more complex sediment dynamics. This chapter is valuable in
understanding the broader impacts of ice cover on riverine hydraulics, particularly in designing
effective river engineering solutions.
Chapter Five: Flow Structure Changes in Vegetated Pools Under Ice Cover
Chapter Five expands the focus to examine the flow structure changes in regional
obstruction in channels (vegetated pools) under ice cover. This chapter explores the interaction
between submerged vegetation patches and ice cover, emphasizing how these interactions
affect flow dynamics and sediment transport.

54

The chapter begins with a review of the role of vegetation in modifying flow structures in
open channels and how these roles change under ice-covered conditions. The experimental
results are then presented, showing how ice cover alters flow velocity profiles, turbulence
intensity, and sediment deposition within and around vegetated patches.
The findings reveal that ice cover enhances the flow resistance created by vegetation,
leading to more complex flow patterns and localized sediment accumulation. This chapter
provides insights into the ecological implications of these flow structure changes, particularly
regarding habitat formation and sediment management in vegetated riverine environments.
Chapter Six: General Conclusion
Chapter Six provides a comprehensive summary of the key findings and contributions of
the study. This chapter synthesizes the results from the previous chapters, highlighting the
significant insights gained into bed deformation and flow field changes caused by local and
regional obstructions under ice cover.
The chapter discusses the study’s implications for river management and hydraulic
engineering in cold regions. It addresses the limitations of the research, acknowledging the
challenges and constraints encountered during the experiments and suggesting areas for further
investigation.
Finally, Chapter Six outlines potential directions for future research, emphasizing the need
for continued exploration of the complex interactions between ice cover, flow dynamics, and
sediment transport in cold-region rivers. This chapter concludes the thesis by reinforcing the
importance of understanding these interactions to develop effective and sustainable river
management practices.

55

2.

CHAPTER TWO: MATERIALS, METHODS AND EXPERIMENTAL
DESIGN

In Chapter Two, the materials and methods for the experimental and numerical study are
meticulously chosen to simulate natural river conditions as closely as possible. This chapter
details the experimental design, focusing on the materials and methodologies used.
The flume, which forms the core of the experimental setup, is described in detail, covering
its dimensions, slope, and overall functionality. Emphasis is placed on how the flume’s
configuration is designed to replicate real-world conditions for examining bed deformation and
velocity field changes. The study also employs a variety of equipment to measure and monitor
flow characteristics, such as velocity, discharge, and stage, with detailed descriptions provided
for each instrument. The purpose, specifications, and data processing methods are discussed,
underscoring these tools’ importance in ensuring the experimental data's accuracy and
reliability. The sand used in the study is analyzed, focusing on its grain size distribution and
standard deviation, factors that significantly influence sediment transport dynamics. The
simulation of smooth and rough ice covers within the flume is also discussed, essential for
replicating the conditions under ice cover and understanding their effects on river restoration
structures like spur dikes and vegetation patches.
This chapter also introduces the submerged spur dike models constructed from marine
plywood. These models play a vital role in the experimental setup, allowing for the detailed
study of flow and sediment interactions with river restoration structures under ice cover. The
artificial submerged vegetation patches, representing rigid leafless vegetation, are also crucial
for this study. The characteristics of these vegetation patches, such as height, are detailed to

56

highlight their impact on flow patterns and sediment transport within the flume.
Finally, this chapter discusses the application of numerical modeling using Flow-3D, a
Computational Fluid Dynamics (CFD) software. Flow-3D simulates and analyzes the complex
interactions between flow, vegetation, and submerged structures, providing additional insights
into the experimental findings and enhancing the overall understanding of the study's objectives.

2.1 Experimental Flume and Apparatus
The experiments were conducted in a large-scale outdoor flume, measuring 38 meters in
length, 2.0 meters in width, and 1.3 meters in depth, as depicted in Figure 2.1. The flume bed
was set at a longitudinal slope of 0.2%. Two different water depths, 20 cm and 30 cm were
utilized by adjusting the tailgates at the downstream end of the flume. These depths were
chosen to reflect real-world scenarios, where spur dikes are constructed in wide channels and
submerged vegetation typically thrives in the shallow regions of rivers. Water was introduced
into the system using a gravitational pump and two valves that controlled the flow to the
upstream holding tank, ensuring a constant water discharge. The target flow rate for this study
was maintained by adjusting the valves. The holding tank, with a capacity of 90 m³, was
designed to sustain a stable water level throughout each experimental session. The flume's
aspect ratio, defined as the ratio of width to water depth (W/H), indicated that the flume could
be categorized as a wide flume, given that the aspect ratio exceeded 5 to 10 for both water
depths tested. This classification suggests that the influence of the side walls and secondary
currents in the central zone of the flume can be considered negligible (Chow, 2009). Further
CFD simulation for non-vegetated open channel flow also verifies the assumption that

57

secondary currents can be ignored (Figure 2.2). Two sandboxes were positioned 10.2 meters
apart within the flume. The upstream sandbox measured 5.60 meters in length, 2.00 meters in
width, and 0.30 meters in depth, while the downstream sandbox was slightly longer at 5.80
meters in length but maintained the same width and depth. Each sandbox was equipped with a
plexiglass viewing window, allowing for clear observation of the scouring and deposition
processes occurring around the sandbed.

(a) Flume schematic for submerged angled spur dike setup

58

(b) Flume schematic for submerged rigid leafless vegetation patch setup.

(c) Field photo of the experimental flume used
Figure 2.1 The layout of the experimental flume.
59

Figure 2.2 Flow-3D simulation results of the cross-sectional velocity contour. Contour lines are distributed evenly
in the flume cross-section, indicating that the impacts of secondary currents and side walls are negligible.

In this experimental study, a down-looking Acoustic Doppler Velocimeter (ADV) with a
frequency of 10 MHz, developed by Nortek, was employed to measure instantaneous threedimensional velocity components at a sampling rate of 25 Hz, with a sampling volume of 0.25
cc. The ADV, known for its precision, reliability, and ease of use, was crucial in recording
velocity data, particularly in turbulent flow around river restoration structures under ice cover.
Each measurement session lasted 2 minutes, yielding 3,000 data points per location, with
vertical intervals of 10 mm between consecutive points in each velocity profile. The ADV’s
capability to measure velocity components in the x, y, and z directions was leveraged to
determine critical flow characteristics such as shear velocity, turbulent kinetic energy, and
overall flow field dynamics around structures like submerged spur dikes. River hydraulic
studies (Ruonan et al., 2016; Zhao et al., 2021) have highlighted the ADV’s effectiveness in
capturing detailed flow properties, making it an invaluable tool in this research.
The study also considered the impact of Doppler noise and turbulence on velocity
measurements, which required careful data post-processing. The filtering method proposed by
Goring & Nikora (2002) and Wahl (2000) was applied to eliminate noise and ensure the
integrity of the data, particularly when analyzing bed shear stress. Given that raw ADV data
60

may contain noises, proper filtering and examination were essential steps before further
analysis. The velocity measurements were processed using WinADV software, ensuring that
data with an average correlation of less than or equal to 70% were filtered out to maintain
accuracy.
A SonTek-IQ Plus maintained a constant flow rate over a 24-hour period and ensured the
scour process’s equilibrium state. With advanced post-processing functions, this robust
apparatus accurately measured average velocity and water depth. To prevent sediment
starvation, as described by Yang et al. (2017), sandboxes were designed deeper than the
maximum equilibrium scour depth, and sediment traps were cleaned and replenished after each
run. Both experimental data and past research confirmed that a 24-hour run duration effectively
avoided sediment starvation (Barahimi & Sui, 2024b; Jafari & Sui, 2024; M. Namaee et al.,
2023; Sediqi et al., 2024; P. Wu et al., 2016). Equilibrium flow within the vegetated zones,
particularly in streamwise velocity, indicated a fully developed state, essential for analyzing
vegetation impacts on flow and sediment transport (Figure 5.7, PF 4). Reaching equilibrium
scour depth, which depends on structural and hydraulic factors, is more complex under ice
cover, as noted by Oliveto and Hager (2002). Namaee and Sui (2020) recommend a 24-hour
duration for scour equilibrium under ice-covered flow, while Mia and Nago (2003) suggest a
criterion of less than 1 mm/hour scour fluctuation. Using this guideline, scour changes at the
dike tip were monitored with ±0.1 mm accuracy, confirming that 24 hours was sufficient to
reach equilibrium without sediment depletion.
Despite the use of a gravitational pump at the Quesnel River Research Center (QRRC),
SonTek IQ Plus readings slightly varied over time due to several factors. Flow instabilities can

61

occur as gravitational pumps, which depend on natural elevation differences, may experience
minor flow rate variations based on head changes. Groundwater sources, while generally stable,
are subject to fluctuations in the water table from factors like nearby irrigation or natural
recharge and discharge events, which can slightly alter pressure and flow. Additionally, small
shifts in the hydraulic gradient driving the gravitational pump may introduce minor variations.
Environmental factors, such as wind, atmospheric pressure changes, and water temperature
gradients, can also subtly affect flow or measurement precision, which can be detected by the
highly sensitive SonTek IQ Plus. Finally, sensor calibration drift and electrical noise may
contribute to slight variations in readings.

2.2 Submerged Spur Dike and Vegetated Pool Setup
Since the erosive process is caused by the shear stress imposed on the bed sediment (Khan
et al., 2016), the influence of spur dike materials was not investigated. Waterproof marine
plywood was selected to build the vertical wall spur dikes. The average depths in the two
sandboxes vary marginally due to the smaller flume slope of 0.20%. Therefore, the height of
the spur dikes above the initial sand bed was set as 15 cm and 20 cm in the upstream sandbox
and 20 cm and 25 cm in the downstream sandbox to keep the overtopping ratios in the two
sandboxes varying within 5.0%. Richardson and Simons (1984) proposed that dikes with
angles between 100° and 110° may be applied to channelize or direct flow. However, Jansen
et al. (1979) stated that no uniform standards should be set for all spur dikes. Thus, the model
spur dikes with a uniform spur dike width of 0.05 m were set up at alignment angles of 90°,
120°, and 135° in the current study.

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The design length of submerged spur dikes in practice is often set as a percentage of the
channel width, typically ranging from 10% to 25% of the bank-full width. Richardson et al.
(1975) recommend lengths of 10% to 15% of channel width for straight reaches and largeradius bends to effectively manage flow and reduce scour near the structure. Studies such as
Bahrami-Yarahmadi et al. (2020) have explored spur dike lengths from 9% to 44% of channel
width in various hydraulic conditions to achieve objectives like flood control, bank stabilization,
or navigation. Generally, a ratio of 0.1 to 0.25 is applied in real-world projects, tailored to sitespecific hydraulic and sediment transport requirements. In this study, a 50 cm dike length—
25% of the 2 m channel width—was selected, with a 35 cm length (cosine of 50 cm) used for
comparison to assess the effectiveness of an alternate length.
Spur dikes are often deployed in groups in river engineering; however, to establish a
foundational understanding of flow and scour mechanisms under ice-covered conditions, the
research was designed to isolate the hydrodynamic behavior around individual submerged spur
dikes. By focusing on single-dike dynamics, this study aims to provide insights that can inform
future research on grouped configurations. Kuhnle et al. (2002) found that scour tail lengths
remain under 20 times the normal length, regardless of dike alignment angles, supporting the
use of a single spur dike in the experimental flume to capture the complete scour profile within
the sandbox’s dimensions. While grouped spur dikes in practice create complex interactions,
such as shielding effects that modify flow and sediment transport between structures, leading
to more pronounced scour at individual dikes (Ning et al., 2019).

63

Figure 2.3 The submerged angled spur dike model was built with marine plywood (120° alignment with flume
wall, water flowing from left to right).

The study examined a flow depth of 20 cm from the flume’s false floor (30 cm in the pool
zone) to simulate shallow river environments. In each sandbox, a pool is constructed. Each
pool consists of three sections, namely, entrance, pool center (or deep pool), and exit section,
as shown in Figure 2.4. In this study, the pools were built with three different slopes for the
pool’s entrance and exit sections. Three different slopes for entrance and exit sections of the
pools were first trialed in non-vegetated channels under open channel conditions, namely, 5°,
7°, and 10°. The 5° and 7° slopes for the entrance and exit sections revealed significant velocity
variations in the transition between the deep pool and slopes of the pools, as indicated by ADV
measurements in the unvegetated open channel. The limited pool area at these 5° and 7° slopes
prevented fully developed flow and constrained the planting of additional vegetation arrays.
Consequently, a 10° slope for both entrance and exit sections was chosen for the numerical
model to address these limitations. The non-uniform gravels were used as the bed material of
both pool entrance and exit sections, with a median particle size of 10 cm. The gravels used in
this study are sourced from the Quesnel River. Non-uniform sand with a median particle size
(d50) of 0.90 mm was used along the deep pool section. The pool entrance section features an
increase in flow depth, forming a decelerating zone; the deep pool, characterized by a flat
64

channel bed, served as a transition zone; and the pool exit section, with a decreasing flow depth,
generated accelerating flow. One case study demonstrates that the slopes of the pool entrance
and exit sections for natural pools range from 4° to 7.80° (Nosrati et al., 2022), suggesting that
the slopes of entrance and exit sections used in this study reasonably approximate actual
conditions found in natural rivers.

(a)

(b)
Figure 2.4 (a) Picture of the non-vegetated pool; (b) Pool section and the cartesian coordinate system for the
experimental setup.

In natural environments, the distribution of aquatic plants is typically random, with
vegetation forming communities that are neither symmetrical nor uniformly distributed.
Engineered stream restoration projects, however, could benefit from adopting standard
65

practices that mimic these natural patterns. Implementing a staggered arrangement of
vegetation in such projects can simplify numerical simulations while enhancing biodiversity,
improving habitat complexity, and providing better erosion control. Therefore, in addition to
single circular vegetation setups, paired or staggered vegetation groups should be considered
to achieve these benefits (Fu et al., 2021; Tinoco et al., 2020). In this study, plastic artificial
flower stems with diameters of 0.5 cm were used to simulate rigid vegetation, such as common
reeds (Phragmites australis). These synthetic vegetation stems were anchored to the sand bed
of the deep pool section and arranged in staggered configurations with a spacing distance of 20
cm between adjacent stems in the same row to cover the sand bed of the entire deep pool section.
The vegetation heights of 10 cm and 15 cm were selected to balance research objectives
with logistical constraints. These heights simulate typical submerged vegetation found in
natural or engineered channels, where vegetation impacts flow resistance, sediment transport,
and turbulence. Field observations show that submergence ratios (water depth to vegetation
height) commonly range between 1 and 2 for rigid vegetation Lu et al. (2024). This range
ensures full submergence while allowing vegetation to influence flow dynamics. Studies on
aquatic vegetation like Zostera noltii similarly report vegetation heights of 10 to 30 cm,
reflecting realistic conditions where vegetation affects both near-bed and water column flow
characteristics (Paul et al., 2012). Practical constraints, including the flume dimensions, also
influenced the choice, as these heights ensured full submergence under the flow conditions,
crucial for studying interactions between flow and submerged vegetation.

66

Figure 2.5 Top view of a vegetation zone and ADV measurement positions within the pool area.

The spacing pattern in this study was chosen to replicate realistic vegetation densities
observed in natural and engineered aquatic environments, allowing flow interaction with
individual stems while maintaining consistent density. In many studies, similar spacings of 20
cm to 30 cm between vegetation stems and 30 cm to 60 cm between rows are used to balance
flow resistance and flow-through, simulating vegetation arrangements that promote turbulence
and sediment deposition without excessive flow blockage (John et al., 2023; USDA, 2021).
This arrangement reflects common practices in engineered vegetation patches, where spacing
is tailored to project goals and environmental needs, ensuring sufficient flow interaction while
maintaining vegetation stability against erosion. In flume studies, such as those by Bouma et
al. (2005) and Paul et al. (2012), similar spacing patterns have been applied to explore flowvegetation interactions, facilitating turbulence and wake formation while allowing comparisons
with prior research. The selected 20 cm by 30 cm pattern in this study thus aligns with these
established practices, supporting both experimental control and real-world relevance in
assessing flow dynamics and sediment transport.

67

2.3 Sediments and Gravel
The sandboxes were filled with non-uniform sediment, with median particle sizes of 0.58
mm and 0.90 mm. The sands used in the experiments were sourced from River Road Landscape
Supply in Prince George, which obtains its sand directly from the Nechako River, representing
sediment found in Northern Canadian rivers. The gravel used for constructing the pool slope
was collected from the Quesnel River near the Quesnel River Research Centre (QRRC).
Similar sediment sizes have been employed in other experiments by Barahimi and Sui (2024b),
Jafari and Sui (2024), Sediqi et al. (2024), Namaee and Sui (2020), and Wu et al. (2016). These
sediment sizes were also chosen to prevent ripple formation, given that sediments with L/d₅₀ ≥
50 are less prone to forming ripples (Rezaie et al., 2023), where L represents the characteristic
length of the hydraulic structure.
The standard deviation (σ) of the sediment sizes was calculated using the equation:
(2.1)

݀
ߪ = ට ଼ସൗ݀

ଵ଺

This parameter was utilized to assess the uniformity of sediment distribution, where d84 and d16
denote the particle diameters at which 84% and 16% of the sample are finer. A lower value of
σ indicates better sorting of the sediment. Sands with geometric standard deviations greater
than 1.6 can be categorized as non-uniform sediments (van der Mark et al., 2008). The standard
deviation (σ) for these sands was calculated as 1.97 and 2.39, making both sands non-uniform.
The grain size distribution was determined using a mechanical shaker and a series of sieves,
with the sediment grain size distributions illustrated in Figure 2.6. The selected d50 represents
the typical sediments found in the natural rivers in northern British Columbia, as revealed by a
survey conducted by Northwest Hydraulic Consultants (2013) (Appendix IV).
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Figure 2.6 Sieve analysis results of the bed sediments used in this study.

2.4 Synthetic Ice Cover
Three major categories of the available materials for model ice cover are rigid, synthetic,
and natural ice. When strength is not a concern, rigid, unbreakable ice replacements such as
wood, paraffin, polyethylene, polypropylene plastic, and polystyrene foam (Styrofoam) have
been utilized effectively (Jafari & Sui, 2021; Wuebben, 1996). This study used Styrofoam
panels to model smooth ice cover, and a rough model ice cover was prepared by attaching 2.5
cm Styrofoam cubes to the panel bottom. Manning’s coefficient for Styrofoam panels (smooth
cover) is estimated as 0.010 (Hains & Zabilansky, 2005). Applying Li’s (2012) equation (Eq.
2.2) for calculating the cover Manning’s n (ni) and adopting 0.025 m as the roughness height,
ni is estimated as 0.021 for rough ice cover. Both values are consistent with the calculated
results for surveyed ice-covered channels using either average roughness height estimation

69

(method I, 0.0075 - 0.029) or logarithmic law (method II, 0.0088–0.033) (Li, 2012). Equation
3 is employed for calculating ni
ଵ/଺

݊௜ = 0.039 k ୱ

(2.2)

in which ks is the average height (m) of the ice cover affected region.
Beltaos and Bonsal (2021) report that ice thickness on the Peace River ranges from 0.4 to
1.4 meters, with river depths between 6 and 20 meters. Similarly, Environment Canada (2013)
data for the Fraser River near Prince George shows depths of 3 to 20 meters, with ice
thicknesses up to 1.09 meters, according to BC Ministry of Agriculture and Lands (2006). In
this study, the flume depth of 20 to 35 cm, combined with 25 mm ice cubes, represents a scaled
version of maximum ice thickness relative to river depth, effectively simulating ice roughness.
A 35 mm spacing between cubes was chosen to replicate realistic river ice roughness, balancing
natural turbulence effects with controlled laboratory conditions while avoiding excessive flow
blockage.
Hains and Zabilansky (2005) noted that the local scour processes under fixed and floating
ice covers were similar, with increased ice cover roughness leading to greater local scour depths.
Since each Styrofoam panel measures 1.95 meters in length, 1.20 meters in width, and 0.025
meters in thickness, it is extremely challenging to keep them fixed. During experiments, these
model ice covers floated freely on the water surface, adjusting with slight changes caused by
surface waves. A sample piece of synthetic Styrofoam ice cover in the flume is shown in Figure
2.7.

70

Figure 2.7 Styrofoam cubes are attached to the Styrofoam panel to simulate the rough ice cover.

Water temperature was not included as a variable in these experiments, as the study
focused on the structural and dynamic interactions among spur dikes, vegetation, and ice cover
under steady flow conditions. This approach isolated the physical effects of these elements
without the confounding influence of temperature fluctuations, allowing a clearer interpretation
of how spur dikes and vegetation impact flow patterns and sediment transport with ice cover
as the primary flow modifier. While temperature can affect flow viscosity and sediment
cohesion in natural environments, the controlled laboratory setting aimed to establish baseline
principles of flow-structure interaction under consistent conditions. The subcritical flow regime
(Froude number < 1) in this study indicated that gravitational forces dominated, with turbulent
flow largely unaffected by minor viscosity changes due to temperature. Given that turbulent
flows are relatively insensitive to viscosity compared to laminar flows, temperature-induced
viscosity changes were expected to minimally impact flow behavior. To ensure consistency, the
analysis in Chapter 4 normalizes Reynolds shear stress (RSS) to critical shear stress (-‫̅ݑ‬′‫̅ݓ‬′/‫∗ݑ‬²),
enabling comparisons across flows with different Reynolds numbers and eliminating densityrelated variations from temperature. This normalization supports the validity of findings across
potential temperature differences.

71

2.5 Numerical Simulation Setup
FLOW-3D® HYDRO, a widely used computational fluid dynamics (CFD) model, was
employed to simulate the velocity profiles for the vegetated pool. This model utilizes the
volume of fluid (VOF) method to track the water's free surface accurately and employs the
Fractional Area/Volume Obstacle Representation (FAVOR) method, developed by Hirt and
Nichols (1981), to effectively manage complex geometries (Flow Science Inc., 2023). Recent
studies have demonstrated the robustness of FLOW-3D in modeling hydrodynamic behaviors
across various engineering applications, confirming its reliability in simulating intricate flow
patterns around structural obstacles (e.g., Namaee et al., 2021, 2023).

2.5.1 Governing equations
The governing equations for an incompressible Newtonian fluid, incorporating the
Reynolds-averaged Navier-Stokes (RANS) equations and continuity equation, are presented in
Equations 5 to 8, including the Fractional Area/Volume Obstacle Representation (FAVOR)
variables (Hirt & Nichols, 1981).
߲
(‫ = ) ܣ ݑ‬0
߲‫ݔ‬௜ ௜ ௜

(2.3)

߲‫ ݑ‬1
߲‫ݑ‬௜
1 ߲ܲ
+ ቆ‫ݑ‬௝ ‫ܣ‬௝
ቇ=−
+ ݃௜ + ݂௜
߲‫ܸ ݐ‬ி
߲‫ݔ‬௝
ߩ ߲‫ݔ‬௜

(2.4)

and
ߩܸி ݂௜ = ߬௕,௜ − ቈ

(2.5)

߲
൫‫ ܵ ܣ‬൯቉
߲‫ݔ‬௝ ௝ ௜௝

where
72

(2.6)

߲‫ݑ‬௜ ߲‫ݑ‬௝
ܵ௜௝ = −(ߤ + ߤ் ) ቆ
+
ቇ
߲‫ݔ‬௝ ߲‫ݔ‬௜

Here, ui represents the velocity component in the i-th direction, VF is the volume fraction
of fluid in each grid cell, and Ai denotes the fractional area open to flow in the i-th direction.
Additionally, P is the pressure, ρ is the fluid’s mass density, and t is time. The term gi
corresponds to the gravitational force in the i-th direction, fi is the diffusion transport term, and
Sij is the strain rate tensor. The wall shear stress is indicated by τb,i, and the total dynamic
viscosity accounts for both molecular viscosity (μ) and eddy viscosity (μT ).
FLOW-3D offers several turbulence models, including the standard k-ε, RNG k-ε, k-ω
models, and large eddy simulation (LES). When turbulent flow encounters obstacles like
vegetation stems, it generates a complex system known as the turbulent horseshoe vortex (THV)
due to the adverse pressure gradient. Large-eddy simulation models, particularly the detachededdy simulation (DES) approach, are effective in resolving most turbulence scales generated
by obstacles while maintaining relatively low computational demands (Kang et al., 2019). Gazi
and Afzal (2020) reviewed the formation mechanisms of vortices, highlighting the separation
of both laminar and turbulent boundary layers, and noted the successful application of DES in
simulating the intricate dynamics of THV. The Re-Normalization Group (RNG) k-ε turbulence
model, which modifies the Navier-Stokes equations to account for smaller-scale motions, is
favored for vegetated channels due to its cost-effectiveness, accuracy, and efficiency in
capturing turbulence structures (Dehrashid et al., 2023). The RNG k-ε model includes
enhancements over the standard k-ε model, improving efficiency. Therefore, in this study, the
RNG k-ε turbulence model is employed to simulate the flow field in the pool zone with
vegetation under ice-covered flow conditions, using this model to close the equations of motion.
73

The transport equations for k and ε can be expressed in various forms. One straightforward
interpretation, which neglects the buoyancy effects, is as follows (Yakhot et al., 1992):
߲
߲
߲
ߤ௧ ߲݇
(ߩ݇) +
(ߩ݇‫ݑ‬௜ ) =
ቈ൬ߤ + ൰
቉ + ܲ௞ − ߩߝ
߲‫ݐ‬
߲‫ݔ‬௜
߲‫ݔ‬௝
ߪ௞ ߲‫ݔ‬௝
߲
߲
߲
ߤ௧ ߲݇
ߝ
ߝଶ
∗
(ߩߝ) +
(ߩߝ‫ݑ‬௜ ) =
ቈ൬ߤ + ൰
቉ + ‫ܥ‬ଵఌ ܲ௞ − ‫ܥ‬ଶఌ
ߩ
߲‫ݐ‬
߲‫ݔ‬௜
߲‫ݔ‬௝
ߪఌ ߲‫ݔ‬௝
݇
݇

(2.7)
(2.8)

where,
∗
‫ܥ‬ଶఌ
= ‫ܥ‬ଶఌ +

‫ܥ‬ఓ ߟ ଷ (1 − ߟ/ߟ଴ )
1 + ߚߟ ଷ

(2.9)
(2.10)

ߟ = ܵ݇/ߝ

(2.11)

ଵ/ଶ

ܵ = ൫2ܵ௜௝ ܵ௜௝ ൯

The turbulent viscosity is calculated using the same method as the standard k-ε model.
Notably, the RNG procedure explicitly derives the values of all constants except for β. The
commonly used values are Cμ = 0.0845, Cε1 = 1.42, Cε2 = 1.68, σk = σε = 0.7194, η0 = 4.38, and
β = 0.012 (Yakhot et al., 1992).
FLOW-3D utilizes the VOF method to solve the governing equations on an orthogonal
mesh grid, which allows for accurate capture of the interface between different fluid phases.
The solver iteratively computes the flow field by updating the velocity and pressure fields until
convergence is achieved, involving the solution of continuity, momentum, and turbulence
transport equations (Lee & Wahab, 2019). The simulation results are validated against
experimental data to ensure accuracy, with model parameters adjusted as necessary to achieve
better alignment with observed data.

74

2.5.2 Model Setup
In the computational domain, no-slip wall conditions were applied to the sidewalls, rigid
vegetation (represented by cylinders with diameters of 0.5 cm), ice cover bottom surfaces, and
mesh boundaries. The cylinders simulate rigid vegetation such as common reed (Phragmites
australis) found in natural rivers (Nosrati et al., 2024). The top boundary was modeled using a
“symmetry” condition, while a “no-slip wall” condition was applied to the bottom boundary.
The upstream inlet of the pool was set with a “specified velocity” condition, and the
downstream outlet of the pool was designated as “outflow.” The inlet velocity (v0), controlling
the flow rate into the channel, was determined using the average flow velocity. The symmetry
condition was chosen for the top boundary to save computational time, a method validated by
Smith and Foster (2005), who observed no significant differences between the usage of
symmetry and a free-surface boundary. A smooth ice cover was simulated at the same flow
depth in the numerical model as the physical model for smooth ice-covered flow conditions.
Rough ice cover was simulated by adjusting the roughness height of the ice cover to match
Manning’s ni value used in the flume experiments. The flow moved from upstream to
downstream across the pool section, passing over the vegetated pool section and causing
changes in flow fields until reaching the outflow boundary.
In numerical modeling, addressing uncertainties related to the mesh resolution and
computational domain size is crucial. To mitigate these uncertainties, sensitivity analyses have
been conducted for domain size and mesh resolution. Initially, two computational domain sizes
were compared under constant conditions: the first domain was set to 5.8 meters, corresponding
to the length used in the experimental studies, with a uniform mesh grid of 20 mm × 20 mm. It

75

was observed that reducing the domain length to 5.0 meters did not alter flow characteristics
near the vegetated zone in the pool, indicating that this reduction had no significant effect on
the flow field. This adjustment was primarily aimed at optimizing simulation time without
compromising the accuracy of the simulation results.
Mesh refinement is crucial for achieving high-precision computational results, given the
complex vegetation arrangements and significant flow variations within these areas. Two
different mesh grids have been tested to optimize the mesh resolution. The computational
domain was divided into two mesh blocks. Initially, all blocks utilized a uniform mesh size of
20 mm × 20 mm. After optimization, the central mesh block encompassing the vegetated pool
area retained a finer grid of 20 mm × 20 mm. In comparison, the pool entry and exit sections
were adjusted to a coarser grid of 30 mm × 30 mm to improve the computational efficiency.
Comparisons of the model outputs indicate that these mesh size adjustments do not
significantly impact the velocity profiles, confirming the model’s robustness. This approach
ensures efficient use of the computational resources while maintaining simulation accuracy.
Figure 2.8 illustrates the simulation model of the vegetated pool area and the boundary
conditions employed in the numerical models.

Figure 2.8 The vegetated pool's simulation model and boundary conditions under ice-covered flow conditions.

76

2.6 Research Innovation
This study represents an extensive experimental investigation into the effects of local
obstruction (i.e., submerged angled spur dike) and regional obstruction (i.e., vegetated pool)
on flow structure and bed deformation. Conducted in a large-scale outdoor flume that closely
mimics natural stream conditions, with dimensions of 2 meters in width, 1.3 meters in depth,
and 38 meters in length, the research systematically examines the impacts of different types of
hydraulic obstructions. The submerged spur dikes were aligned with deflecting and retracting
angles, namely, 90°, 120°, and 135°. The vegetation patches were arranged in staggered arrays
with 20 cm between vegetation elements and 30 cm between planting rows. Two different nonuniform sands were utilized to explore local scour and flow field change around submerged
angled spur dike under ice cover and flow field variation in the vegetated pool area. The
analysis focused on key parameters such as velocity profiles, Reynolds shear stress, turbulent
kinetic energy (TKE), bed deformation, and scouring. In this thesis, the term “obstruction”
denotes artificial and constructed nature-based solutions, such as spur dikes and vegetation
patches. These obstructions are introduced strategically within the channel to influence flow
dynamics and sediment behavior, particularly under ice-covered conditions. The study
examines how these interventions impact hydrodynamics, turbulence, and bed morphology,
highlighting their role in shaping flow patterns within submerged, ice-affected environments.
This research provides insights into the combined effects of hydraulic obstructions and
ice cover on flow resistance and channel bed deformation. It elucidates the relationship
between ice-cover roughness, bed roughness, and scour hole depth, identifying the most
significant variables influencing scour formation under ice-covered conditions. These findings

77

are valuable for predicting and managing channel bed erosion in cold regions and for enhancing
the design of hydraulic structures to mitigate the impacts of ice cover. The study also explores
the relationship between vegetation and ice cover roughness on velocity profiles, which is
crucial for understanding sediment transport, pollutant dispersion, and habitat suitability.
A novel estimation equation for the maximum scour depth around angled submerged spur
dikes was developed, showing strong agreement with experimental data. Additionally,
computational fluid dynamics (CFD) simulations using Flow-3D software were applied to
vegetated pools to investigate flow-related parameters such as TKE, further enhancing the
study’s contribution to understanding the complex interactions between vegetation, ice cover,
and river hydraulics. This research advances the field by comprehensively addressing these
factors simultaneously.

78

3.

CHAPTER THREE: LOCAL SCOUR AROUND SUBMERGED ANGLED
SPUR DIKES UNDER ICE COVER

3.1 Introduction
Spur dikes are common structures in riverine and coastal engineering. They are mainly
used to protect riverbanks from erosion and alter channel water depth for better navigation.
Based on the submergence level, spur dikes can be distinguished into submerged and nonsubmerged types (Wei et al., 2018). Spur dikes will significantly change the flow patterns in
the vicinity of where they are built, causing powerful vortices that can enhance erosion. Deep
scour holes can affect the stability of the spur dike foundation, posing significant safety
concerns (Hong et al., 2019). Therefore, the scour depth around a spur dike is an essential
parameter in the design of this type of infrastructure.
Currently, studies on local scour around spur dikes have primarily focused on nonsubmerged spur dikes. In practice, however, non-submerged spur dikes on the flood plain may
be submerged during the flood season if the flow exceeds the design flood (Keshavarzi et al.,
2010). For submerged spur dikes, the repelling type is preferable since the sediment can be
carried to the side of the river bank, which is conducive to sediment deposition after the water
flows over the top of the spur dike (Kuhnle et al., 2002). The attracting alignment for
submerged spur dikes will function adversely, causing deposition in the river center and
endangering the safety of the dike foundation. It has been reported that the flow patterns near
submerged spur dikes are more complex than those for non-submerged spur dikes, and the
contributing factors are also more diverse (Fang et al., 2006; Kuhnle et al., 2002). As claimed
by Fang et al. (2006), a sloped upstream face of a submerged spur dike plays a significant role

79

in the local scour pattern around the submerged spur dike. The milder the slope of the upstream
face of a submerged spur dike, the higher the approaching velocity and Froude number needed
for scour initiation and the smaller the maximum scour depth resulting from submerged spur
dikes.
It also has been found that the alignment angle between the axis of a dike and the streamwise direction of water flow plays a significant role on the local scour process around a spur
dike. According to the alignment angle between the axis of a dike and the stream-wise direction
of water flow, spur dikes can be classified as attracting (acute angles), deflecting (right angle),
and repelling (obtuse angles). These three types of spur dikes have very different effects on
flow patterns. Nagy (2005) examined impacts of the dike alignment angles (denoted as a in the
current study) on the local scour imposed by submerged spur dikes. The potential near-bank
erosion was found to be at a minimum for an angle of 135° according to measured maximum
scour volume. Giglou et al. (2018) tested a single spur dike with angles of 45°, 75°, 90°, 105°,
and 120°, and reported that by increasing the spur dike angle relative to the flow direction, the
length and diameter of the produced vortex grow. The velocity decreased the most when the
spur dike model was oriented at 120°. However, Yazdi et al. (2010) studied the angles that
deviated from the normal orientation (90°) and concluded that the length and width of the
recirculation zone (reattachment length) remained virtually constant at varied angles (a < 20°).
Han et al. (2022) used the porous medium method (PMM) in a three-dimensional
numerical model to simulate the flow fields and scouring processes around grouped attracting
and deflecting spur dikes. It was found that compared to grouped deflecting spur dikes,
attracting spur dikes reduced the blockage of approaching flow, leading to a moderate increase

80

in the flow velocity magnitude from upstream to downstream within the grouped spur dikes
field. Shampa et al. (2020) investigated the characteristics of three-dimensional flow fields
around slit-type grouped permeable spur dikes. They found that deflecting spur dikes more
effectively generated transverse flow to the opposite bank. To simulate the flow recirculation
characteristics of grouped non-submerged spur dike sequences oriented at different angles in a
60° channel bend, the MIKE3 FM model was applied by Chen et al. (2019). The results
revealed that increasing the angle of the spur dike changed the flow field and surface
morphology surrounding the spur dike. For the attracting arrangement of spur dikes, the range
of the recirculation zone expanded, and the center of the vortex moved further away from the
dike with the increase of the alignment angle. Contrarily, for the repelling arrangement of spur
dikes, the range of the recirculation zone steadily shrinks with the increase of the alignment
angle.
Previous research on local scour at in-stream infrastructure, including spur dikes, has
mainly focused on non-submerged structures, and open channel flow conditions. However, in
natural rivers, ice cover often develops in rivers in cold regions during winter. Thermally grown
ice cover has a small roughness, and its water-immersed bottom is smooth. Contrarily, a rough
ice cover is formed if shoving and mechanical thickening processes are involved (Valela et al.,
2021). The presence of an ice cover on the water surface causes complicated local scour
development processes due to the dynamic interactions among the ice cover, water flow, and
channel morphology evolution. The sedimentation process consequently exhibits drastic
changes compared to that under open-channel flow conditions (Pan & Shen, 2022). Zabilansky
and White (2005) identified a river as narrow when the variations in water levels do not alter

81

the position of the ice cover, based on which the experimental flume can be categorized as a
narrow channel. When the discharge exceeds the freeze-up datum in a narrow river, the ice
cover will induce a pressurized flow state underneath, which causes a shifting in the maximum
velocity position. Additionally, the formation of a stationary ice cover increases the wetted
perimeter and shifts the maximum velocity to the boundary with a smoother roughness (Sui et
al., 2010).
Local scour under ice-covered flow conditions has attracted more attention from
researchers over the past decade: Sui et al. (2009) did local scour experiments under open
channel flow and smooth and rough ice-covered conditions. They discovered that the local
scour process differs between covered and open channels, and that the rougher the ice cover,
the deeper the scour hole. Wu et al. (2014a, b, 2015, 2016) investigated the impacts of channel
bed sediment composition on scour around bridge abutments and bridge piers under icecovered flow conditions, and their results showed that the maximum scour depth is affected by
the roughness of ice cover, grain size of bed material, abutment shape, densimetric Froude
number, and grain size of the armor layer in scour holes. Valela et al. (2021) found that an
increase in ice cover submergence results in a greater maximum velocity and an associated
increase in the near-bed velocity gradient. Rough ice cover generates more scour than smooth
ice cover. Sirianni et al. (2022) studied the effects of developing ice covers on bridge pier scour.
Namaee and Sui (2019a, b, 2020) established empirical equations for the maximum local scour
depth around two side-by-side bridge piers under both open channel flow and ice-covered
conditions. Jafari and Sui (2021) analyzed the velocity fields and turbulence patterns along
unsubmerged spur dikes under ice cover with dike orientation angles of 45°, 60°, and 90°. As

82

the dike becomes oriented closer towards the upstream, the velocity component values
increased correspondingly, resulting in a deeper scour hole.
Overall, in comparison to open channel flow, very little research has been done on the
local scour process under ice-covered conditions. The impacts of alignment angles of
submerged spur dikes on equilibrium scour depth under ice-covered flow conditions have never
been explored. And thus, in the current study, the variations of the maximum depth of scour
holes around submerged spur dikes with changes in the submerged spur dike’s design
parameters (length, overtopping ratio, and alignment angle) under different cover conditions
are analyzed based on laboratory experiments done in a large-scale outdoor flume.

3.2 Materials and Methods
3.2.1 Site description
The experiments were done in a large-scale outdoor flume at the Quesnel River Research
Centre (QRRC) in Likely, British Columbia. This flume is 38.20-m long, 2.00-m wide, and
1.30-m deep. A holding tank was built to provide constant discharge feeding to the flume, and
two valves were installed to regulate the flow rate at the end of the holding tank. An adjustable
tailgate was installed at the downstream end of the flume to control the flow depth. The distance
from the tailgate to the downstream edge of the downstream sandbox is 5.3 m. The upstream
sandbox is 5.60-m long, 2.00-m wide, and 0.30-m deep, while the downstream sandbox is 5.80m long, 2.00-m wide, and 0.30-m deep, and these two sandboxes are located 10.20 m apart
from each other (Figure 3.1).
In natural rivers, channel beds are filled with non-uniform sediment particles. To better

83

understand the contrasts between mechanisms of clear-water and live-bed scour, non-uniform
channel bed materials have been utilized for flume experiments since the 1980s (Guan et al.,
2022). As pointed out by Yang (2003), non-uniform sediment particles will form an armor layer,
a barrier consisting of a residue of coarser particles when the finer sediment particles are
transported more rapidly by the flow. Local scour caused by an in-stream hydraulic structure
will grow through the armor layer and into the finer, more erodible sediment. Occasionally, it
can also produce a more widespread local scour area when the armor layer starts to erode
(Raudkivi & Ettema, 1985). Utilizing non-uniform sediment particles to represent natural
riverbeds could result in a better knowledge of local scour mechanisms, improving the
authenticity of experimental simulations.
Hydraulic modeling is subject to scale effects. Scale effects are the distorted model
outputs caused by the force ratio mismatch between a laboratory model and a field prototype.
Deeper scour holes can be caused by a scale effect inherent in laboratory flume experiments,
and this limitation necessitates the use of sediment that is the same size as or no smaller than
0.1 of the size of natural channel bed sediment in the field for flume studies (Ettema et al.,
1998). Thus, in the current study, non-uniform sediment particles with median particle sizes
(d50) of 0.90 mm and 0.59 mm were selected for the clear water scour experiments for
simulating the natural erodible sand bed.
The channel bed Manning roughness coefficient (nb) can be calculated using Equation
(3.1) and was determined as 0.018 and 0.020 for d50 = 0.58 mm and d50 = 0.90 mm, respectively
(Julien, 2018).
ଵ/଺

݊௕ = 0.064݀ହ଴

84

(3.1)

As reported by Kuhnle et al. (2002) the measured tail length of the scour area is below 20 times
of the dike normal length regardless of the alignment angles. In the current study, considering
the dimension of the model spur dikes and the sandboxes, the position of the model spur dikes
was determined to be at one-third of each sandbox to eliminate interferences to the downstream,
as shown in Figure 3.1. Figure 3.2 is a photo of the laboratory flume.

Figure 3.1 Schematic diagram of the experimental flume setup for local scour around submerged angled spur
dikes.

85

Figure 3.2 Field photo of the Quesnel River Research Center (QRRC) experimental flume.

Since the erosive process is caused by the shear stress imposed on the bed sediment (Khan
et al., 2016), the influence of spur dike materials was not investigated. Waterproof marine
plywood was selected to build the vertical wall spur dikes. The average depths in the two
sandboxes vary marginally due to the smaller flume slope of 0.20%. Therefore, the height of
the spur dikes above the initial sand bed were set as 15 cm and 20 cm in the upstream sand box
and 20 cm and 25 cm in the downstream sandbox to keep the overtopping ratios in two
sandboxes varying within 5.0%. Richardson and Simons (1984) proposed that dikes with
angles between 100° and 110° may be applied to channelize or direct flow. However, Jansen
et al. (1979) stated that no uniform standards should be set for all spur dikes. Thus, the model
spur dikes with a uniform spur dike width of 0.05 m were set up at alignment angles of 90°,
120°, and 135° in the current study.
When the strength is not a concern, rigid unbreakable ice replacements such as wood,
paraffin, and Styrofoam have been utilized effectively for ice cover simulation (Jafari & Sui,
2021; Wuebben, 1996). In the current study, the styrofoam panels were used as the smooth ice
86

cover, and the rough ice cover was prepared by attaching 2.5 cm Styrofoam cubes to the bottom
of the smooth Styrofoam panels. Manning’s coefficient for the synthetic smooth cover (ni) is
estimated as 0.010 (Hains & Zabilansky, 2005). The rough cover Manning’s roughness
coefficient is estimated as 0.021 by applying Equation (3.2) (Li, 2012).
ଵ/଺

݊௜ = 0.039 ݇௦

(3.2)

in which ks is the average roughness height (m). Field observations in natural rivers prove that
ice covers appearing in most rivers belongs to smooth, floating ice covers (Turcotte et al., 2011).
The Styrofoam panels used as model ice cover in the current study were positioned using wires
to simulate the presence of stable floating ice cover in a natural channel. The flow under the
ice cover resembles a turbulent pipe flow (Sirianni et al., 2022). Equation (3.3) can be used to
estimate the entry length for fully developed flow (le) (Çengel & Cimbala, 2014).
݈௘ = 1.359‫ܴ݁ܮ‬ଵ/ସ

(3.3)

where Re is the flow Reynolds number, and L is the characteristic length. In the current study,
the lengths and widths of the model ice cover on the water surface are 9.60 and 2.00 m for the
upstream sandbox, and 9.80 and 2.00 m for the downstream sandbox (extending 2.0 m toward
upstream from the frontal edge of the sandbox and 2.0 m toward downstream from the rear
edge of the sandbox). The model ice cover encompassed sufficient upstream area from the spur
dike tip for the underneath flow to become fully developed.

3.2.2 Instrumentation
A SonTek Acoustic Doppler Velocimeter (ADV) was used to measure the approaching
flow velocity. The Sontek ADV is a single-point, high-resolution velocity meter comprising

87

one transmitter and three receivers in accordance with the acoustic Doppler effect to detect the
change in received frequency (Doppler shift) reflected by the moving solid particles scattered
in the water body (Rehmel, 2007). The WinADV software was applied to post-process data by
filtering the measured reflected signal and other parameters. The signal-to-noise ratio (SNR)
and correlation (COR) were selected as data filtration criteria. The COR indicates the
uniformity of the particle movement during the sample interval, whereas the SNR denotes the
relative density of the scatters in the flow (Wahl, 2000). At the selected ADV frequency of 25
Hz, SNRs greater than 15 dB are advised, and CORs over 70% should be set as the acceptable
data threshold (SonTek/YSI Inc., 2001). In the current study, both aforementioned values were
set for filtering data collected using the ADV. The approaching water depth, flow rate, and
average flow velocity were monitored using a SonTek-IQ Plus (SonTek, 2012).

3.2.3 Experimental Protocol
Initially, the sandboxes were filled with non-uniform sand, and the surface was leveled to
the same elevation as the flume bed. The tailgate was adjusted to the desired height. One valve
then was opened slightly to allow water to gradually soak the sandboxes. The sandbox surface
was monitored carefully to avoid initial scour. Once the desired flow depth was reached, the
two control valves were turned on completely.
The duration required to attain an equilibrium state is crucial in investigating a local scour
process. Oliveto and Hager’s (2002) experimental research found that the time variation of
local scour development is mainly determined by the in-stream structure geometrical variables,
the hydraulic parameters, and the granulometric characteristics. The local scour under an ice88

covered flow condition is more complicated than that under an open channel flow condition.
Namaee and Sui (2020) did an experimental investigation on local scour under ice-covered
flow conditions and suggested that equilibrium scour depth should be reached after 24 h. The
current study applied the criteria for reaching the equilibrium scour process proposed by Mia
and Nago (2003), namely when the scour depth fluctuation was less than 1 mm/h. A thin
standard ruler with millimeter increments and a reading error of +/- 0.1 mm was attached at the
dike tip to observe the temporal scour changes during the test trial, after which the duration of
24 h was selected for all experimental runs.
Once the scour process reached equilibrium, the ADV was used to measure the
instantaneous velocity to verify readings from the SonTek IQ. After all required measurements
were finished, the valves were carefully closed to allow the water to recede gradually to avoid
disturbances in the scour pattern. After water was drained completely from the flume, the
deformation zone including both scour hole and deposition dune was divided into a grid which
has a side length of 1-cm. The depths at the vertices of the grids were carefully recorded using
a laser distance measurer with an accuracy of 3 mm. When all the measurements were done,
the spur dike was aligned to another desired angle to prepare for the next experimental run. If
a new overtopping ratio was required, the aforementioned procedures were repeated. Table 3.1
lists the experimental conditions under the smooth ice-covered flow condition, which was
repeated for both open-channel and rough ice-covered flow conditions.
Table 3.1 Summary of working parameter setups under the smooth ice cover
Design

Run

Sandbox

Median grain

Spur dike

#

position

size d50 (mm)

height T (m)

1

Upstream

0.90

0.15

0.50

2

Upstream

0.90

0.15

0.50

length L
(m)

89

Flow

Average

depth h

velocity U

(m)

(m/s)

90

0.21

0.37

120

0.21

0.37

Alignment
angle α (°)

3

Upstream

0.90

0.15

0.50

135

0.21

0.40

4

Upstream

0.90

0.15

0.35

90

0.20

0.38

5

Upstream

0.90

0.15

0.35

120

0.20

0.37

6

Upstream

0.90

0.15

0.35

135

0.20

0.38

7

Upstream

0.90

0.20

0.50

90

0.20

0.39

8

Upstream

0.90

0.20

0.50

120

0.20

0.38

9

Upstream

0.90

0.20

0.50

135

0.20

0.35

10

Upstream

0.90

0.20

0.35

90

0.21

0.37

11

Upstream

0.90

0.20

0.35

120

0.21

0.38

12

Upstream

0.90

0.20

0.35

135

0.21

0.37

13

Downstream

0.58

0.20

0.50

90

0.25

0.28

14

Downstream

0.58

0.20

0.50

120

0.25

0.31

15

Downstream

0.58

0.20

0.50

135

0.26

0.27

16

Downstream

0.58

0.20

0.35

90

0.26

0.25

17

Downstream

0.58

0.20

0.35

120

0.25

0.28

18

Downstream

0.58

0.20

0.35

135

0.26

0.31

19

Downstream

0.58

0.25

0.50

90

0.25

0.32

20

Downstream

0.58

0.25

0.50

120

0.26

0.33

21

Downstream

0.58

0.25

0.50

135

0.25

0.31

22

Downstream

0.58

0.25

0.35

90

0.25

0.32

23

Downstream

0.58

0.25

0.35

120

0.25

0.27

24

Downstream

0.58

0.25

0.35

135

0.25

0.27

3.3 Results and Discussions
The critical velocity (Uc) for beginning of motion of sediment particles was calculated and
compared to the measured approach velocity (U). Clear-water scour occurs when Uc > U at the
cross section where the spur dike tip is located. The equation proposed by Laursen (1963) was
applied to calculate Uc.
ଵ/ଷ

ܷ௖ = ‫ܭ‬௨ ℎଵ/଺ ݀ହ଴

(3.4)

where h is the average approaching flow depth (m) and Ku is equal to 6.19 in S.I. units. The
measured U all fell below the calculated Uc, affirming the clear-water scour assumption.
Figure 3.3 was generated using the Surfer 2D/3D Mapping Software to exemplify the
scour pattern around submerged spur dikes under open, smooth ice-covered, and rough ice-

90

covered flow conditions, where d50, T, L, and α are 0.90 mm, 0.20 m, 0.35 m, and 90°,
respectively. Terrain elevation change contours for all experiments can be found at Appendix
I. The depths of scour holes are represented by negative values, while the positive values depict
the heights of deposition dunes. The maximum scour depths were observed at the upstream toe
of the submerged spur dike. Meanwhile, downstream of a spur dike, the wake zone yielded the
highest deposition values.

91

Figure 3.3 Channel bed elevation contours around a spur dike: (a) Open channel flow; (b) Smooth ice-covered
flow; and (c) Rough ice-covered flow (units: mm).

92

3.3.1 Impacts of spur-dike related parameters on local scour around spur dikes
The submergence ratio is one of the most crucial variables for a submerged spur dike
design. This study applied the submergence ratio as the ratio of flow depth to the spur dike
height (S = h/T), also referred to as the overtopping ratio by McCoy et al. (2007). The variation
of the non-dimensional maximum scour depth related to normal length ds/(Lsin α) (where ds is
the measured scour depth) is plotted against different cover conditions for both minor
submergence (left) and moderate submergence (right) for different bed material (d50) in Figure
3.4.

Figure 3.4 Variations of ds/(Lsin α) values for different cover conditions under different submergence levels.

The spur dike normal length (Lsin α) is the vertical distance from the flume sidewall to
the outer edge of the spur dike. Figure 3.4 shows that the presence of ice cover led to the
increase of ds/(Lsin α) regardless of d50 and submergence levels. Under the smooth cover
condition, the scour depths increased to a moderate degree compared to that under an open
channel flow condition, namely, about 12 and 36% for minor and moderate submergence,
respectively. Under the rough cover condition, a significant increase in the scour depth was
found, namely, about 20 and 64% for minor and moderate submergence, respectively. The

93

greater the distance from the dike tip to water surface was, the smaller the ds/(Lsin α) became.
Results showed that the range of the ds/(Lsin α) values for the moderate and minor submergence
scenarios is 0.10–0.15 and 0.25–0.38, respectively. Figure 3.5 shows a noticeable decreasing
trend of the ds/(Lsin α) values when the submergence ratio (S) grows. The decreasing trend is
due to the boundary layer flow passing over the spur dike tip, weakening the energy carried
through the wake vortices, thereby reducing the sediment load carried by the flow and
decreasing the scour depth (Du et al., 2022).

Figure 3.5 Dependence of ds/(Lsin α) values on submergence ratio (S).

In the current study, the alignment angle (α) is defined as the angle between the spur dike
axis and flow direction. For all experimental runs, the alignment angles were set as the nonattracting angles (≥ 90°). Özyaman et al. (2022) examined the relation between the nondimensional maximum scour depth related to design length (ds/L) to assess the effects of α. For
94

the current study, the variation of the (ds/L) values against the alignment angle (α) is illustrated
in Figures 3.6 and 3.7.

Figure 3.6 Variation of ds/L against α (minor submergence).

For a constant α, the larger the dike length (L) is, the more the sediment movement would
be, reflected by a higher (ds/L)-value. When the spur dike height (T) and dike length (L) stay
identical, it can be observed that the (ds/L)-value decreases with the increase of α. This decrease
can be explained by the sidewall effects posed by the channel confinement, which alters the
flow pattern and changes the strength of the vortices. A plexiglass wall installed at the
observation station, poses sidewall effects on the local scour mechanisms. The influence of the
sidewalls on the flow can be linked to the effect of the corner vortex found in wide duct flows
(Kohyama et al., 2022). Yang et al. (2012) did a mathematical analysis and revealed that the
presence of sidewalls would lead to secondary flows. Rodríguez and García (2008) claimed

95

that sidewall effects are more prominent when the aspect ratio (channel width (B) to the flow
depth, B/h) is less than 5. Blanckaert et al. (2010) investigated secondary flows across gravel
beds in a channel with the aspect ratio (B/h) ranging from 6.2 to 11.9, and found that the
secondary flows were present across the entire width of the flow for all aspect ratios. However,
the strength of the secondary flow reduced as the distance got further from the channel sidewall.
Since the aspect ratio (B/h) ranges from 6 to 10 in the current study, secondary flow disturbs
the flow field around the submerged spur dike.

Figure 3.7 Variation of ds/L against α (moderate submergence).

As the alignment angle (α) changed, the distance of the channel wall to the dike tip where
the scour hole would appear also altered. The closer the dike tip to the channel wall, the more
prominent the sidewall effects will be. One can also see from Figures 3.6 and 3.7 that a rougher
cover exacerbates the change in the (ds/L)-value more significantly. Compared to the open-

96

channel flow scenario, the increase in the (ds/L)-value under the rough cover is about 10–37%
regardless of the alignment angle (α) and the submergence levels, whereas the increase in the
(ds/L)-value under the smooth cover is about 5–28%. The dike with an alignment angle of 90°
will be the least vulnerable to the covered flow. Contrarily, the dike with the alignment angle
of 135° experiences the most drastic changes in the (ds/L)-value when ice cover is introduced.

3.3.2 Impacts of hydraulic parameters on local scour around spur dikes
Scale effects are unavoidable in physical models, but their impacts on experimental
outcomes might be minimized by ensuring the flow Froude number (Fr = U/(gh)1/2, where g is
the acceleration of gravity) similarity between the model and prototype (Heller, 2011). The
variation of the ds/(Lsin α) values against Fr is shown in Figure 3.8.

Figure 3.8 Dependence of the dimensionless maximum scour depth ds/(Lsin α) on Froude number (Fr).

It is apparent from Figure 3.8 that the ds/(Lsin α)-value can be fitted relatively well to cover
the specified range of Fr despite the differences in other factors. The measured ds/(Lsin α)
values show a growing trend with the increase of Fr. Based on the interpolated best-fitting
curves for data collected in the downstream sandbox, when Fr = 0.17 representing flows with
a lower Fr, the ds/(Lsin α) values under open channel, smooth, and rough ice cover are 0.14,

97

0.19, and 0.22, respectively. When Fr = 0.21 representing flows with a higher Fr, the ds/(Lsin
α) values under open channel, smooth, and rough ice cover are 0.32, 0.34, and 0.35,
respectively. Comparable trends can also be observed for the upstream sandbox.
Regardless of the cover roughness, the ds/(Lsin α) values and Fr values universally
maintain a high correlation, indicating that the flow around the spur dike is exceedingly
turbulent (Chanson, 2004). The calculated Fr in the downstream sandbox ranging from 0.14 to
0.22 are smaller than those in the upstream sandbox that ranged from 0.22 to 0.31, partially
due to the decrease in U resulting from the energy dissipation by the flume wall and bed.
Additionally, since the SonTek-IQ readings proved that the pumps supplied steady, nonuniform flow in a prismatic flume, the flow is considered as gradually varied flow (GVF)
(Gadissa, 2017). The depth increases gradually as the water flows toward downstream and
forms backwater when it hits the tailgate at the downstream end of the flume.
Since non-uniform sediment particles are used as bed materials, after the initiation of
scour, the coarsening process of non-uniform sediment has an inhibitory effect on the further
development of a scour hole. Thus, the densimetric Froude number (Frd) (Eq. 3.5) is used as
an alternative parameter to characterize the local scour process (Namaee & Sui, 2019a).
‫ݎܨ‬ௗ =

ܷ

(3.5)

ඥ(‫ ݏ‬− 1)݃݀ହ଴

where, s = ρs/ρ, is the ratio of sediment density (ρs) to water density (ρ). Figure 3.9 shows the
relations between ds/(Lsin α) and Frd for different submergence levels.

98

Figure 3.9 Comparison of dependence of ds/(Lsin α) on Frd for different submergence levels under different
cover conditions.

As shown in Figure 3.9, the ds/(Lsin α)-value increases with the increase of Frd regardless
of submergence levels and cover conditions. Comparing fitted curves in Figure 3.9, one can
see that for a given Frd and cover condition, the more immersive the spur dike is positioned,
namely, a larger S, the shallower the scour hole. Variations under different cover conditions
can be explained by the expansion of the separation zone around the submerged spur dike
accompanied by the increase of channel cover roughness. Greater cover roughness shifts the
maximum velocity closer to the channel bed and consequently increasing the bed shear stresses,
resulting in deeper scour holes (Sui et al., 2010). Further, regardless of the cover roughness,
under the same Frd, the differences in the ds/(Lsin α) values between minor and moderate
submergence remain relatively consistent and can be determined at any Frd where data are

99

available.
Figure 3.10 shows the variation of ds/(Lsin α) with Frd under different cover conditions.
Figure 3.10 confirms the trend found in Figure 3.4 that for the same bed material and approach
velocity, the appearance of an ice cover resulted in a higher scour depth. Additionally,
regardless of the submergence level, results show that to reach the same dimensionless scour
depth, Frd is the smallest under the rough cover condition, followed by smooth cover and the
open channel flow condition (e.g., when ds/(Lsin α) = 0.30, Frd = 4.89, 5.19, and 5.34,
respectively, for rough ice cover, smooth ice cover, and open channel under moderate
submergence). Referring to Equation (5), a smaller approach velocity is required to reach the
same dimensionless scour depth for covered flow compared to that under the open channel
flow condition.

Figure 3.10 Dependence of ds/(Lsin α) on Frd under different cover conditions for different submergence levels.

3.3.3 Modification of existing equation
Researchers have derived several formulas to predict the maximum scour depth around
in-stream hydraulic structures. Based on the ratio of wetted embankment length (Lw) to the
approach flow depth (h), the Highways In the River Environment (HIRE) equation (Richardson
100

et al., 1989) is recommended when Lw/h > 25, whereas the Froehlich (1989) equation is advised
when Lw/h ≤ 25 (USACE, n.d.). Dey and Barbhuiya (2005) proposed an empirical scour depth
equation based on 99 experiments using uniform sediment and 27 experiments using nonuniform sediment. They determined that the excess abutment Froude number, the ratio of flow
depth to abutment length, and the ratio of abutment length to sediment size influence the
equilibrium scour depth. Due to the intricacy of the scour processes, predictions of scour depth
using existing scour equations around abutments will yield results with significant differences
when applying them to spur dikes (Oğuz & Bor, 2022).
Lim (1997) proposed the following equation for determining the dimensionless maximum
scour depth (ds/h) based on 252 datasets using non-uniform sediment for laboratory
experiments under the clear water scour condition,
݀௦ /ℎ = ‫ܭ‬௦ (0.9ܺ௔ − 2)

(3.6)

where Ks is the abutment shape factor, taken as 1.0 for vertical wall structures (such as the
model spur dike in the current study), and Xa is calculated as
ܺ௔ = {(ߠ௖௔ )ି଴.ଷ଻ହ (‫ݎܨ‬ௗ )଴.଻ହ (݀ହ଴௔ /ℎ)଴.ଶହ [0.9(‫ ܮ‬sin ߙ /ℎ)଴.ହ + 1]}

(3.7)

in which θca is Shield’s (1936) entrainment function and d50a is the median grain size for the
armor layer, obtained by sieve analysis of the samples collected from the armor layer. Shield’s
diagram offers a reference for critical shear stress by plotting it against the boundary shear
Reynolds number, helping contextualize sediment movement tendencies in this study. Equation
(3.6) is valid when Xa is over 2.2 and Lim (1997) proposed that θca can be calculated based on
the following functions:

101

0.055, ‫∗ܦ‬௔ > 150
⎧
଴.ଶଽ
⎪0.013‫∗ܦ‬௔ , 20 < ‫∗ܦ‬௔ ≤ 150
ି଴.଺ଵ
, 10 < ‫∗ܦ‬௔ ≤ 20
ߠ௖௔ = 0.04‫∗ܦ‬௔
⎨ 0.14‫ିܦ‬଴.଺ସ , 4 < ‫ ≤ ܦ‬10
∗௔
∗௔
⎪
ିଵ
⎩
0.24‫∗ܦ‬௔
, ‫∗ܦ‬௔ ≤ 4

(3.8)

where ‫∗ܦ‬௔ is the armor layer particle parameter, calculated as
‫∗ܦ‬௔ = ݀ହ଴௔ [(‫ ݏ‬− 1)݃/‫ ݒ‬ଶ ]ଵ/ଷ

(3.9)

where v is the kinematic viscosity of water at the experiment temperature. However, in the
equation proposed by Lim (1997), the channel cover and submergence level are not considered.
The current study proposes a new factor (X’) to replace Xa in Lim’s (1997) equation by
incorporating the channel roughness factor (N) and the overtopping ratio (S). Data for
derivation of the new equations are attached in Appendix II. Flume experiments are generally
impacted by the flume's sidewall. Since the hydraulic radius (Rh) reflects an effective flow
depth that compensates for sidewall effects, Equations (3.6) and (3.7) may be adjusted by
substituting Rh for h. The experimental data were randomly split into two samples such that
80% of the measurement data were used to train the model and 20% were used for the model
validation. Regression analyses yielded the following equations.
ܺ′ = 0.21(ߠ௖௔ )ି଴.ଷ଻ (‫ݎܨ‬ௗ )ି଴.ଵଵ (݀ହ଴௔ /ܴ௛ )ି଴.ଵ଻ (‫ܮ‬sin ߙ/ܴ௛ )଴.ଵହ (ܰ)଴.଴ଵଷ (ܵ)ି଴.ଶ଻

(3.10)

where
ܰ=

݊଴ ܷ

(3.11)

ଶ/ଷ

ܴ௛

Brunner (2016) suggested using Equation (3.12) for determining the composite roughness
coefficient for an ice-covered flow, n0, as follows:
ଶ

(݊௕ )ଵ.ହ + (݊௖ )ଵ.ହ ଷ
݊଴ = ቈ
቉
2

102

(3.12)

where nb and nc are the Manning roughness coefficients for the channel bed and ice cover,
respectively. For open channel flow, n0 is taken as nb. The resulting coefficient of determination
(R2) and root mean square error (RMSE) for the modified equation are 0.846 and 0.018,
respectively. The comparison of the calculated relative maximum scour depth (ds/Rh) to those
of measurements is shown in Figure 3.11.

Figure 3.11 Comparison between measured and calculated (using Equation (10)) values of maximum relative
scour.

The percent bias (PBIAS) and root mean deviation ratio (RSR) are applied to further
assess the accuracy of the modified equation. The calculated PBIAS and RSR are 0.00193 and
0.0637, based on which the modified equation predicts the local scour relatively well
(Abeysingha et al., 2015). Type III sum of squares (SS) analysis was done to assess the
influence of each independent variable on the relative maximum scour depth (ds/Rh). The Type
III SS was selected because the sequence in which the variables are chosen has no influence on
the scores. The higher the model SS, the lower the residual SS, and, hence, the greater the
variable’s impacts (Neter et al., 1991). By means of the Type III sum of squares analysis, both
“F” and “p” values have been calculated. Table 3.2 lists the performance of each predictor in
the new equation.

103

Table 3.2 Type III sum of squares analysis results
Sum of

Mean squares

F

Pr > F

Significance codes1

0.002

0.002

2.993

0.089

.

1.000

0.004

0.004

11.750

0.001

***

d50a/Rh

1.000

0.000

0.000

0.456

0.502

°

Lsinα/Rh

1.000

0.039

0.039

114.478

<0.0001

***

N

1.000

0.001

0.001

0.497

0.484

°

S

1.000

0.064

0.064

187.009

<0.0001

***

Source

DF

θca

1.000

Frd

squares

1

Significance codes: 0 < *** < 0.001 < ** < 0.01 < * < 0.05 < . < 0.1 < ° < 1, generally, values less than 0.05

are considered statistically significant; note: DF is the degrees of freedom in the statistical test.

In Table 3.2, “Pr>F” is the probability of the test results that are at least as extreme as the
observed results assuming the null hypothesis applies, is also called the p-value. “F” is called
the F-value and represents how predictive the model is, which helps to determine whether
statically significant differences exist in the means of multiple data groups. The dependent
variable, the relative maximum scour depth (ds/Rh) is found to be significantly influenced by
following dimensionless variables: Frd, Lsin α/Rh, and S. On the other hand, other
dimensionless variables including θca, d50a/Rh, and N do not show a high statistical significance.
The overtopping ratio S (with F = 187.009, p < 0.0001) displays the highest model SS (0.064)
and is deemed to be the most significant variable in determining the relative maximum scour
depth (ds/Rh), whereas d50a/Rh (with F = 0.001, p = 0.502) representing the impacts of the nonuniformity of sediment has the least statistical significance. The general form of the modified
equation is as follows:
݀௦ /ܴ௛ = ‫ܭ‬௦ (0.9ܺ′ − 2)

(3.13)

ܺ′ = ݂(ߠ௖௔ , ‫ݎܨ‬ௗ , ݀ହ଴௔ /ܴ௛ , ‫ܮ‬sin ߙ/ܴ௛ , ܰ, ܵ )

(3.14)

where

104

Additional investigations should be done for individual spur dike designs to validate this
equation and determine the function in Equation (3.14).

3.4 Chapter Summary
Chapter three describes the study that utilized the physical model testing method, focusing
on the non-dimensional maximum equilibrium scour depths around angled, submerged spur
dikes under open and ice-covered flow conditions. The impacts of parameters related to spur
dike design and water surface cover conditions on local scour have been inspected. Based on
data analysis, the following conclusions have been obtained.
1) The non-dimensional scour depth related to the dike normal length ds/(Lsin α) decreases
with the increase of the overtopping ratio (S), implying that the wake vortices are
weakened more by the boundary layer flow on the top of the spur dike as the
submergence increases. For a submerged vertical wall spur dike, non-dimensional scour
depth related to the non-dimensional maximum scour depth related to design length
(ds/L) decreases with the increase in the alignment angle (α). However, the sensitivity
towards the addition of an ice cover on the water surface increases with α. Moreover,
for a fixed α, the longer the design length of a spur dike (L) is, the more aggressive the
sediment movement becomes, as shown by a higher ds/L value.
2) With an increase in the Froude number (Fr), the non-dimensional scour depth related
to the spur dike normal length ds/(Lsin α) increases. Regardless of the cover condition,
variables ds/(Lsin α) and (Fr) are strongly correlated, indicating that the flow near a
spur dike is exceptionally turbulent. The calculated Fr in the downstream sandbox has

105

a smaller range than those in the upstream sandbox, potentially caused by energy
dissipation because of the channel sidewalls and bed. For a given densimetric Froude
number (Frd) and cover condition, the more immersed the spur dike is positioned
(namely, a greater S), the smaller the relative maximum scour depth ds/(Lsin α). The
presence of an ice cover on the water surface, regardless of the cover roughness, reduces
the difference in the rates of change between the minor submergence and moderate
submergence. When other factors don’t change, to reach the same relative maximum
scour depth ds/(Lsin α), the densimetric Froude number, Frd, under a rough cover is the
least, followed by smooth ice-covered and open-channel flow conditions.
3) To modify the equation for estimating scour depth proposed by Lim (1997), the
hydraulic radius (Rh) has been proposed to substitute for the approach flow depth (h) to
minimize the sidewall effect inherent in flume experiments. Type III Sum of Squares
analysis was done to determine the individual factors’ significance in the modified
equation. The results show that the submergence level is the most influential predictor
in determining the maximum local scour depth. Both PBIAS and RSR were selected as
the statistical criteria used to further to validate the accuracy of the modified empirical
equation. Coupled with the coefficient of determination (R2) and root mean square error
(RMSE) values, the performance of the modified equation for calculating the relative
maximum scour depth ds/(Lsin α) is relatively good.
The current study is limited to the analyses of the equilibrium scour depths (namely, the
maximum scour depths around spur dikes). However, the results of field observations showed
that the time-development of scour holes also varies under different experimental setups (i.e.,

106

open channel flow or ice-covered flow conditions). Further research in this field should be done
to examine the temporal development of scour holes and the protection mechanisms of the
armor layer inside scour holes around angled, submerged spur dikes.

107

4.

CHAPTER FOUR: TURBULENT FLOW STRUCTURE AROUND
SUBMERGED ANGLED SPUR DIKES UNDER ICE COVER

4.1 Introduction
Installing spur dikes in a channel represents a typical engineering practice to enhance
channel functions and control floods. Spur dikes are designed to interrupt the flowing water
and sediment transport along the shoreline or riverbank, thereby preventing erosion and
ensuring the stability of channel banks. Spur dikes extend from riverbanks into the water,
forming a barrier that alters flow patterns compared to rivers without them. This alteration aids
in trapping sediment, thus preventing further erosion along the coastline or river. Spur dikes
can induce turbulence and the formation of eddies in the flow field. The interaction between a
dike and flowing water generates vortices and swirling motions, which lead to increased mixing
and turbulence. These turbulent conditions can affect sediment transport, erosion, and
deposition patterns near the dike and can also result in local scour (Fang et al, 2006; Li et al.,
2023). The modified flow fields in the presence of spur dikes are complex and depend on
various factors such as dike geometry, flow velocity, sediment characteristics, and overall
hydraulic conditions. Various hydraulic modeling and site-specific studies are typically
conducted to understand and predict the flow behavior around spur dikes before their
construction to minimize adverse effects and optimize their designs. Spur dikes can be
classified into submerged and non-submerged categories based on their submergence level.
Based on the alignment angle (α) between the axis of a dike and the streamwise direction of
the flowing water, spur dikes can also be grouped into attracting (acute angles), deflecting
(right angles), or repelling (obtuse angles). The repelling type is preferred for submerged spur

108

dikes, as the sediment can be directed toward the side of the river bank, contributing to the
sediment deposition and mitigating the damage to the dikes’ foundation as the water passes
over the top of the spur dike (Zhang et al., 2018).
Rivers in cold regions seldom experience periods without ice cover development. Ice
cover exerts non-negligible influence on the evolution of channel bed morphology (F. Wang et
al., 2021). Hydraulic riverine structures, such as spur dikes and bridge piers/abutments, result
in complex flow fields under ice-covered flow conditions. Hu et al. (2022) investigated the
evolution of channel bed deformation and ice jam around a single pier. The study concluded
that turbulence intensities in the scour hole around the pier increased when ice cover was
present on the water surface without initiating ice jams. Zabilansky and White (2005)
characterized a river as narrow if changes in water level have no impact on the position of the
ice cover. When the flow discharge in a narrow river exceeds the freeze-up datum, the ice cover
induces a pressurized flow condition beneath, shifting the maximum velocity position towards
the channel bed. Moreover, a stationary ice cover increases the wetted perimeter and pushes
the maximum velocity toward a smoother boundary (Smith et al., 2023; Sui et al., 2010).
The research focuses on turbulent flow characteristics around non-submerged spur dikes,
analyzing velocities in three dimensions at specific locations. Barbhuiya and Dey (2004)
employed an Acoustic Doppler Velocimeter (ADV) to assess the three-dimensional turbulent
flow field around a vertical semicircular cylinder affixed to the sidewall of a rectangular
channel in a laboratory setting. The vector graphs of the flow field in the azimuthal and
horizontal planes indicate the presence of a main vortex upstream from the cylinder. Hei et al.
(2009) utilized a laser three-dimensional particle dynamics analyzer (3D-PDA) to determine

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the flow velocity around a spur dike. They categorized the general flow field into three subregions according to velocity distribution: the reverse-velocity region, the positive-velocity
region, and the central flow region.
Kline et al. (1967) identified the burst phenomenon through visual and quantitative
investigations into turbulent boundary layers. Low-speed streaks (areas of slow-moving flow)
interact with the flow’s outer edges through a slow “lift-up” followed by rapid oscillation,
bursting, and ejection. The quadrant analysis proposed by Lu and Willmarth (1973) for
analyzing the bursting phenomenon is frequently utilized to examine turbulent flow
configurations and identify the coherent structures responsible for the turbulent transport of
momentum (Huai et al., 2019).
Realistically, due to the changes in hydraulic conditions in a river, a spur dike should be
aligned at variable angles. Considering extreme precipitation events’ increasing frequency and
intensity, non-submerged spur dikes can fully submerge when the design flood is exceeded.
Also, the presence of an ice cover or ice jam in a river significantly increases the water level
(Sui et al., 2002, 2005), and thus, non-submerged spur dikes become submerged. To the authors’
knowledge, the flow fields around submerged angled spur dikes under ice-covered flow
conditions have never been investigated.
This research investigates turbulent flow dynamics near a single submerged spur dike
within a laboratory flume, utilizing a SonTek Acoustic Doppler Velocimeter (ADV) to measure
instantaneous velocities under both open-channel and ice-covered conditions. The study
examines how the geometries of such single submerged spur dike influence turbulent flow
characteristics through quadrant analysis of velocity fluctuation components, thereby

110

quantifying the contribution of each quadrant and assessing changes in dominant burst
processes near angled submerged spur dikes across different flow conditions and experimental
configurations. The objectives include identifying velocity field patterns using ADV data,
quantifying Reynolds shear stress, and analyzing dominant turbulent events via quadrant
analysis to understand the interaction between flow conditions, dike geometry, and turbulent
flow structures. Although real-world applications often involve groups of spur dikes, this study
isolates single structures to provide fundamental insights into hydrodynamic behavior under
ice-covered conditions.

4.2 Material and Methods
4.2.1 Facilities for Experiments
Experiments were conducted in a large concrete outdoor flume at the Quesnel River
Research Center (QRRC) in Likely, British Columbia, measuring 38.20 m in length, 2.00 m in
width, and 1.30 m in depth. A staff gauge accurate to 1 mm recorded the approaching flow
depth upstream of the leveled sandbox surface, ensuring flow uniformity during each
experimental run. At the flume exit, a tailgate ensured the flow reached the desired depths along
the flume. The current study utilized two sandboxes. As shown in Figure 4.1a, the upstream
sandbox measures 5.60 m in length, 2.00 m in width, and 0.30 m in depth, while the
downstream sandbox is 5.80 m long, 2.00 m wide, and 0.30 m deep. The distance from the
downstream sandbox's exit to the tailgate measures 5.30 m. The flume bed features a 0.20%
slope. Due to the backwater effect, water levels at the two sandboxes slightly vary.

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Figure 4.1 Schematic diagram of the experimental flume: (a) Side view; (b) Cartesian coordinate system.

The aspect ratio B/h, where B is the channel width, and h is the approaching flow depth,
is a key hydraulic parameter used to classify channels as narrow or wide. This study considers
channels wide when B/h > 5, consistent with laboratory conditions where sidewalls are
assumed smooth. In natural settings, however, lateral roughness elements such as vegetation
along riverbanks can increase flow resistance and reduce effective channel width. As a result,
a higher aspect ratio threshold may be required to account for these roughness effects (Knight
& Macdonald, 1979). A Cartesian coordinate system is established for three-dimensional
velocity measurements in the flume. The x-axis runs longitudinally along the streamwise flow,
the y-axis laterally towards the opposite side of the observation station, and the z-axis vertically
towards the water surface. The Cartesian coordinate system's origin is positioned at the center

112

of the spur dike surface attached to the sidewall. The z = 0 plane corresponds to the flume
bottom (or the sandbox's initial surface), with velocity fluctuation components in the x-, y-, and
z-directions denoted by u’, v’, and w’, respectively. The placement of the model submerged
spur dikes was based on the findings of Kuhnle et al. (2002), who reported that the scour
region's tail length around the dike is less than 20 times the spur dike length, regardless of the
alignment angles. The model spur dike's width (thickness) is 5 cm, buried at the sandbox
bottom, with heights (T) of 20 cm and 25 cm above the initial flat channel bed. The
submergence level was quantified using the overtopping ratio S, defined as the ratio of flow
depth h to spur dike height T (S = h/T), in accordance with Li et al. (2023) and McCoy et al.
(2007). For this study, “minor submergence” corresponds to S = 1, where the flow depth
approximately equals the dike height. “Moderate submergence” occurs when S = 1.25, where
a larger portion of the dike is submerged. Considering the dimensions of the spur dikes and
sandboxes, the model submerged spur dikes were positioned at one-third the length of each
sandbox to minimize downstream interferences, as depicted in Figures 4.1a and 4.1b,
illustrating the adopted coordinate system.
Velocity data were collected with a SonTek Acoustic Doppler Velocimeter (ADV). The
SonTek ADV, featuring a high-resolution current meter, includes a downward-looking probe
and three receivers. It monitors flow velocity through the Doppler effect, identifying changes
in frequency (Doppler shift) reflected by moving solid particles in the water. Velocity data was
analyzed with WinADV to preclude aliasing. WinADV analyzes signal quality through a
correlation coefficient (COR) and signal-to-noise ratio (SNR). Following SonTek/YSI's
guidance, the study applied criteria of SNRs above 15 dB and CORs exceeding 70% at 25 Hz,
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rendering 85% of the data suitable. A definitive strategy and standard for determining suitable
ADV sampling times for turbulent flow still needs improvement. Previous methods lack
universal applicability and are heavily dependent on researchers’ judgments. Proposed criteria,
rooted in statistical methods, have drawbacks related to experiment scale and flow conditions.
Park and Hwang (2021) suggested a sampling time based on the integral time scale (Ti),
calculated using Equation 4.1, with a recommended range from 150Ti to 200Ti:
௧ 〈௨೔ (௧)௨೔ (௧ାఛ)〉

ܶ௜ ≡ ∫଴ బ

〈௨೔ (௧)〉మ

݀߬

(4.1)

where τ denotes the lag between two points, t0 represents the first zero-crossing time in the
normalized autocorrelation function, ui(t) denotes the velocity component, and the subscript i
specifies the x, y, and z direction (O’Neill et al., 2004).
The laboratory experiment results in this study show an integral time ranging from 0.21
to 0.74 seconds. Park and Hwang (2021) suggested that the sampling period should range from
31.5 to 148 seconds. In this study, each measurement event's sampling period was 120 seconds,
which is considered adequate for accurate turbulence statistics determination (Jafari and Sui,
2021; Namaee and Sui, 2020). Experiments showed that the open-channel flow condition
produced the shallowest scour depth (G. Li et al., 2023), which was used as a reference point
for the timing of positioning the ADV during instantaneous velocity measurements.
Specifically, the ADV was deployed when the scour depth approached the equilibrium depth
observed under open-channel conditions. Velocity measurements were restricted to the area
near the dike head to further reduce potential interferences of varied terrain elevations under
ice-covered flow conditions. Flow velocity measurements started from the lowest point, 3 mm
above the bed. Measurements span three cross sections: one 10 cm upstream of the dike,
another near the dike's tip, and a third 10 cm downstream. Seven locations were selected for

114

measurements in each spur dike layout. Measurements at each location were conducted
vertically from the channel bed to the water surface, covering 8–10 different flow depths. One
thousand five hundred (1500) instantaneous velocities in three directions were recorded at each
point with 120-second sample periods. Figure 4.2 shows the measuring point locations where
instantaneous velocities were recorded. Table 4.1 presents the flume setups and model spur
dike features for open-channel studies, consistent across smooth and rough ice-covered
conditions.

Figure 4.2 Schematic plot of measuring positions (dike length = 50cm).
Table 4.1 Summary of experimental conditions and features of the flume and spur dikes under the open channel
condition.
Run #.

Sandbox position

Spur dike height, T

Alignment angle, α

(m)

(°)

Discharge, Q (L/s)

1

Upstream

148

0.15

90

2

Upstream

148

0.15

120

3

Upstream

160

0.15

135

4

Upstream

156

0.20

90

5

Upstream

152

0.20

120

6

Upstream

140

0.20

135

7

Downstream

112

0.20

90

8

Downstream

124

0.20

120

9

Downstream

108

0.20

135

10

Downstream

128

0.25

90

115

11

Downstream

132

0.25

120

12

Downstream

124

0.25

135

4.2.2 Ice Cover and Sediment Setups
The available materials for modeling ice cover fall into three categories: rigid, synthetic,
and natural. When strength is not a priority, researchers often use rigid, unbreakable substitutes
for ice cover, including wood, paraffin, polyethylene, polypropylene plastic, and Styrofoam
(Jafari & Sui, 2021). Styrofoam panels modeled smooth ice cover, while rough ice cover was
created by affixing Styrofoam cubes (with a 2.5 cm edge length) to the panel bottoms. The
Manning's coefficient for smooth Styrofoam panels is estimated at 0.013 (Jafari & Sui, 2021).
Using Li's equation to calculate Manning's coefficient (ni) for rough model ice cover, with a
roughness height of 0.025 m, ni is calculated as 0.021 (Li, 2012). These values align with
calculated results for surveyed ice-covered channels, either through average roughness height
estimation (0.0075 to 0.029) or the logarithmic law (0.0088 to 0.033) (Li, 2012). Equation 4.2
expresses the calculation for ni:
ଵ/଺

݊௜ = 0.039 ݇ୱ

(4.2)

where ks denotes the average roughness height at the ice cover's bottom. Field observations
indicated that most rivers form smooth, floating ice covers (Turcotte et al., 2011). This study
modeled the ice cover using a horizontally fixed, slightly buoyant styrofoam layer anchored at
both ends with wires. The attached styrofoam cubes were submerged for rough ice conditions
by placing weighted plywood on top. Although floating ice in natural rivers can exhibit lateral
movement and minor vertical adjustments due to flow forces and variations in ice thickness,
the experimental setup ensured horizontal stability, maintaining controlled conditions for
consistent measurement. This design facilitated the analysis of key flow dynamics beneath the
ice while minimizing the complexity introduced by vertical fluctuations. Furthermore, the local

116

scour processes observed under fixed and floating ice covers were comparable, with increased
ice cover roughness correlating with greater local scour depths (D. Hains & Zabilansky, 2004).
The entrance length for fully developed flow (le) can be estimated using the following
equation (Çengel & Cimbala, 2014):
݈௘ = 1.359‫ܮ‬௖ ܴ݁ଵ/ସ

(4.3)

where Re represents the flow Reynolds number, and Lc represents the characteristic length. The
model floating ice cover, consisting of Styrofoam panels, measures 9.60 m long and 2.00 m
wide for the upstream sandbox and 9.80 m long and 2.00 m wide for the downstream sandbox,
extending 2.00 m before and after each sandbox (Figure 4.1a). This configuration ensured the
model ice cover spanned sufficient space for the flow to fully develop.
Non-uniform bed materials have been utilized in flume studies to understand the clearwater scour processes comprehensively. In laboratory flume investigations, sediment sizes
must match or exceed 10% of the natural channel bed sediment sizes in the field (Ettema et al.,
1998). This study used non-uniform sediments with a median particle size (d50) of 0.90 mm to
imitate the natural riverbed. The channel bed Manning roughness coefficient (nb) for the sand
used as bed material was calculated as 0.020 using Equation 4.4 (Julien, 2018).
ଵ/଺

݊௕ = 0.064݀ହ଴

(4.4)

4.2.3 Quadrant Analysis
Huai et al. (2019) noted that quadrant analysis frequently assessed turbulent flow
structures through conditional statistics of streamwise and vertical velocity variations (u’ and
w’). This study employed quadrant analysis to investigate how spur dike parameters influence
sweep, ejection, outward, and inward movements. A spur dike’s submergence level and
alignment angle significantly impact turbulence structure under consistent approaching flow
conditions (Jafari & Sui, 2021; Vaghefi et al., 2016). In quadrant analysis, the u’-w’ plane is
117

divided into four quadrants: Q1, Q2, Q3, and Q4.
The hole size parameter Ht (threshold level) is introduced through filtration using a
hyperbolic area to calculate the frequency of each bursting event, focusing on the predominant
തതതതത. This approach allows for extracting of significant Reynolds shear stress
contributions to −‫’ݓ’ݑ‬
values in each quadrant while filtering out minor background events (Huai et al., 2019). The
conditional function, Ht, differentiates between background disturbances from large magnitude
burst events, the latter of which could significantly affect sedimentation processes. Ht is defined
as:
‫ܪ‬௧ ≡

ቚ௨ೕᇲ ௪ೕᇲ ቚ
ඥതതതതത
௨ᇲమඥതതതതത
௪ ᇲమ

(4.5)

The fluctuation of Ht enables the computation of the fractional contributions to total
Reynolds stress from events of varying magnitudes within each quadrant, excluding the hole
area, expressed as:
ଵ
തതതതതത
‫ ݑ‬ᇱ ‫ݓ‬௦ᇱ = ௡ ∑௡௝ୀଵ ‫ ܫ‬൫‫ݑ‬௝ᇱ ‫ݓ‬௝ᇱ ൯

(4.6)

where തതതതതത
‫ݑ‬ᇱ ‫ݓ‬௦ᇱ represents the proportion of turbulent bursts exceeding the threshold, ‫ݑ‬௝ᇱ ‫ݓ‬௝ᇱ denotes
the conditional Reynolds stresses, n signifies the number of events, and the indicator function
I is defined to complete the conditional averaging technique:
ᇱ ‫ ݑ‬ᇱ )଴.ହ (‫ݓ‬
ᇱ ‫ ݓ‬ᇱ )଴.ହ
തതതതതത
തതതതതതത
1, ݂݅ |‫ݑ‬ᇱ ‫ ݓ‬ᇱ | ≥ ‫ܪ‬௧ (‫ݑ‬
‫=ܫ‬ቊ
ᇱ
ᇱ
଴.ହ
ᇱ ‫ ݑ‬ᇱ ) (‫ݓ‬
ᇱ ‫ ݓ‬ᇱ )଴.ହ
തതതതതത
തതതതതതത
0, ݂݅ |‫ܪ < | ݓ ݑ‬௧ (‫ݑ‬

(4.7)

The stress proportion, Si, for the quadrant i is defined as the flux contribution to u’ and
w’ from that quadrant using:
〈௨ᇲ ௪ ᇲ 〉

೔
ܵ௜ = ห௨തതതതതതത
ᇲ௪ᇲ ห

(4.8)

where
1 ்೟ ᇱ
න ‫ ݓ)ݐ( ݑ‬ᇱ (‫ݐ݀ ܫ)ݐ‬
௧→ஶ ܶ௧ ଴

〈‫ݑ‬ᇱ ‫ ݓ‬ᇱ 〉௜ = lim

118

(4.9)

where Tt denotes the total time. S1 and S3 are positive (> 0), while S2 and S4 are negative (< 0).
A computer program in RStudio was developed to analyze the bursting phenomena and
ascertain each quadrant’s contribution to the Reynolds shear stress.

4.3 Results and Discussions
4.3.1 Distributions of Velocity around Angled Spur Dikes
Although the flow fully develops before reaching the cross-section with the spur dike,
the dike’s obstruction induces a new boundary layer. This study’s laboratory setup consists of
two isolated, non-interacting spur dikes, with hydrodynamics analyzed individually around
each. Despite the presence of two dikes, no interaction effects are considered. Velocity fields
around a single spur dike were measured at three cross-sections: 10 cm upstream, at the tip of
the dike, and 10 cm downstream. For each dike alignment angle, velocity measurements were
taken at seven positions along these cross-sections (CSs, Figure 4.2). Due to ADV device
limitations, velocity data can only be acquired 0.10 m away from the probe head. Thus, velocity
measurements cannot fully cover the entire depth (z-axis) (Namaee and Sui, 2020). In
laboratory flume settings, channel confinement can cause sidewall effects that alter the flow
pattern and vortex intensity, leading to velocity dips and shifting maximum velocity below the
open channel flow's free surface. The dip phenomena's mechanisms are often qualitatively
discussed regarding secondary currents. However, in this study's wide channel, where the flow
becomes 2-dimensional in the middle section, the impact of secondary currents is minimal and
will not be further discussed (Khanarmuei et al., 2020).
The streamwise velocity (u) is the most critical 3D velocity component for characterizing
turbulence structure, demonstrating the highest value and variability compared to the other two
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velocity components (v, w). Distortion in the streamwise velocity profiles decreases as the dike
orientation angle exceeds 90°, leading to more uniformly distributed measured velocities,
evidenced by u/uavg values fluctuating less around 1.0. As Figure 4.3 illustrates, increasing the
dike orientation angle from 90° to 135° results in lower streamwise velocities under any water
surface condition. Of note, uavg. represents the depth-averaged value of u.

Figure 4.3 The non-dimensional streamwise velocities (u/uavg.) in front of the spur dike tip (minor submergence
of spur dikes, T = 25 cm).

Figure 4.4 depicts the effects of the alignment angle on velocity vectors in the X-Y plane
(z/h = 0.45, the dike height above the initial sand bed T =25 cm). The origin (0,0) is at the
center of the spur dike surface attached to the sidewall. The magnitude of the vortex at the front
surface of the spur dike tip increases with the spur dike angle in the flow direction, as shown
by denser and longer vector arrows. Due to the ADV device’s limitations, this study presents
only time-averaged velocity fields near the spur dike tip. Therefore, the time-averaged velocity
fields do not capture the complete vortex profile in this study. However, in setups with
deflecting spur dikes (angles over 90°), the X-Y plane flow field near the dike tip shows low
sensitivity to water surface conditions. Unlike the altered vertical velocity profiles in Figure

120

4.3, ice cover presence minimally affects the X-Y plane velocity vectors. Subsequent analysis
further illustrates the velocity distribution in the Y-Z plane at various cross-sections around the
spur dike.

Figure 4.4 Flow velocity vectors generated from measured data in the X-Y plane close to the dike tip for different
alignment angles (z/h = 0.45). Note: The origin (0,0) is located at the center of the spur dike surface attached to
the sidewall, and the flow direction is from left to right.

Figure 4.5 illustrates the distribution of the dimensionless time-averaged streamwise flow
velocity (u/U) at the spur dike's rear side, where U represents the average flow velocity, and L’
denotes the projected normal length of the spur dike, calculated as Ld sinα. The dimensionless
streamwise velocity values at the spur dike’s rear side reveal a recirculation zone where reverse
flow (u/U. < 0) occurs due to the spur dike’s obstruction. With minor submergence of the spur
121

dike (T = 25 cm), reverse flow velocity magnitudes are higher than moderate submergence.
Conversely, in the moderate submergence case, the water flowing over the spur dike reduces
the reverse flow’s magnitude, depicted by the lighter color.

Figure 4.5 Time-averaged streamwise velocity contours at the rear side of the spur dike (x = 0.025 m, α = 90°).
The outline of the spur dike is denoted in dash lines, and the flow is oriented towards the viewer and perpendicular
to the paper’s plane.

Figure 4.6 displays the dimensionless time-averaged lateral velocity (v/U). Similar to the
u/U contour patterns, negative v/U values are observed near the channel bed behind the dike (x
= 0.025 m). Under open flow conditions, more flow moves laterally above the spur dike when
less submerged. However, under ice-covered flow conditions, confirming the impacts of
submergence on v/U at the dike's rear side was challenging due to ADV device limitations.
Conversely, with ice cover on the water surface, the submergence impact on v/U at the dike's
rear side becomes less detectable, regardless of ice cover roughness, as indicated by v/U
contours.
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Figure 4.6 Time-averaged lateral velocity contours at the rear side of the spur dike (x = 0.025 m, α = 90°). The
outline of the spur dike is denoted in dash lines, and the flow is oriented towards the viewer and perpendicular to
the paper's plane.

Figure 4.7 displays the distribution of the dimensionless time-averaged vertical velocity
(w/U). The most notable difference from the u/U and v/U distributions is the absence of vertical
downward flow near the bed. Under ice-covered conditions, with moderate submergence of a
spur dike, downward flow motion is observable near the dike tip, passing through the gap
between the dike tip and the ice cover. Negative vertical velocity also occurs under open flow
conditions but is less concentrated. The negative vertical velocity is believed to indicate the
presence of a horseshoe vortex, characterized by a U-shaped vortex attaching to the dike's rear
side, enveloping it, and directing vertical flow toward the bed (Koken & Constantinescu,
2008a). However, detailing the precise profile of the horseshoe vortex is challenging due to
limited ADV measurements.

123

Figure 4.7 Time-averaged vertical velocity contours at the rear side of the spur dike (x = 0.025 m, α = 90°). The
outline of the spur dike is denoted in dash lines, and the flow is oriented towards the viewer and perpendicular to
the paper's plane.

Figure 4.8 displays vector graphs from velocity data in the X-Z plane for various cover
conditions, located 10 cm in front of the dike tip (y = 60 cm, T = 25 cm, α = 90°). Due to the
down-looking ADV device’s limitations, the flow’s velocity field’s top 10 cm (z-direction)
cannot be monitored or featured in the vector diagrams (M. R. Namaee et al., 2019). Figure 8
shows that the downward flow extends further to the bed under ice-covered conditions. A rough
ice cover shifts the downward motion closer to the bed. However, despite the SonTek ADV’s
capability for high-frequency sampling, preliminary data processing showed excessive data
noise at frequencies above 50 Hz. The sampling volume diameter measured approximately 0.6
cm, positioned 10 cm below the probe transmitter. The ADV device’s limitation prevented a
more accurate capture of the recirculation zone and vortices. Furthermore, despite logistical
constraints, using a single ADV for velocity measurements notably limits accurately capturing
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temporal and spatial intricacies of recirculation zones and vortices in the flume.

Figure 4.8 Flow vectors in the X-Z plane at the dike tip (y = 60 cm, T = 25 cm, α = 90°). (a) Open channel, (b)
Smooth ice cover, (c) Rough ice cover. The spur dike outline is shaded in light grey, and the flow direction is
from left to right.

The following analysis focuses on the streamwise velocity component, which has the
highest magnitude among the three velocity components. Under ice-covered conditions, the

125

maximum flow velocity occurs between the ice cover and channel bed, influenced by their
roughness coefficients, regardless of dike orientation angle and submergence levels. Increasing
the ice cover's roughness coefficient relocates the maximum velocity closer to the bed. For
example, with a spur dike at a 90° alignment angle and minor submergence, umax occurs at flow
depths of z/h = 0.31 under smooth cover and 0.27 under rough cover. Additionally, water
surface cover conditions affect the location and magnitude of umax (Figure 4.3). A smooth ice
cover can increase maximum streamwise velocity by up to 20%, while a rough ice cover can
lead to a 24% increase compared to open channel flow at the same flow depth.
These findings align with experimental studies and analytical simulations (Namaee and
Sui, 2020). The study's results indicate that ice cover's influence on velocity distributions
increases with increasing dike alignment angles. Moreover, the impact of dike alignment angles
becomes more pronounced with increasing ice cover roughness. Negative flow velocity values
indicate flow separation, generating a recirculating region. An impermeable spur dike changes
the approaching streamwise flow direction, causing the boundary layer to break away from the
frontal surface of the dike.
According to the law of the wall (also known as the logarithmic law), turbulent flow's
average velocity at a given depth is proportional to the logarithm of the distance from that point
to the boundary. The log-law (Equation 4.10) serves as a general expression for velocity
distribution across depth in alluvial channels:
‫ݑ‬௔௩௚. (‫= )ݐ‬

‫∗ݑ‬
‫ ݖ‬+ ܹ݇௘
൰+‫ܥ‬
ln ൬
ߢ
݇௘

(4.10)

where uavg (t) is the time-averaged streamwise velocity, u* is the shear velocity, κ is the von
Karman constant, W is a coefficient of adjustment of the origin below the top roughness
126

elements, C is an empirical constant, and ke is the equivalent sand grain roughness (or
Nikuradse roughness), approximated by d50. W is estimated through trial and error, aiming to
maximize the coefficient of determination (R2) between u and ln[(z+Wke)/ke]. When W equals
0, experiments indicate that κ is approximately 0.41 and C approximately 5.20 for a smooth
wall (Afzalimehr & Rennie, 2009). This study analyzed experimental data under open channel
flow conditions to determine the best-fit values for W and C using κ = 0.41. Figure 4.9 displays
a sample logarithmic law fitting for measured velocity data under open channel flow conditions.
The origin adjustment coefficient W is estimated to be 0. Table 4.2 lists the constants in the
sample curve-fitting process.
Table 4.2 Examples of curve-fitting constants in the logarithmic law equation for L = 50 cm spur dike.
Submergence level Alignment angleα (°) u*/κ
C
Root mean square R2
Minor

90

4.64

4.99

0.89

Minor

120

4.20

4.66

0.95

Minor

135

4.29

4.98

0.88

Figure 4.9 Fitting logarithmic law distribution on measured data under the open channel flow condition.

Kuhnle et al. (2008) applied the logarithmic law to simulate mean velocity near the
boundary, setting ke to 0 on the submerged dike surface and 1.0 mm on the sand channel bed.
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For minor submergence (T = 25 cm, h ≈ T), the logarithmic equation was modified using
empirical coefficients and adjusted ke for moderate submergence to simulate the streamwise
velocity profile under open channel flow conditions.
Under ice-covered flow conditions, the vertical streamwise velocity profile is divided
into the lower layer mainly affected by channel bed and upper layer mainly affected by ice
cover. The logarithmic law approach applies separately to each layer under ice-covered
conditions (Zhang, et al., 2021), as expressed in the following equation:
‫∗ݑ‬௕
‫ݖ‬
⎧ ‫ݑ‬௕ = ߢ ln ൬30 ݇ ൰
௘௕

⎨‫∗ݑ = ݑ‬௜ ln ൬30 ℎ − ‫ݖ‬൰
⎩ ௜
ߢ
݇௘௜

(4.11)

where subscripts b and i represent the corresponding variables in the lower bed layer and upper
ice cover layer, respectively, with z denoting the distance to the channel bed. The bed layer
shear velocity (‫∗ݑ‬௕ ) is determined through regression analysis of the data before the decrease
in streamwise velocity (u). Given that the two-layer theory posits that both layers share the
same maximum velocity, Equation 4.11 is iteratively solved using the Microsoft Math Solver.
Figure 4.10 shows the estimated velocity profiles under open channel (using Equation
4.9) and ice-covered flow conditions (using Equation 10) for minor submergence cases of spur
dikes. Dots with different shapes represent the measured data. Figure 4.10 demonstrates that
laboratory measurements’ velocity profile trends apply across the flow depth. Additionally,
Figure 10 confirms that an ice cover shifts the maximum velocity location to a certain depth
beneath it, with the maximum velocity closer to the channel bed under rough ice conditions
than under smooth ice conditions (Namaee & Sui, 2019). Note that the flow velocities and
depths in Figure 4.10 are not normalized, reflecting the parabolic relationship between
128

instantaneous flow velocity and distance to the channel bed, as shown by the equations.

Figure 4.10 Comparison of the measured (Obs.) and equation-estimated (Est.) velocities.

4.3.2 Variation of Reynolds Shear Stress at Different Measurement Positions
Reynolds stress (τij) accounts for turbulent variations in fluid momentum. It leads to
vertical mixing and longitudinal and vertical momentum exchange (Feddersen & Williams,
2007). Theoretically, Reynolds stress distribution is linear along the flow depth and follows an
exponential function for turbulence intensity. Shan et al. (2016) proposed a method for
estimating bed shear stress in smooth and vegetated compound channels. For a single channel
like the experimental flume, the direct covariance method (COV) (Equation 4.12) provides an
unbiased estimation of channel bed stress, considered optimal by Kim et al. (2000):
ᇱ‫ ݓ‬ᇱ
തതതതതത
߬௜௝ = −ߩ‫ݑ‬

(4.12)

where ρ represents the fluid’s mass density, u′ and w′ are instantaneous longitudinal and vertical
velocity variations. Given the water temperature around 8°C (± 2°C), mass density is

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approximated at 1 g/cm3. The COV method calculates Reynolds shear stress (RSS) using
fluctuating velocity components measured by ADV, efficiently applied amidst sediment
movement (Shahmohammadi et al., 2021). The RSS component is normalized by dividing it
by the square of the time-averaged shear velocity.
ᇱ ‫ ݓ‬ᇱ /‫ ݑ‬ଶ ) aids in comparing flows with
തതതതതത
Normalizing RSS to critical shear stress (−‫ݑ‬
∗

varying Reynolds numbers and eliminates density variation effects from water temperature
changes. Results for the 90° dike alignment case were selected to analyze RSS variation, as
velocity profiles with this alignment show the most significant magnitude and variation.
Figures 4.11 and 4.12 display the vertical profiles of the RSS at measuring points 10 cm
upstream the dike tip CS (C-10), 10 cm downstream the dike tip CS (C10), and the dike tip CS
(C0) in the X-Z plane for the 90° alignment dike under minor and moderate submergences,
respectively.

ᇱ ‫ ݓ‬ᇱ /‫ ݑ‬ଶ ) for the minor submergence case of the spur dike.
തതതതതത
Figure 4.11 Vertical RSS profiles in the X-Z plane (−‫ݑ‬
∗

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ᇱ ‫ ݓ‬ᇱ /‫ ݑ‬ଶ ) for moderate submergence case of the spur dike.
തതതതതത
Figure 4.12 Vertical RSS profiles in the X-Z plane (−‫ݑ‬
∗

As observed from Figures 4.11 and 4.12, downstream of the spur dike (C10), the RSS
exhibits significant variation compared to those at two other positions due to the recirculation
wake zone behind the spur dike, which is generated from flow separation, causing the water to
flow in the opposite direction of the main flow in this zone. RSS values decrease steadily in
the streamwise flow direction. However, owing to the impacts of a broader separation zone
above the dike tip, the monotonic decrease in RSS for moderate submergence spur dikes is
more pronounced than for minor submergence cases. A negative RSS value was observed at
the dike tip CS (C0), where local scour occurs. These negative RSS values near the channel
bed suggest an upward vertical momentum transfer is occurring, attributed to a negative
streamwise velocity gradient (du/dz <0) (Jafari & Sui, 2021). RSS is more pronounced under
ice-covered flow conditions than in open-channel flows. On average, at the same measuring
depth for the minor dike submergence case, the absolute RSS values under smooth and rough
ice-covered flow conditions are 5% and 12% higher than in open channel flow conditions. For
the moderate dike submergence case, the RSS values under smooth and rough ice cover
conditions are 7% and 15% higher than those in open channel conditions.
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In both minor and moderate dike submergence cases, RSS increases in the near-bed zone
(z/H = 0.2–0.3), followed by an immediate drop. RSS shows a more drastic decrease above the
near-bed zone for the moderate submergence case than in the minor submergence scenario. As
the submergence ratio increases, more significant variability in RSS values around a
moderately submerged dike is directly influenced by the increased breadth of the separation
zone above the dike tip. Given the occurrence of local scour around the spur dike tip, the
vertical distribution of Reynolds shear stress at C0 has been selected for further analysis.
Shahmohammadi et al. (2022) corroborated findings from reported studies,
demonstrating that the vertical distribution of Reynolds stress in shallow transitional flows
exhibits three distinct zones: the increasing, damping, and decreasing zones. Figure 4.13
illustrates these three zones by extending the linear regression line in the decreasing zone to a
0 value at the water surface. Upon applying the linear regression extension to the measured
data, irregular shapes are revealed for the moderate submergence case of a spur dike. This
anomaly is hypothesized to arise from the inadequacy of Acoustic Doppler Velocimetry (ADV)
measurements in capturing the separation zone near the spur dike. Consequently, an in-depth
RSS analysis is undertaken explicitly for the minor submergence case, wherein the spur dike
height closely approaches the flow depth. It is observed that with increasing cover roughness,
both the RSS-increasing zone and RSS-decreasing zone expand.
Correspondingly, with increased cover roughness, the RSS-damping zone diminishes by
37.50% and 81.25% for smooth and rough ice-covered flows, respectively, compared to open
channel conditions. In the case of the minor dike submergence, the maximum normalized RSS
value occurs at depths of z/H = 0.1, 0.2, and 0.2 for the open channel, smooth, and rough ice132

covered flow conditions, respectively. Table 4.3 summarizes the normalized depths for three
zones—RSS-increasing, RSS-damping, and RSS-decreasing zones—at the dike tip under
various water surface cover conditions in the case of minor dike submergence.

Figure 4.13 Reynolds shear stress distribution in the RSS-increasing, RSS-damping, and RSS-decreasing zones
Table 4.3 Comparison of the RSS-increasing, RSS-damping, and RSS-decreasing zones under open, smooth, and
rough ice-covered flow conditions.
Water surface cover conditions
Variable

a

Open

Smooth

Rough

z1/H

0.11

0.19

0.23

z2/H

0.27

0.26

0.26

% change of |z2/H - z1/H|

N/A

-37.50

-81.25

z1 and z2 represent the lower and upper boundaries of the damping zone. The percentage change refers to results

compared to that under open-channel flow, and negative values indicate decreasing trends. N/A refers to not
applicable.

Spatial variations in Reynolds stress components may be influenced by factors beyond
mean velocity gradients, including the rotation of the coordinate axes and diffusion. This spatial
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inhomogeneity in velocity and Reynolds stresses results in wake production, characterized as
the excess kinetic energy generated from the work of mean flow against the form drag. Wake
phenomena can erode riverbeds and induce local scour, maintaining sediment in suspension
and transporting bed materials downstream via eddies protected by the hydraulic structure
(Keshavarzi et al., 2018). Analyzing Reynolds shear stress is crucial for comprehending the
near-wall region of a boundary layer, where the presence of a solid surface influences fluid
dynamics.

4.3.3 Analysis of Dominant Turbulent Events
The spatial variability of flow fields, encompassing both lateral and vertical dimensions,
contributes to the turbulent structure in a channel (Yang et al., 2023). Quadrant analysis
represents a fundamental yet effective method for processing turbulence data, particularly
useful in studying turbulent shear flows to account for the spatial variability of flow fields. The
determination of the threshold hole size (Ht) value is somewhat arbitrary, accompanied by
significant uncertainties and contradictions regarding the recommendation of an Ht value in the
literature (Wan Mohtar et al., 2020).
Analysis of velocity and Reynolds shear stress results indicates that the 90° dike
alignment produces the most significant values and variations in the velocity field. At the same
time, the ADV sampling volumes are less affected by the dike top flow separation. In this study,
different Ht values are investigated, including Ht = 0, 0.1, 0.2, and 0.3, utilizing data from the
experimental setup featuring a dike alignment angle (α) of 90°, a dike design length (Ld) of 50
cm, and a dike height approximating flow depth. Figure 4.14 illustrates the percentage of

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dominant turbulent events at the dike tip across the flow depth, as measured by the ADV under
open channel, smooth, and rough ice-covered flow conditions.

Figure 4.14 Percentage of the dominating turbulent events at the dike tip across the measured flow depth with
different hole size values (Ht) (α = 90°, L = 50 cm, T = 25 cm).

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The case of Ht = 0 is further examined in this section, as it does not eliminate any
Reynolds stress values in the four quadrants. With a hole size of zero (Ht = 0), all recorded
events are subject to burst analysis. Results indicate that with Ht = 0, the sweep event (Q4)
dominates under all water surface conditions. As the hole size increases, the percentage of
ejection events (Q2) grows, becoming the predominant occurrence at Ht = 0.3 for both open
channel and covered flows. The predominant sweep and ejection events are vital in facilitating
transverse momentum exchange.
Under ice-covered flow conditions, while the sweep event remains dominant, the
percentages for ejection events closely follow those of the sweep event. Moreover, the
substantial contributions of sweep and ejection events lead to increased momentum flux and
more severe shear under ice-covered conditions than open channel flows. As ice cover
roughness increases, the distribution percentages of inward (Q1) and outward (Q3) interactions
become more similar, and the likelihood of these events disappearing (0%) decreases,
indicating increasingly complex turbulence with greater ice cover roughness.
Figure 4.15 illustrates the absolute values of the contributions of each quadrant (|Si|,
according to Equation 8) across various dike alignment angles under both open channel and
ice-covered flow conditions, specifically for the case where Ht = 0, at multiple distances from
the channel bed. Regardless of flow depth, ejection (Q2) and sweep (Q4) events significantly
contribute to the Reynolds stress under smooth and rough ice-covered flow conditions alike.
In contrast, sweep events (Q4) emerge as the sole dominant contributor under open channel
flow conditions. An increase in dike alignment angle beyond 90° leads to a decrease in the dike
blockage ratio (the ratio of the dike’s frontal area to the flow cross-sectional area), diminishing

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the absolute contributions values (|Si|) from both ejection and sweep events. Furthermore, as
the dike alignment angle increases, the disparity between dominant (|S2| and |S4|) and marginal
contributions (|S1| and |S3|) gradually narrows.

Figure 4.15 Variation of the absolute contributions values |Si| along the measured results around spur dikes for
the case of Ht = 0.

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Spur dikes with an alignment angle of 90° (deflecting dike) have been widely adopted in
both submerged and non-submerged configurations (Zhang et al., 2018). Therefore, burst
events around the 90° alignment dike are further analyzed. Drawing on laboratory experiments,
the results of burst events at three cross-sectional positions at the lowest measuring depth (z/H
= 0.04) are depicted in Figure 4.16, illustrating scoured bed turbulence. Irrespective of water
surface conditions, burst events concentrate in the second and fourth quadrants upstream of the
dike, dispersing evenly across all four downstream quadrants. The predominance of the second
and fourth quadrants indicates that sweep and ejection events play a pivotal role in mobilizing
sediment particles within the scour hole. In the presence of ice cover, the disparity in
contribution percentages between sweep and ejection events diminishes. Furthermore, it is
observed that an increase in ice cover roughness correlates with higher contribution
percentages for inward and outward interactions, suggesting a decrease in the significance of
ejection and sweep events as roughness increases. It is important to note that near the dike tip,
noise becomes more pronounced, leading to reduced data that is considered valid by the
WinADV software.

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Figure 4.16 Probability distributions of u’/u* and w’/u* at z/H = 0.04 when Ht = 0 (α = 90°, L = 50cm, T = H).

4.4 Limitations and Recommendations
The constrained spatial coverage beyond designated measuring points around the spur
dike limits this study. Data collection, confined to specific locations, may overlook the broader
dynamics of flow influenced by the spur dike's alignment angle and submergence. Furthermore,
the study relies solely on an Acoustic Doppler Velocimeter (ADV) for point velocity
measurements. Although an ADV yields valuable velocity data, its application at discrete points
may not capture the full complexity and variability of turbulent flow structures across a wider
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area. Thus, the measurement technique used in this study may overlook subtle variations and
intricacies in flow patterns. Due to logistical constraints, using a single ADV for velocity
assessments introduces significant limitations in capturing the temporal and spatial
characteristics of recirculation zones and vortices within a fluid system. The inherent
complexity of fluid dynamics necessitates a comprehensive assessment that accounts for the
dynamic nature of flow phenomena. Reliance on a single ADV device overlooks nuanced
variations from the spur dike’s obstruction. Consequently, using only one ADV device led to
an incomplete flow field characterization, limiting the precision and comprehensiveness of the
obtained velocity measurements.
Future research should prioritize expanding spatial coverage of data collection beyond the
existing measuring points. Employing a broader array of measurement devices or deploying
multiple ADVs simultaneously could contribute to a more comprehensive understanding of the
turbulent flow structures around spur dikes of varying alignment angles. Combining data
measured by ADV devices with other techniques, such as imaging technologies or numerical
simulations, is recommended to provide a more holistic view of flow dynamics. Integrating
multiple approaches would enhance the findings' accuracy and reliability, facilitating a more
detailed analysis of turbulent flow structures in the presence of submerged spur dikes and ice
cover on the water surface.

4.5 Chapter Summary
Chapter four describes the study conducted within a large-scale flume environment,
investigates the turbulence dynamics surrounding submerged spur dikes under various ice140

cover conditions, and analyzes three-dimensional velocity components, Reynolds shear stress,
and turbulent burst events. It delineates the intricate interactions between dike geometry, flow
conditions, and ice cover, offering insights into hydrodynamic behavior influenced by
submerged spur dikes. Key findings include:
1) Despite the experimental flume used in this study having an aspect ratio greater than 5.0,
hydrodynamic instabilities in the flow fields, attributed to the additional boundary layer
from the spur dike, have been observed through the examination of the three time-averaged
velocity components (u/U, v/U, w/U) at the dike-tip cross-section (CS) in the Y-Z plane.
Velocity contours derived from the measured data suggest that as the submergence level
of a spur dike increases, the water flow over the dike mitigates the impact of the
recirculation region by diminishing the amplitude of reverse flow. Measured data reveal
that near the dike front, the distributions of streamwise (u/U) and lateral (v/U) velocities
indicate transverse flow regions (negative values) near the channel bed. In contrast, the
negative vertical (w/U) flow region is not discernible at the channel bed but is higher in
the flow region.
2) Irrespective of dike alignment angles in minor submergence cases and with consistent
approaching flow depth, ice cover on the water surface leads to an average increase in
maximum streamwise velocity by 12% for smooth and 20% for rough ice-covered
conditions. Increasing the dike alignment angle from 90° to 135°, thereby reducing the
blockage ratio of the cross-sectional area, decreases flow velocity (u/uavg) irrespective of
water surface cover conditions. With the increase in the spur dike alignment angle, the
amplitudes of measured velocities (in the X-Y plane) at the front surface of the spur dike

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also increase. The measured streamwise velocity profile trends align with the original and
adjusted logarithmic laws for flows, applicable under open channel and ice-covered
conditions.
3) Downstream of submerged spur dikes, the Reynolds Shear Stress (RSS) varies
significantly due to the recirculation wake zone formed by flow separation behind the dike,
causing water to flow opposite to the main flow in this zone. Along the streamwise
direction, RSS values steadily decrease. However, with a moderately submerged dike, the
monotonic decreases in RSS values are more pronounced than in cases of minor
submergence due to a more extensive separation zone above the dike tip. RSS distribution
across flow depth is categorized into increasing, damping, and decreasing zones. A linear
regression line extends to a zero value at the water surface within the RSS-decreasing zone.
As ice cover roughness increases, both the RSS-increasing and RSS-decreasing zones
expand while the RSS-damping zone contracts.
4) Quadrant analysis results show that irrespective of flow depth, ejection and sweep events
significantly contribute to Reynolds shear stress in both smooth and rough ice-covered
conditions. In contrast, sweep events alone contribute to open channel flow. With an
increase in the dike alignment angle from 90° to 135°, a reduced contribution from ejection
and sweep events results from a decreased blockage ratio of the flow cross-section.
Furthermore, as the alignment angle exceeds 90°, the disparity between dominant
contributors (sweep and ejection events) and marginal contributors (inward and outward
interactions) gradually diminishes.
This study advances knowledge of turbulent flow characteristics around submerged spur
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dikes under ice-covered conditions. It elucidates the nuanced effects of dike geometry and ice
cover on flow dynamics, providing valuable insights for river engineering and management.
Further investigations should expand the spatial and methodological scope to encompass the
complex interrelations between environmental factors and hydraulic structures. Integrating
advanced measurement techniques and numerical simulations is recommended for a more
holistic understanding of flow dynamics in natural river systems.

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5.

CHAPTER FIVE: HYDRODYNAMIC CHARACTERISTICS IN POOLS
WITH LEAFLESS VEGETATION UNDER ICE COVER

5.1 Introduction
Natural riverbeds often feature uneven structures, forming pools and riffles. During lowflow periods, pools serve as reservoirs, sustaining baseflow in streams, while during floods,
they decelerate flow velocity and facilitate the sedimentation of debris transported by the water.
Recent research on pool structures in channel environments has significantly enhanced our
understanding of their formation, dynamics, and ecological significance. Pools, characterized
by deeper water zones within a channel, are critical for sediment transport, energy dissipation,
and providing habitat for aquatic organisms (Nosrati et al., 2024). Pools often contain diverse
living and dead vegetation, such as underwater grasses, shrubs, and tree trunks. Pools in a poolriffle sequence are known to have calmer waters compared to other sections, such as riffles or
slopes, making them more conducive to nutrient enrichment and the growth of aquatic
vegetation (Calderon & An, 2016; Rodríguez et al., 2013). The interaction between flow
dynamics and pool morphology has been thoroughly studied, with particular attention to the
effects of discharge, channel slope, and sediment size on pool stability and development
(Mofrad et al., 2023). Results of experimental and field studies have shown that pools are
shaped and sustained by complex hydraulic processes, including turbulence and secondary
currents, which contribute to their persistent yet dynamic nature (Shumilova & Sukhodolov,
2023). However, to the authors’ knowledge, no research has been conducted on the impact of
vegetation on the flow field within pools under ice-covered flow conditions. Understanding
these interactions is crucial for effective river management and restoration, especially given

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the increasing anthropogenic pressures and climate change impacts on fluvial systems.
Traditionally, underwater vegetation is recognized for its ability to slow water flow, reduce
soil erosion, stabilize riverbanks, and enhance water quality and aesthetics, making it a costeffective and efficient measure of ecological river management (Cui et al., 2023). However,
during flood events, the presence of vegetation in channels can significantly alter the original
flow structure. The interaction between vegetation and water can convert part of the flow's
energy into turbulent kinetic energy near the vegetation, reducing the river's flood-carrying
capacity (Rahimi et al., 2023). Understanding the disturbance characteristics of submerged
vegetation on flow dynamics and evaluating its advantages and challenges is crucial for
effective flood control, embankment engineering, and river ecological protection and
restoration. The impact of submerged vegetation on embankment stabilization, bank protection,
and flood control has increasingly become a focal point of research. Numerous researchers
have conducted experiments in vegetated channels to investigate flow parameters, including
turbulent kinetic energy (TKE) and shear stress under open channel flow conditions. For
instance, Barahimi and Sui (2023) found that a staggered arrangement of deflected and nonbending vegetation on the channel bed resulted in higher streamwise velocity, TKE, and
Reynolds shear stress (RSS) than a square configuration. To date, only limited research has
been conducted to investigate the flow characteristics in the presence of vegetation in channel
beds and ice cover on water surfaces. Based on extensive laboratory experiments conducted in
a large-scale flume, Sediqi et al. (2024) and Barahimi & Sui (2024a, 2024b) assessed the effects
of varying vegetation densities arranged in square and staggered patterns, incorporating the
influence of ice covers with differing roughness (smooth and rough). Key turbulence

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parameters, such as turbulence intensity, RSS, and TKE, were analyzed. The findings indicate
that flow velocity profiles over a vegetated channel bed transition from an S-shaped curve
under open flow conditions to a convex shape under ice-covered flow conditions. Their
experiments, conducted under open channel and ice-covered flow conditions using three types
of non-uniform sands as bed material, revealed that vegetation patches, combined with ice
cover, produced distinctive velocity profiles with two peak values.
With advancements in computing power and numerical algorithms, numerical simulation
techniques have been successfully applied to experimental flumes, lakes, rivers, bays, and
coastal environments. Numerous studies have utilized two-dimensional (2D) and threedimensional (3D) mathematical models to simulate flows in open channels with submerged
vegetation. For example, Zeng et al. (2022) employed a large eddy model to simulate 3D flow
characteristics in open channels influenced by vegetation, elucidating the interaction patterns
between rigid plants and water flow. Rahim et al. (2020) investigated the effects of a twolayered cylindrical vegetation system on water flow and proposed an analytical model that
aligns with field-measured data. Koken and Constantinescu (2021) utilized 3D eddy-resolving
numerical simulations to examine the interactions between emerged cylinders and water flow
in open channels, revealing significant upwelling and downwelling near the leading and side
edges of vegetation patches and within the shear layer. Toda et al. (2020) combined four submodels to study the dynamics of riparian vegetation and the interactions between river flow
and sediment transport, concluding that riparian vegetation plays a crucial role in enhancing
the stability and relative elevation of fluvial bars. Zhang et al. (2021) solved the width-averaged
Navier-Stokes equations with a first-order closure scheme for the Reynolds stress, successfully

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obtaining vertical velocity profiles in open-channel flows with submerged flexible canopies.
Rahim et al. (2023) applied ANSYS Fluent and the k–ϵ turbulence model to simulate and
analyze complex flow dynamics in considering different vegetation arrangements in channel
beds. The results of simulations indicated a reduction in turbulent kinetic energy in the gaps
between vegetation patches, which was attributed to the drag force exerted by vegetation.
Aydogdu (2023) examined the behavior of rigid vegetation using two distinct turbulence
models (Realizable k-ε and Reynolds Stress) within the CFD software ANSYS Fluent,
exploring the formation of vortices and complex turbulent flows from the channel bottom to
the water surface, influenced by the diameter and arrangement of rigid vegetation rods. Lama
et al. (2020) evaluated two resistance models, the Baptist and Stone & Shen (S&S) models, in
a reclamation channel with common reeds. Their study found that combining the S&S
resistance predictor model and the Horton composite cross-section method yielded the lowest
relative prediction error. Qiu et al. (2024) used large eddy simulation to investigate the impact
of emergent vegetation on flow dynamics in natural rivers, identifying two distinct stages of
flow alteration: the development of a stable wake region behind densely vegetated areas and a
more gradual velocity recovery in regions with sparse vegetation.
Recent research has further explored the complex hydrodynamics of compound channels
influenced by submerged vegetation on channel beds, emphasizing that vegetation density,
arrangement, and height significantly affect flow dynamics. However, the specific effects of
rigid, leafless submerged vegetation on flow conveyance in pools and how varying vegetation
heights influence hydrodynamics still need to be more adequately understood. Most existing
studies utilize simple drag force models to quantify vegetation resistance, with detailed

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simulations of hydrodynamic-vegetation interactions still limited. Therefore, further
investigation in this area is crucial.
Submerged vegetation helps maintain suitable temperatures for aquatic organisms, even
during winter when ice cover forms (Sebilian Wittyngham et al., 2019). However, studies on
the impact of ice cover on flow fields in vegetated channels have revealed significant changes
in flow dynamics and turbulence. Vegetation in channels, particularly under ice-covered flow
conditions, introduces complex interactions that alter velocity distribution and turbulence
characteristics. Research indicates that ice cover shifts the maximum flow velocity closer to
the riverbed, increasing turbulence and bed shear stress (Sui et al., 2010), especially around
vegetative patches and in-stream structures (Sui, 2023). Additionally, laboratory experiments
have demonstrated that the combination of ice cover and vegetation significantly influences
hydrodynamic behavior, leading to distinct velocity profiles and elevated turbulent kinetic
energy near the vegetation (Barahimi & Sui, 2024b). These results highlight the need for
detailed modeling - encompassing analytical, computational, and experimental approaches - of
vegetated channels under ice-covered conditions to enhance our understanding of their
hydraulic and ecological functions.
In this study, laboratory experiments have been conducted in a large-scale outdoor flume
considering different water surface cover conditions, submergence heights of vegetation, pool
features, and hydraulic conditions to investigate the effects of leafless vegetation on flow
velocity, TKE, and secondary flow variations. Then, the computational fluid dynamics software
Flow3D was utilized to perform numerical simulations of flow in channels with rigid
submerged vegetation in pools under various cover conditions. The model’s accuracy was

148

validated against flume experiment data. Flow field distribution patterns were analyzed for
different vegetation submergence heights, focusing on the distribution of side and bottom flow
velocities and turbulence kinetic energy along the vertical profile under varying inflow
conditions. An analytical model for the streamwise velocity vector has also been developed
based on experimental results. The objective is to simulate the turbulent behaviors of flow
passing through rigid, leafless vegetation in channels with pool - scenarios that are difficult to
capture through experimental flumes - thereby providing scientific support for flood control,
riverbank restoration, and ecological protection efforts.

5.2 Laboratory Experiments
A series of experiments were conducted in a large-scale outdoor flume measuring 38
meters in length, 2 meters in width, and 1.3 meters in depth, as shown in Figure 5.1. The flume
bed was designed with a gentle longitudinal slope of 0.2%. Within this setup, two sandboxes
were positioned 10.2 meters apart. The upstream sandbox measures 5.6 meters in length, 2
meters in width, and 0.3 meters in depth, while the downstream sandbox is slightly longer at
5.8 meters, maintaining the same width and depth. To ensure consistency in experimental
conditions, the water level in the upstream holding tank was kept constant, supporting a steady
flow rate of up to 120 L/s, controlled via a pump and two valves. The study examined a flow
depth of 20 cm from the flume's false floor (30 cm in the pool zone) to simulate shallow river
environments. In each sandbox, a pool is constructed. Each pool consists of three sections:
entrance, pool center (or deep pool), and exit section, as shown in Figures 5.1 and 5.2. In this
study, the pools were built with three different slopes for the pool’s entrance and exit sections.

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Three different slopes for entrance and exit sections of the pools were first trialed in nonvegetated channels under open channel conditions, namely, 5°, 7°, and 10°. The 5° and 7°
slopes for the entrance and exit sections revealed significant velocity variations in the transition
between the deep pool and slopes of the pools, as indicated by ADV measurements in the
unvegetated open channel. The limited pool area at these 5° and 7° slopes prevented fully
developed flow and constrained the planting of additional vegetation arrays. Consequently, a
10° slope for both entrance and exit sections was chosen for the flume experiments and
numerical model to address these limitations. The non-uniform gravel was used as the bed
material of both pool entrance and exit sections, with a median particle size of 10 cm. The
gravels used in this study are sourced from the Quesnel River. Non-uniform sand with a median
particle size (d50) of 0.90 mm was used along the deep pool section. Figure 5.2b shows the
Cartesian coordinate system with the origin (0, 0, 0) located at the center of the pool edge. The
pool entrance section features an increase in flow depth, forming a decelerating zone; the deep
pool, characterized by a flat channel bed, served as a transition zone; and the pool exit section,
with a decreasing flow depth, generated accelerating flow. One case study demonstrates that
the slopes of the pool entrance and exit sections for natural pools range from 4° to 7.80°
(Nosrati et al., 2022), suggesting that the slopes of entrance and exit sections used in this study
reasonably approximate actual conditions found in natural rivers. The relationship between the
channel width (W) and flow depth (H) is referred to as the aspect ratio (W/H). In this study,
with flow depths of 30 cm in the deep pool section and 20 cm in the false bed zones, this
channel, including the entire pool section, is considered a wide channel since the aspect ratios
in this study significantly exceed the typical range of 5 to 10. As a result, the influence of the

150

channel’s sidewalls and secondary currents on flow dynamics in the central zone of the channel
can be negligible. This assumption simplifies the analysis by allowing the focus to remain on
primary flow characteristics without interference from side effects (Jing et al., 2019).

Figure 5.1 (a) Front view and (b) plan view of the experimental flume.

(a)

(b)

Figure 5.2 (a). Picture of the non-vegetated pool; (b) Pool section and the cartesian coordinate system for the
experimental setup.

In natural environments, the distribution of aquatic plants is typically random, with
vegetation forming communities that are neither symmetrical nor uniformly distributed.
Engineered stream restoration projects, however, could benefit from adopting standard
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practices that mimic these natural patterns. Implementing a staggered arrangement of
vegetation in such projects can simplify numerical simulations while enhancing biodiversity,
improving habitat complexity, and providing better erosion control. Therefore, in addition to
single circular vegetation setups, paired or staggered vegetation groups should be considered
to achieve these benefits (Fu et al., 2021; Tinoco et al., 2020). In this study, plastic artificial
flower stems with diameters of 0.5 cm were used to simulate rigid vegetation, such as common
reeds (Phragmites australis). These synthetic vegetation stems were anchored to the sand bed
of the deep pool section and arranged in staggered configurations with a spacing distance of 20
cm between adjacent stems in the same row to cover the sand bed of the entire deep pool section.
This study measured the 3D velocity components using an Acoustic Doppler Velocimeter
(ADV). The ADV had a sampling volume of 0.25 mL and operated at a sampling rate of 25 Hz,
with each measurement at a specific point lasting two minutes, capturing 3,000 instantaneous
velocity data points. Measurements were taken at vertical intervals of 10 mm. The strength of
the received acoustic signal relative to the ambient electronic noise was assessed using the
signal-to-noise ratio (SNR) recorded in the ADV’s data log. Adequate SNR values - exceeding
5 dB for mean flow velocity and over 15 dB for turbulence measurements - were essential for
reliable data (Namaee & Sui, 2019a, 2019b). The data filtering approach that Goring and
Nikora (2002) recommended was employed, and WinADV software was used to process the
data. This setup included generating a statistical correlation as a real-time output to verify the
accuracy of the velocity measurements and discarding any data where the average correlation
fell below 70%. After removing spikes using WinADV software, the velocity fluctuations in
the x, y, and z directions were calculated and are represented as u’, v’, and w’, respectively

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(Namaee & Sui, 2019a, 2019b).
‫ݑ‬ᇱ = ‫ݑ‬௜ − ‫ݑ‬ത,

‫ ݒ‬ᇱ = ‫ݒ‬௜ − ‫ ̅ݒ‬,

‫ ݓ‬ᇱ = ‫ݓ‬௜ − ‫ݓ‬
ഥ

(5.1)

in which, ‫ݑ‬ത , ‫ ̅ݒ‬, and ‫ݓ‬
ഥ are the mean velocities in the x, y, and z directions. Instantaneous
velocities corresponding to these directions are denoted as ui, vi, and wi. To achieve precise data
collection of flow characteristics, this study also employed a SonTek-IQ Plus, which measures
mean velocity and water depth, leveraging its advanced post-processing capabilities.
Figure 5.3 shows the details of the placement of vegetation and measurement positions.
The location of the ADV, positioned between adjacent vegetation stems, was carefully selected
to avoid noise interference from the stems and adequately represent the entire wake zone.
Circles indicate the locations of individual vegetation elements, while squares represent the
points where ADV measurements were taken. Measurements were conducted at various crosssections along the entire pool, including entrance and exit sections. The flow becomes fully
developed as the velocity profiles remain consistent after traveling a certain distance from the
upstream edge of each sandbox. Upon reaching the vegetation patch in the deep pool section,
the flow transitions to a mixing layer condition, leading to the formation of a shear layer and
the development of Kelvin-Helmholtz (KH) vortices (Wang et al., 2023). When equilibrium is
achieved, characterized by the stabilization of streamwise velocity within the vegetation zone,
the flow inside the submerged vegetation patch becomes fully developed again (Barahimi &
Sui, 2024a).

153

Figure 5.3 Top view of a vegetation zone and ADV measurement positions within the pool area.

Styrofoam panels were used to simulate ice cover on the water surface. These panels
floated on the water surface, with two types of model ice covers employed: smooth and rough
ice cover. The model smooth ice cover was created using untreated Styrofoam panels, while
the model rough cover was formed by attaching small Styrofoam cubes to the underside of the
smooth panels. Each Styrofoam cube measured 25 mm on each side, with a spacing distance
of 35 mm between adjacent cubes (Figure 5.4). The roughness of the channel bed and ice covers
significantly influences the flow structure (Beltaos, 2008; Li et al., 2023; Sui et al., 2010). The
Manning roughness coefficient for the channel bed (nb) was calculated using Equation (5.2)
(Julien, 2018) and determined as 0.020 for the sand bed of d50 = 0.90 mm in the deep pool
section.
(5.2)

ଵ/଺

݊௕ = 0.064݀ହ଴

Manning’s coefficient for the model smooth ice cover (ni) is estimated to be 0.010, as reported
by Hains and Zabilansky (2005). For the model rough ice cover, Manning's roughness
coefficient is determined to be 0.021 using Equation (5.3), as proposed by Li (2012).

154

(5.3)

ଵ/଺

݊௜ = 0.039݇௦

where ks is the average roughness height (m) and is calculated from
(5.4)

݇௦ = 30‫ݕ‬௜ exp[−(1 − ‫ݒ‬௜ /‫ݒ‬௠ )]

in which yi is the ice-affected thickness irregular layer, taken as the Styrofoam cube edge length
(0.025 m), vi is the depth-averaged velocity of the ice-affected layer, and vm is the maximum
velocity.

Figure 5.4 Styrofoam cubes are attached to the Styrofoam panel to simulate the rough ice cover.

5.3 Numerical Model
FLOW-3D® HYDRO, a widely used computational fluid dynamics (CFD) model, was
employed to simulate the velocity profiles. This model utilizes the volume of fluid (VOF)
method to track the water’s free surface accurately and employs the Fractional Area/Volume
Obstacle Representation (FAVOR) method, developed by Hirt and Nichols (1981), to
effectively manage complex geometries (Flow Science Inc., 2023). Recent studies have
demonstrated the robustness of FLOW-3D in modeling hydrodynamic behaviors across various
engineering applications, confirming its reliability in simulating intricate flow patterns around
structural obstacles (e.g., Namaee et al., 2021, 2023).

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5.3.1 Governing Equations
The governing equations for an incompressible Newtonian fluid, incorporating the
Reynolds-averaged Navier-Stokes (RANS) equations and continuity equation, are presented in
Equations 5.5 to 5.8, including the Fractional Area/Volume Obstacle Representation (FAVOR)
variables (Hirt & Nichols, 1981).
߲
(‫ = ) ܣ ݑ‬0
߲‫ݔ‬௜ ௜ ௜

(5.5)

߲‫ ݑ‬1
߲‫ݑ‬௜
1 ߲ܲ
+ ቆ‫ݑ‬௝ ‫ܣ‬௝
ቇ=−
+ ݃௜ + ݂௜
߲‫ܸ ݐ‬ி
߲‫ݔ‬௝
ߩ ߲‫ݔ‬௜

(5.6)

and
ߩܸி ݂௜ = ߬௕,௜ − ቈ

(5.7)

߲
൫‫ ܵ ܣ‬൯቉
߲‫ݔ‬௝ ௝ ௜௝

where
(5.8)

߲‫ݑ‬௜ ߲‫ݑ‬௝
ܵ௜௝ = −(ߤ + ߤ் ) ቆ
+
ቇ
߲‫ݔ‬௝ ߲‫ݔ‬௜

Here, ui represents the velocity component in the i-th direction, VF is the volume fraction
of fluid in each grid cell, and Ai denotes the fractional area open to flow in the i-th direction. P
is the pressure, ρ is the fluid’s mass density, and t is time. The term gi corresponds to the
gravitational force in the i-th direction, fi is the diffusion transport term, and Sij is the strain rate
tensor. The wall shear stress is indicated by τb,i, and the total dynamic viscosity accounts for
both molecular viscosity (μ) and eddy viscosity (μT ).
FLOW-3D offers several turbulence models, including the standard k-ε, RNG k-ε, k-ω
models, and large eddy simulation (LES). When turbulent flow encounters obstacles like
vegetation stems, it generates a complex system known as the turbulent horseshoe vortex (THV)

156

due to the adverse pressure gradient. Large-eddy simulation models, particularly the detachededdy simulation (DES) approach, effectively resolve most turbulence scales generated by
obstacles while maintaining relatively low computational demands (Kang et al., 2019). Gazi
and Afzal (2020) reviewed the formation mechanisms of vortices, highlighting the separation
of both laminar and turbulent boundary layers, and noted the successful application of DES in
simulating the intricate dynamics of THV. The Re-Normalization Group (RNG) k-ε turbulence
model, which modifies the Navier-Stokes equations to account for smaller-scale motions, is
favored for vegetated channels due to its cost-effectiveness, accuracy, and efficiency in
capturing turbulence structures (Dehrashid et al., 2023). The RNG k-ε model includes
enhancements over the standard k-ε model, improving its efficiency. Therefore, in this study,
the RNG k-ε turbulence model is employed to simulate the flow field in the pool zone with
vegetation under ice-covered flow conditions, using this model to close the equations of motion.
The transport equations for k and ε can be expressed in various forms. One straightforward
interpretation, which neglects the buoyancy effects, is as follows (Yakhot et al., 1992):
߲
߲
߲
ߤ௧ ߲݇
(ߩ݇) +
(ߩ݇‫ݑ‬௜ ) =
ቈ൬ߤ + ൰
቉ + ܲ௞ − ߩߝ
߲‫ݐ‬
߲‫ݔ‬௜
߲‫ݔ‬௝
ߪ௞ ߲‫ݔ‬௝
߲
߲
߲
ߤ௧ ߲݇
ߝ
ߝଶ
∗
(ߩߝ) +
(ߩߝ‫ݑ‬௜ ) =
ቈ൬ߤ + ൰
቉ + ‫ܥ‬ଵఌ ܲ௞ − ‫ܥ‬ଶఌ
ߩ
߲‫ݐ‬
߲‫ݔ‬௜
߲‫ݔ‬௝
ߪఌ ߲‫ݔ‬௝
݇
݇

(5.9)
(5.10)

where
∗
‫ܥ‬ଶఌ
= ‫ܥ‬ଶఌ +

‫ܥ‬ఓ ߟ ଷ (1 − ߟ/ߟ଴ )
1 + ߚߟ ଷ

(5.11)
(5.12)

ߟ = ܵ݇/ߝ

(5.13)

ଵ/ଶ

ܵ = ൫2ܵ௜௝ ܵ௜௝ ൯

The turbulent viscosity is calculated using the same method as the standard k-ε model.
157

Notably, the RNG procedure explicitly derives the values of all constants except for β. The
commonly used values are Cμ = 0.0845, Cε1 = 1.42, Cε2 = 1.68, σk = σε = 0.7194, η0 = 4.38, and
β = 0.012 (Yakhot et al., 1992).
FLOW-3D utilizes the VOF method to solve the governing equations on an orthogonal
mesh grid, which allows for accurate capture of the interface between different fluid phases.
The solver iteratively computes the flow field by updating the velocity and pressure fields until
convergence is achieved, involving the solution of continuity, momentum, and turbulence
transport equations (Lee & Wahab, 2019). The simulation results are validated against
experimental data to ensure accuracy, with model parameters adjusted as necessary to achieve
better alignment with observed data.

5.3.2 Model Setup in Flow 3D
Twenty-seven numerical models with and without the presence of vegetation in the section
of pool bed with non-uniform bed material of d50 = 0.90 mm have been developed to generate
distinct datasets and compare them to the results of flume experiments. In the computational
domain, no-slip wall conditions were applied to the sidewalls, rigid vegetation (represented by
cylinders with diameters of 0.5 cm), ice cover bottom surfaces, and mesh boundaries. The
cylinders simulate rigid vegetation such as common reed (Phragmites australis) found in
natural rivers (Nosrati et al., 2024). The top boundary was modeled using a “symmetry”
condition, while a “no-slip wall” condition was applied to the bottom boundary. The upstream
inlet of the pool was set with a “specified velocity” condition, and the downstream outlet of
the pool was designated as “outflow.” The inlet velocity (v0), controlling the flow rate into the

158

channel, was determined using the average flow velocity. The symmetry condition was chosen
for the top boundary to save computational time, a method validated by Smith and Foster
(2005), who observed no significant differences between the usage of symmetry and a freesurface boundary. A smooth ice cover was simulated at the same flow depth in the numerical
model as the physical model for smooth ice-covered flow conditions. Rough ice cover was
simulated by adjusting the roughness height of the ice cover to match Manning’s ni value used
in the flume experiments. The flow moved from upstream to downstream across the pool
section, passing over the vegetated pool section and causing changes in flow fields until
reaching the outflow boundary.
In numerical modeling, addressing uncertainties related to the mesh resolution and
computational domain size is crucial. Sensitivity analyses have been conducted for domain size
and mesh resolution to mitigate these uncertainties. Initially, two computational domain sizes
were compared under constant conditions: the first domain was set to 5.8 meters, corresponding
to the length used in the experimental studies, with a uniform mesh grid of 20 mm × 20 mm. It
was observed that reducing the domain length to 5.0 meters did not alter flow characteristics
near the vegetated zone in the pool, indicating that this reduction had no significant effect on
the flow field. This adjustment was primarily aimed at optimizing simulation time without
compromising the accuracy of the simulation results.
Mesh refinement is crucial for achieving high-precision computational results, given the
complex vegetation arrangements and significant flow variations within these areas. Two
different mesh grids have been tested to optimize the mesh resolution. The computational
domain was divided into two mesh blocks. Initially, all blocks utilized a uniform mesh size of

159

20 mm × 20 mm. After optimization, the central mesh block encompassing the vegetated pool
area retained a finer grid of 20 mm × 20 mm. In comparison, the pool entry and exit sections
were adjusted to a coarser grid of 30 mm × 30 mm to improve the computational efficiency.
Comparisons of the model outputs indicate that these mesh size adjustments do not
significantly impact the velocity profiles, confirming the model’s robustness. This approach
ensures efficient use of the computational resources while maintaining simulation accuracy.
Figure 5.5 illustrates the simulation model of the vegetated pool area and the boundary
conditions employed in the numerical models. Simulation time was optimized based on the
program tips to enhance computing efficiency, as seen in Appendix III.

Figure 5.5 The vegetated pool's simulation model and boundary conditions under ice-covered flow conditions.

5.4 Results and Discussions
This section examines the experimental results under varying flow and cover conditions,
focusing on the flow field in the vegetated pool. The validity of the simulation model is
assessed by comparing the simulation results to the results of measured velocity in pools
without vegetation and with vegetation in the pool bed under open channel flow scenarios.
Additionally, the velocity vectors and streamlines in the vegetated pools are analyzed to gain
insights into the flow dynamics. Table 1 summarizes the conditions for 27 experimental runs
160

and the data used for the numerical simulations. In this table, Q denotes the approaching
discharge, dL refers to the line spacing (distance between two rows), dR indicates the distance
between two adjacent vegetation elements in the same row, and h represents the vegetation
height.
Table 5.1 Parameters in the Pool Section and Model Setups
Water surface cover
Run #
Q (L/s)
conditions
1
Open
50
2
Smooth
50
3
Rough
50
4
Open
50
5
Open
50
6
Smooth
50
7
Smooth
50
8
Rough
50
9
Rough
50
10
Open
100
11
Smooth
100
12
Rough
100
13
Open
100
14
Open
100
15
Smooth
100
16
Smooth
100
17
Rough
100
18
Rough
100
19
Open
120
20
Smooth
120
21
Rough
120
22
Open
120
23
Open
120
24
Smooth
120
25
Smooth
120
26
Rough
120
27
Rough
120

dL (m)

0.3
0.3
0.3
0.3
0.3
0.3

0.3
0.3
0.3
0.3
0.3
0.3

0.3
0.3
0.3
0.3
0.3
0.3

Planting patterns
dR (m)
Non-vegetated
Non-vegetated
Non-vegetated
0.2
0.2
0.2
0.2
0.2
0.2
Non-vegetated
Non-vegetated
Non-vegetated
0.2
0.2
0.2
0.2
0.2
0.2
Non-vegetated
Non-vegetated
Non-vegetated
0.2
0.2
0.2
0.2
0.2
0.2

h (m)

0.15
0.10
0.15
0.10
0.15
0.10

0.15
0.10
0.15
0.10
0.15
0.10

0.15
0.10
0.15
0.10
0.15
0.10

5.4.1 Validation of Numerical Model
The flow fields in the pool section with three different slopes (5°, 7°, and 10°) were
simulated using Flow-3D for a non-vegetated channel under open flow conditions. Based on
the ADV measurements, the experimental data validated the numerical model, confirming that
pools with entrance and exit slopes of 5° and 7° are not ideal for achieving fully developed
flow within the deep pool section, given the length of the deep pool required for the vegetation
161

arrangement used in the experiment (Figure 5.6). Therefore, the slope of 10° for both entrance
and exit sections of the pool was selected for further analysis.

(a)

(b)

(c)
Figure 5.6 Simulated streamwise velocity profiles using Flow-3D for non-vegetated flume under open channel
conditions for pools with entrance and exit slopes of (a) 5°, (b) 7°, and (c) 10°. Simulation results for the pool
with an entrance and exit slope of 10° show optimal conditions for fully developed flow, consistent with ADV
measurements.

The simulation was conducted for Scenario 1 (open channel, non-vegetated pool) to verify
the accuracy of the model parameter settings in Flow-3D software. In this scenario, the
numerical results were non-dimensionalized, with the horizontal and vertical coordinates
represented by z/H (relative height), where z is the distance from the measurement point to the

162

pool bed, and H is the water depth. Thus, the relative height is zero (0) at the pool bed and one
(1) at the water surface. The relative velocity is denoted as u/U0, where u is the streamwise
instantaneous flow velocity, and U0 is the depth-averaged velocity. Figure 5.7 compares the
numerical results to those of experiments, showing six time-averaged streamwise velocity
profiles (PF1 – PF6, y = 0) normalized by depth-averaged velocity (u/U0) at various points
along the channel centerline across the entire pool, including both entrance and exit sections.
Due to the positioning of the ADV measuring volume, which requires 0.10 m away from the
probe head, the measured velocity profiles cannot extend entirely to the water surface. The
numerical simulation results generally fall within 10% of the experimental results, with the
vertical distribution of streamwise velocity under open channel flow conditions at six
measurement positions typically exhibiting a logarithmic profile. Due to the frictional
resistance at the channel bottom, the velocity near the bed is relatively low and increases with
the distance from the bed. However, at PF2 and PF5, slight underpredictions and
overpredictions of the near-bed velocities were observed (with measured results scattering
around the simulation curve), likely due to the uncertainty of experiments associated with the
ADV measurement technique. This point-measurement method is less accurate in regions of
high turbulence, such as near the transition zone between the entrance/exit slopes and the pool
bed (PF2 and PF5).
Figure 5.7(c) compares the calculated and measured streamwise velocities along the water
depth for Case 4. With vegetation in the pool bed, the vertical distribution of streamwise
velocity in the deep pool section (PF3 and PF4) deviates from the typical logarithmic pattern.
Within the vegetated zone, the velocity change is minimal. However, a significant velocity

163

gradient is observed in the transition layer between the vegetation canopy and the flow above
vegetation, primarily due to the resistance caused by the vegetation patch. Above the vegetation
patch, the velocity resumes a logarithmic distribution pattern. The velocity profile PF4 showed
that the calculated and measured velocities agree very well, with only slight differences. This
discrepancy is mainly attributed to the numerical model’s inability to account for plant
deformation under flow conditions and the complex flow patterns in the boundary region,
where secondary flows may influence the lateral deformation of the vegetation. Along the
entrance and exit sections of the pool, where the flow has not yet interacted with the vegetation,
a relatively consistent logarithmic distribution of u/U along the depth is still observed.
Interestingly, the simulated velocity at the bed of the entrance section is no longer zero, which
may be attributed to numerical diffusion. Numerical schemes in CFD simulations, particularly
those involving complex geometries like vegetated beds, can exhibit numerical diffusion,
which may artificially elevate velocity magnitudes near boundaries (such as the bed) where
they would theoretically be zero (Karadimou et al., 2018). Despite these calculated non-zero
bed velocities using the RNG k-ε model, the results remain scientifically valid due to wellaccepted model assumptions, such as the Boussinesq hypothesis, which does not fully capture
the range of turbulence structures, especially in complex flows (Briganti et al., 2004). These
simplifications, typical in turbulence modeling, are acknowledged within the scientific
community and do not significantly detract from the overall applicability of the findings in
capturing major flow characteristics. As shown in Figure 7, streamwise velocity profiles in the
non-vegetated slope sections follow the logarithmic law regardless of the presence of
vegetation in the deep pool section. Therefore, the focus of this research is on the flow field

164

within the deep pool section with the presence of vegetation in the pool bed.

Figure 5.7 Validation of numerical results against those of experiments. Red lines indicate the slope. However,
the figures indicate the velocity variation with depth, and thus velocity measurements were all conducted above
the channel bed and slope. (a) ADV measurement locations along the centerline; (b) Averaged streamwise
velocity profiles in the pool without vegetation under open flow conditions; (c) Averaged streamwise velocity
profiles in the pool with vegetation under open flow conditions.

Note that the non-zero velocity at the channel bed in this figure results from the inherent
characteristics of numerical simulations. In computational fluid dynamics (CFD), convergence
is achieved when residuals, or errors between iterations, decrease to negligible levels, while
stability ensures bounded, physically meaningful results. Stability was maintained through
careful selection of solver parameters, such as time step size and relaxation factors, and
convergence was monitored via residual reduction, particularly near the no-slip boundary at
165

the bed. Mesh resolution impacted velocity profile accuracy; finer meshes improved alignment
with expected results. However, due to numerical representation, CFD methods calculate
velocity at the first node adjacent to the wall, not directly on it, resulting in a slight non-zero
velocity at the bed. This standard practice does not indicate poor convergence or instability but
reflects a recognized limitation of numerical post-processing. Nonetheless, the results are
congruent with figures displayed in Eraky et al. (2022). Equilibrium, as indicated in Figure 5.7
(PF 4), signifies that flow inside the submerged vegetation has stabilized, particularly in the
streamwise velocity component. This stabilization shows that the flow has fully adapted to the
vegetation’s presence, leading to a steady velocity profile and fully developed flow.
5.4.2 Velocity Profiles
In fluvial hydraulics, the cross-sectional velocity is typically assessed to capture the
distribution of momentum and the influence of secondary flows. The cross-sectional velocity
refers to the resultant velocity vector obtained by summing the velocity components in the ydirection (lateral direction) and z-direction (vertical direction) within a given cross-section of
a flow field. This velocity is significant as it provides a detailed representation of the flow
characteristics across the cross-section. Understanding the cross-sectional velocity is crucial
for accurately predicting flow patterns, assessing turbulence kinetic energy, and evaluating the
stability and uniformity of the flow field.
Figure 5.8 presents simulated cross-sectional velocity contour plots under various
conditions, including with and without the presence of vegetation (vegetation height = 15 cm)
under different water surface cover conditions. In the absence of vegetation on the pool bed,
both the y-velocity (lateral direction) and z-velocity (vertical direction) are negligible,
166

indicating the absence of secondary currents and allowing the sidewall effect to be ignored.
However, when vegetation is present in the pool bed, the flow velocity contour in the zone near
the bed significantly bends due to the obstructive effect of the vegetation. This creates distinct
high-velocity zones within the vegetated area and shifts the maximum flow velocity behind the
vegetation stems. The proximity of high-velocity flow to the channel bed can result in elevated
bed shear stress, potentially increasing sediment transport, bed erosion, and scour in the zone
directly behind the vegetation. While vegetation typically increases flow resistance, the
presence of fast flow zones near the pool bed alters overall energy dissipation patterns, which
can affect the hydraulic efficiency of the channel and alter flow conveyance. This impact will
be further discussed in detail in the Turbulent Kinetic Energy section. Under ice-covered flow
conditions, although the cover bottom surface shows negligible secondary current activity
(with velocity contours approaching zero), the low-velocity region near the cover bottom
surface expands its size, which can lead to decreased transport of frazil ice or debris when ice
cover begins to melt. This effect becomes more pronounced as the surface roughness of the ice
cover increases.

(a)

167

(b)

(c)

(d)

Figure 5.8 Simulated cross-sectional velocity contours in the pool (a) without the presence of vegetation in the
pool (open channel flow); (b) with vegetation in the pool (vegetation height =15 cm, open channel flow); (c) with
vegetation in the pool (vegetation height =15 cm, smooth ice-covered flow); (d) with vegetation in the pool
(vegetation height =15 cm, rough ice-covered flow) (unit: m/s).

Figure 5.9 shows the computed cross-sectional flow vector field for different water surface
cover conditions in the presence of vegetation in the pool bed (vegetation height = 15). Results
of the analysis reveal that the resistance caused by vegetation generates non-negligible lateral
velocity near the vegetated zone, acting as a strong disturbance source that diffuses outward.
168

This secondary flow moves toward the channel wall, forming a circulating secondary flow
pattern. Under ice-covered flow conditions, the secondary currents are more detectable, and a
more prominent circular motion has been observed under a rough ice-covered flow condition.

(a) Cross-sectional velocity vector plot for open channel flow in the presence of vegetation (vegetation height = 15cm).

(b) Cross-sectional velocity vector plot for smooth ice-covered flow in the presence of vegetation (vegetation height = 15cm).

(c) Cross-sectional velocity vector plot for rough ice-covered flow in the presence of vegetation (vegetation height = 15cm).

Figure 5.9 Secondary flow velocity vector diagram in the presence of vegetation in the pool bed under different
water surface cover conditions (vegetation height = 15cm; unit: m/s).

Figures 5.10(a) and (b) present the calculated streamwise velocity field under different
water surface cover conditions at z/H = 0.25 from the pool bed in the presence of vegetation in
169

the pool bed with a vegetation height of 15 cm. The results indicate that the flow field in front
of each vegetation element remains relatively steady. One can observe from these figures that
a low-velocity zone appears behind each vegetation element, but the flow velocity between
individual vegetation elements in the sheath layer increases. Regardless of the water surface
cover conditions, the wake vortex zone behind each vegetation element expands downstream.
The presence of an ice cover on the water surface does not significantly alter the velocity field
in the sheath layer of the vegetated zone.
Figure 5.10(c) illustrates the spatial distribution of streamwise velocity contours at the
distance of z/H = 0.25 from the pool bed in the presence of vegetation with a vegetation height
of 10 cm under open channel conditions. Similar to the velocity profile observed for deeper
vegetation (15 cm), when the flow reaches the first row of vegetation, the obstruction from
vegetation causes backflow, reducing velocity in front of the vegetation but sharply increasing
it on both sides of each vegetation element in the sheath layer. In the rear side of vegetation
elements, wake and vortex are formed, with flow velocity increasing between vegetation
elements in the sheath layer until it stabilizes after overcoming the obstructive effects. This
flow pattern repeats as the flow encounters subsequent rows of vegetation elements. Within the
vegetated section of the pool, the velocity exhibits a sawtooth pattern, peaks at the edges of the
vegetation, and the velocity in the sheath layer increases as the vegetation height grows. This
occurs due to the decrease in the effective cross-sectional area for passing flow, which
compresses the flow and increases velocity immediately entering the vegetation patch. The
maximum velocities occur in the sheath layer between the adjacent vegetation elements in the
first row of vegetation elements, as subsequent vegetation elements cause kinetic energy
170

dissipation, reducing flow velocities. The velocity behind the vegetation patch is lower than
that passing through the vegetation patch due to the decrease in the cross-sectional area for
passing flow caused by the obstruction of vegetation. As vegetation height increases, the wake
area expands (Figures 5.10a and 5.10c). Such detailed flow structures around cylindrical
vegetation elements are challenging to capture experimentally, highlighting the importance of
numerical simulations. Previous studies suggest that the wake zones behind vegetation
elements promote the deposition of fine particles, stimulating the growth and expansion of
aquatic organisms (Kondziolka & Nepf, 2014). This creates a positive feedback loop between
the aquatic ecosystem and sediment deposition (Yamasaki et al., 2021).

(a)

171

(b)

(c)

Figure 5.10 Streamwise velocity contour diagram near the vegetation zone in the pool (unit: m/s): (a) open flow,
vegetation height = 15 cm, (b) smooth ice-covered flow, vegetation height = 15 cm, (c) open channel flow,
vegetation height = 10 cm

Results of the numerical simulations indicate that the slope zones of both entrance and
exit sections of the pool where the cross-section changes significantly influence the flow and
turbulence patterns within the pool. The time-averaged velocity contours reveal higher
velocities over the slopes of both entrance and exit sections and lower velocities near the pool
bed (Figure 5.11). Additionally, turbulence intensities increase near the slope bed in the
172

convectively decelerating flow (CDF) zone where the average velocity is low. The flow pattern
in the model closely resembles that observed in flume experiments. In the absence of vegetation
under open flow conditions, high-velocity zones are observed in the entrance and exit sections
of the pool. The time-averaged velocity is evenly distributed throughout the deep pool section,
with slow flow zones at the channel bed and water surface (Figure 5.11a). In the presence of
vegetation in the deep pool section, flow velocity decreases starting at the upstream edge of the
vegetated patch, with the highest time-averaged velocity occurring in the water column above
the vegetation (Figure 5.11b). Additionally, taller vegetation introduces an elongated slow
surface flow zone in the water column between the entrance slope and the deep pool sections
(Figure 5.11c). Initially, high turbulence zones are concentrated beneath the water surface and
near the bed, with zones of significant velocity variation observed both near the water surface
and the bed over the entrance slope section, namely the dip phenomenon. As the flow
progresses downstream, the velocity variation becomes more distributed across the entire flow
depth, and the surface slow flow zone disappears after passing the deep pool (about the fifth
row in the planting array). Under ice-covered flow conditions, in the presence of vegetation,
the velocity profile in the X-Z plane becomes more symmetrical, resembling a pipe flow in the
deep pool section. Under ice-cover flow conditions, with the increase in ice-cover roughness,
the low flow zone elongates in the deep pool section, and forming a conduit-shaped velocity
profile is delayed. It has been observed that a quasi-uniform velocity profile develops under
smooth ice-covered flow conditions after passing the third row of vegetation elements in the
deep pool. In contrast, under rough ice-covered flow conditions, the velocity profile becomes
quasi-uniform after passing the fifth row of vegetation elements.

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(a)

(b)

(c)

(d)

(e)

Figure 5.11 Time-averaged velocity fields along the central axis (X-Z plane) of the pool channel: (a) Non-

174

vegetated open channel flow; (b) vegetated open channel flow (vegetation height =10 cm); (c) vegetated open
channel flow (vegetation height =15 cm); (d) vegetated smooth ice-covered flow (vegetation height =15 cm); (d)
vegetated rough ice-covered flow (vegetation height =15 cm)

To investigate the impact of vegetation height on flow patterns in the vegetated pool,
various scenarios were considered by varying the vegetation heights on the deep pool bed,
specifically with vegetation heights of 10.0 cm and 15.0 cm under open channel conditions.
Given that the water depth before approaching the upstream cross-section of the entrance
section of the pool is set at 20.0 cm (approximately 30.0 cm deep in the deep pool section),
these vegetation settings in this study represent the condition of fully submerged vegetation.
Figure 5.12 illustrates the positions for analyzing the streamwise velocity profiles. A 2D slice
is taken in the X-Z plane, where the solid line denotes vegetation elements within the slice, and
the dashed line represents vegetation elements in the adjacent planting arrays.

Figure 5.12 Profiling positions for the streamwise velocity in the numerical model (staggered vegetation
arrangement).

Figure 5.13 compares the streamwise velocities (u) at various measurement points with
different vegetation heights. It is observed from Figure 5.13 that the vegetation height
significantly affects the streamwise velocity along the centerline (y = 0), particularly in the
vegetation-flow transition zone. In the deep pool section near the pool entry section (R2) and
exit section (R8), vegetation height variations notably influence streamwise velocity

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distribution. Despite differences in vegetation height, the vertical distribution trend of
streamwise velocity remains generally consistent in the middle of the deep pool section. Within
the vegetation zone, before the relative streamwise velocity (u/U0) suddenly increases, the
relative velocity (u/U0) shows a consistent pattern as z/H increases.

Figure 5.13 Comparison of streamwise velocity at various positions with different submerged vegetation
heights (staggered vegetation arrangement).

When ice cover is introduced in the model, the position of the maximum streamwise
velocity under the ice is influenced by the relative roughness of the channel bed and the ice
cover. The maximum velocity typically shifts toward the surface that offers the least resistance
to the flow (Sui et al., 2009, 2010). Figure 5.14 presents streamwise velocity profiles under the
open channel, smooth, and rough ice-covered flow conditions downstream of the vegetation
patch. These profiles differ from those observed without vegetation on the channel bed, as
shown in the verification case. Figure 5.14 captures the velocity profiles immediately
downstream of the wake zone of individual vegetation elements, where severe fluctuations can

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be observed, mirroring trends seen in experimental data from plain channels (Barahimi & Sui,
2024b). The velocity profiles in Figure 5.14 reflect the combined effects of ice cover, turbulent
flow, and the interaction between vegetation and the sand bed of the pool. In the presence of
vegetation, velocity profiles measured closely behind the vegetation element where vegetation
is present in the measuring 2D slice (R1, R5, R9) under ice-covered flow conditions exhibit
two peak values: one at the sheath section of the vegetation (or stem section) and another above
the vegetation tops. The sheath section reduces the cross-sectional area for passing flow,
accommodating greater flow velocity. The second velocity peak occurs between the ice cover
and the vegetation. Results show that the ice cover shifts the maximum velocity to the region
between z/H = 0.50 and 0.70. Under open flow conditions, the streamwise velocity (u) profile
above the vegetation zone follows a logarithmic function, with the maximum velocity near the
water surface. In contrast, under ice-covered flow conditions, the streamwise velocity profile
resembles that of a pipe flow, with the peak velocity between the vegetation canopy and ice
cover depending on the relative roughness of the ice cover to that of the vegetation canopy.
Velocity fluctuations are prominent behind the vegetation elements, with more significant
variations observed near the transition between the slope and deep vegetated pool sections (R1
and R9).

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Figure 5.14 Streamwise velocity under different surface cover conditions behind vegetation elements
(vegetation height = 10 cm, staggered vegetation arrangement).

5.4.3 Turbulent Kinetic Energy
Vortex formation in the wake behind vegetation elements extracts energy from the mean
flow, converting it into turbulent kinetic energy (TKE). The turbulence levels are mainly driven
by vegetation-induced drag and are largely unaffected by bed shear stress. Local turbulent
kinetic energy is defined as follows:
ܶ‫= ܧܭ‬

1 തതതതଶ തതതതଶ തതതതതଶ
൫‫ݑ‬′ + ‫ݒ‬′ + ‫ݓ‬′ ൯
2

(5.14)

where
்

1
തതതത
‫ݑ‬′ଶ = න (‫ )ݐ(ݑ‬− ‫ݑ‬ത)ଶ ݀‫ ≥ ݐ‬0
ܶ ଴

(5.15)

തതതതଶ and തതതതത
and ‫ݒ‬′
‫ݓ‬′ଶ are calculated in a similar approach.
Figure 5.15 illustrates the calculated turbulent kinetic energy (TKE) values using the yaxis (X-Z plane) as the cutting plane for the 2D slice under the open channel flow condition

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with the vegetation height of 15 cm (Scenario 4). While theoretically, TKE should approach
zero at the very bottom due to the no-slip condition, a peak in TKE, with values ranging from
0.0017 to 0.0020 m²/s², is observed just above the pool bottom immediately after the flow
passing through the vegetation zone (within the boundary layer). This peak reflects the
interaction between the fluid flow and the vegetation, which is accurately captured by the
simulation. Within the vegetation zone, particularly near the bottom, high-velocity gradients
exist due to the interaction between the moving fluid and the stationary vegetation elements.
These gradients can generate significant shear stress, producing turbulence and elevated TKE.
Additionally, the RNG k-ε model predicts higher TKE near the boundary due to the turbulence
closure scheme, which calculates TKE based on local velocity gradients. These gradients are
steepest near the pool bed, thus predicting higher TKE in this region. As the distance from the
bed (z/H) increases, the turbulent kinetic energy gradually decreases and levels off near the
water surface, consistent with the findings of Huang et al. (2019).

Figure 5.15 The numerical model simulated the TKE contour in the X-Z plane (staggered vegetation
arrangement).

Figure 5.16 presents the vertical distribution curves of the calculated TKE in the presence
of vegetation with different heights under open channel flow conditions. As shown in Figure
16, when the flow is obstructed by vegetation, the TKE curves in the presence of submerged
vegetation exhibit a mirrored “C” shape in the stem zone, with a transition point near the top
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of the vegetation canopy. As the relative distance from the bed (z/H) increases, the interference
of the vegetation stem with the flow gradually decreases. Results showed that the vegetation
height significantly influences the TKE at the water surface, with the TKE for vegetation 10
cm high being, on average, twice that observed for the submerged vegetation 15 cm high.

Figure 5.16 Comparison of turbulent kinetic energy across various positions in the vegetated pool zone (y = 0,
staggered vegetation arrangement).

Figure 5.17 shows the depth-averaged turbulent kinetic energy (TKE) distribution along
the longitudinal section (or streamwise direction) at a distance from the bed of z/H = 0.25. In
the model constructed in Flow-3D, x represents the longitudinal coordinate, with x = 0
positioned at the center of the deep pool, while the y and z axes are consistent with Figure 2.
As shown in Figure 17, flow disturbances caused by vegetation create significant nonuniformity in the TKE distribution. In all simulation scenarios, the TKE gradually increases as
the flow encounters vegetation in the deep pool. It peaks at x = -1.34 m as it passes the first
row of vegetation elements. This sharp increase is attributed to the vegetation's substantial drag,
elevating the TKE value. Then, the TKE value decreases sharply but rises again between

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vegetation clusters, with additional peaks observed at x = -0.72 m, x = -0.12 m, x = 0.48 m, and
x = 1.08 m as the flow passes the second, third, fourth, and fifth rows of vegetation elements.
After passing the last row of vegetation elements, the TKE value drops to the average value
found in the middle between two adjacent vegetation columns (y = 0.15 m) and stabilizes due
to the absence of vegetation, with the TKE value primarily influenced solely by bed drag force,
which remains constant. The TKE distribution exhibits a sawtooth pattern as the flow moves
through zones with low and high flow velocities, aligning with findings by Wang et al. (2019).
The overall variation of the TKE values between vegetation clusters shows a decreasing trend.
From upstream to the downstream of the vegetated pool, in the longitudinal zone between the
columns of vegetation elements (y = 0.15 m), the TKE values in the non-vegetated zone change
gradually along a certain distance from x = -1.5 m to -0.86 m, and then stabilizes when x > 0.86 m until the end of the deep pool. This is because vegetation elements do not directly
influence the TKE in the zone between the columns of vegetation elements but are affected by
wake vortices generated by the vegetation elements toward this zone. As the influence of
vegetation diminishes, the TKE values stabilize beyond x = 1.5 m. The presence of an ice cover
leads to the reduction of the TKE values at the entrance section of the pool, which increases
near the exit section of the pool. Results showed that, within the vegetation patch, for instance,
at a distance from the bed of z/H = 0.25, under smooth ice-covered flow condition (n = 0.010
was used in this model), the TKE value reduces on average by 15% more than that of rough
ice-covered flow condition (n = 0.021).

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Figure 5.17 Streamwise turbulent kinetic energy distribution along the vegetated deep pool.

Figure 5.18 presents the TKE profiles behind vegetation elements arranged in staggered
configuration (vegetation height = 15 cm) under different water surface cover conditions. In
the open channel scenarios, the TKE profiles typically exhibit peaks at the sheath section,
followed by a general decrease as the water flows downstream. Under both smooth and rough
ice-covered flow conditions, the TKE profiles show an increasing trend toward the ice cover.
In the region near the vegetation canopy (z/H ≈ 0.60), the TKE values reach their maximum
due to significant velocity gradients arising from the interaction between the moving fluid and
the vegetation canopy, except in the regions near the pool entrance in the open channel scenario.
In the pool region with the distance from the pool bed to z/H = 0.60 (or inside of the vegetation
patch), vegetation blockage reduces the cross-sectional area for flow, thereby reducing the TKE
fluctuations. Around the distance from the channel bed of z/H = 0.80, which marks the
boundary zone influenced by the ice cover, the TKE values increase again. Near the bottom
surface of the ice cover, the TKE value gradually increases due to the no-slip condition.

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Figure 5.18 Comparison of turbulent kinetic energy (TKE) behind vegetation elements arranged in a staggered
configuration under different water surface cover conditions.

To investigate the impact of the inflow rates on turbulent kinetic energy (TKE) in the
vegetated pool, this study examined three inflow conditions with flow rates of 50, 100, and 120
L/s. According to the continuity theory, with a constant water depth, a higher inflow rate results
in a higher approaching velocity. Figure 5.19 compares the simulated turbulent kinetic energy
at different cross sections under different inflow conditions in the presence of vegetation in the
deep pool (vegetation height = 15 cm) in open channel. In the sheath section of vegetation (near
the pool bed), the impact of the inflow rates on the TKE values is less than in the zone of
vegetation canopy. One can see from Figure 5.19 that, with the increase in the inflow rate, the
TKE value in the vegetation canopy increases first and decreases later. When the flow
encounters the first row of vegetation elements, the TKE value consistently increases with the
inflow. However, the vertical TKE profile on the rear side of the first-row vegetation indicates
more intense turbulence than in other locations. Figure 5.19 shows a noticeable decrease in the
TKE value as the flow moves further downstream (or as the longitudinal distance x increases).
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Under open channel flow conditions, after the TKE value reaches a maximum, the TKE value
decreases and stabilizes at a distance from the pool bed of approximately 0.6 < z/H < 0.8.

Figure 5.19 Comparison of the simulated turbulent kinetic energy (TKE) under different inflow conditions under
open channel flow.

Interestingly, ice-covered flow demonstrates higher TKE at the surface below the ice cover.
In Reynolds-Averaged Navier-Stokes (RANS) simulations, turbulent fluctuations are not
directly resolved but approximated through turbulence closure models, so TKE is not derived
from the instantaneous flow field but predicted via a modeled equation, referred to as “modeled
TKE.” The TKE profiles in this study align with existing literature for open-channel flows,
where peak TKE is observed within vegetation stems and near-zero values occur at the free
surface (Farhadi et al., 2018; Jing et al., 2023; P. Kumar et al., 2024). Although flume studies
of ice-covered flows are limited, literature and field data indicate that TKE near the ice interface
is not necessarily near-zero, as suggested by studies on radiatively driven convection (Mironov
et al., 2002). Additionally, Kumar et al. (2024) observed elevated TKE near a solid wall under
non-slip conditions, which is consistent with the results here. The styrofoam panel used in this

184

study floated, allowing minimal wave action that has little impact on scour (Hains & Zabilansky,
2005). However, the ice cover in FLOW-3D was modeled as a fixed plate, simulating
Poiseuille-type flow conditions that support higher TKE near boundaries (Gretler & Meile,
1997). Despite this, very low TKE values were recorded near the bed, attributable to the nonslip condition applied to the sandbox bottom at -0.3 m rather than porous sands.
5.4.4 Analytical Model
Research has been conducted on flow fields in the presence of vegetation in open channels
based on various approaches, such as the logarithmic law (also known as the law of the wall)
and the boundary layer method. As observed in the velocity profiles, turbulence forms within
the vegetation zone, but in the zone above the vegetation patch under the ice cover, the
streamwise velocity profiles resemble those of a pipe flow once the flow is fully developed
(Figure 5.11).
Since the streamwise velocity shows the most drastic variations, the following discussion
targets the streamwise velocity vector (u) above the vegetation zone under ice-covered flow
conditions, assuming the flow becomes mildly disturbed. The derivation of the analytical
model for the flow field in the presence of a vegetation patch in the deep pool bed under an ice
cover begins with applying the fundamental Navier-Stokes equations for incompressible flow,
which describe the conservation of momentum. These equations can be expressed as:
߲‫ܝ‬
ߩ ൬ + ‫ܝ∇ · ܝ‬൰ = −∇‫ ݌‬+ ߤ∇ଶ ‫ ܝ‬+ ܎௩௘௚௘௧௔௧௜௢௡ + ܎௜௖௘
߲‫ݐ‬

(5.16)

where p is the pressure, ρ is the fluid density, μ is the dynamic viscosity, fvegetation represents the
drag force caused by vegetation, and fice represents the boundary effects due to the ice cover.
To simplify the problem, assuming the flow reaches a steady state, where ∂u/∂t = 0, and the
185

water is incompressible, implying ∇⋅u = 0. The vegetation drag is a significant factor in this
model, as it acts as a resistive force proportional to the square of the flow velocity. This drag
force can be modeled using the following equation:
1
܎௩௘௚௘௧௔௧௜௢௡ = − ‫ܥ‬஽ ߩ‫ܣ‬௏ ‫|ܝ|ܝ‬
2

(5.17)

where CD is the drag coefficient, and Av represents the frontal area of the vegetation per unit
volume. Additionally, the effect of the ice cover is incorporated through a boundary condition
that assumes a no-slip condition at the ice-water interface, i.e., the flow velocity at the ice
boundary (at depth z = h) is zero.
Potential flow conditions are assumed to solve for the flow field, where the flow is
irrotational, allowing the introduction of a stream function ψ such that u = ∇ψ. This assumption
leads to the Laplace equation for the stream function, ∇2ψ = 0, which serves as the basis for
incorporating the effects of both vegetation and ice cover into the model. The influence of the
ice cover is modeled as an exponential decay in velocity with depth, while the spatial variation
of the flow field is represented using a cosine function. The resulting expression for the velocity
field is derived using RStudio based on data collected from the vegetated pool in the upstream
sandbox:
‫ݖ‬
2ߨ‫ݔ‬
2ߨ‫ݕ‬
൰ cos ൬
൰
‫ݔ(ܝ‬, ‫ݕ‬, ‫ܷ = )ݖ‬଴ exp ቀ−ߙ ቁ cos ൬
‫ܪ‬
‫ܮ‬
‫ܤ‬

(5.18)

where U0 is a characteristic velocity, α is a decay coefficient that captures the suppressive effect
of the ice cover on the flow, L is the characteristic streamwise length scale of the deep pool
section, and B is the width of the pool zone. The origin (0, 0, 0) of the coordinate system is set
at the midpoint of the last cross-section of the entrance section of the pool (Figure 5.2). Finally,
the vegetation drag force is incorporated as a loss term in the momentum equation, leading to
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the final form of the model:
‫ݖ‬
2ߨ‫ݔ‬
2ߨ‫ݕ‬
1
൰ cos ൬
൰ − ‫ܥ‬஽ ߩ‫ܣ‬௏ ‫|ܝ|ܝ‬
‫ݔ(ܝ‬, ‫ݕ‬, ‫ܷ = )ݖ‬଴ exp ቀ−ߙ ቁ cos ൬
‫ܪ‬
‫ܮ‬
‫ܤ‬
2

(5.19)

Since the derived equation targets the flow above the vegetation zone, the distance from
the pool bed (z) is always greater than h. Equation (5.19) is further modified by introducing
some non-dimensional variables: u/U0 and Av/A, let α = k·ni/nb, and CD = m·h/H, where A is the
cross-sectional area where the vegetation is situated, ni and nb are the Manning roughness
coefficient of the ice cover and the channel bed respectively, h is the vegetation height, k and
m are empirical constants influenced by pool geometry and vegetation patch layouts such as
entry and exit slopes and vegetation density. Then, Equation (5.19) is modified as follows:
‫ݑ‬
݊௜ ‫ݖ‬
2ߨ‫ݔ‬
2ߨ‫ݕ‬
݉ߩ‫ܣ‬௏ ܷ଴ ℎ ‫ݑ ݑ‬
൰ cos ൬
൰ cos ൬
൰−
= exp ൬−݇
ฬ ฬ
ܷ଴
݊௕ ‫ܪ‬
‫ܮ‬
‫ܤ‬
2‫ܷ ܪ ܣ‬଴ ܷ଴

(5.20)

defining a non-dimensional parameter β:
ߚ=

݉ߩ‫ܣ‬௏ ܷ଴
2‫ܣ‬

(5.21)

then Equation (5.20) can be written as
‫ݑ‬
݊௜ ‫ݖ‬
2ߨ‫ݔ‬
2ߨ‫ݕ‬
ℎ ‫ݑ ݑ‬
൰ cos ൬
൰ cos ൬
൰−ߚ
= exp ൬−݇
ฬ ฬ
ܷ଴
݊௕ ‫ܪ‬
‫ܮ‬
‫ܤ‬
‫ܷ ܪ‬଴ ܷ଴

(5.22)

The non-dimensional term, u/U0, is present on both sides of Equation (5.22), suggesting
that u/U0 is influenced by a function that includes u/U0 as an input. Therefore, solving for u/U0
requires iterative methods. This equation does not apply to open channels, as the profile I the
upper region no longer resembles pipe flows.
Using all ADV measured results from experiments in the pool in the upstream sandbox, k
and m are determined as 0.56 and -0.017. The ADV-measured streamwise velocities in the pool
in the downstream sandbox are used to verify the derived equation. As shown in Figure 20, the
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experimental results are compared to those calculated using Equation (5.22). The results
showed that the experimental results align well with the analytical solution with R 2 = 0.876,
indicating that Equation (5.22) can effectively simulate the streamwise velocity distribution
above the submerged vegetation in the pool center section under ice-covered flow conditions.

Figure 5.20 Comparison of measured velocity values (u/U0) to calculation using Equation (5.22).

5.5 Chapter Summary
In this chapter, laboratory experiments have been conducted in a large-scale outdoor flume
considering different water surface conditions, different submergence heights of vegetation,
pool features, and hydraulic conditions to investigate the effects of leafless vegetation on flow
velocity, turbulent kinetic energy, and secondary flow variations. A numerical simulation model
of the 3D flow field in pools with submerged vegetation in the pool bed has been conducted
using Flow3D software. The focus was on the impact of the pool bed vegetation on the pool
section's hydrodynamic characteristics under ice-covered flow conditions. The comparison of
measured velocity values (u/U0) to those of calculation using the derived equation exhibits

188

good agreement, indicating that the Flow-3D model can accurately replicate the flow
characteristics of the flow in the vegetated pool under ice-covered flow conditions. The
following conclusions can be drawn from this study:
1) Vegetation on the pool bed significantly alters flow distribution, particularly redirecting
the main flow towards the water surface. As submerged vegetation height increases (or the
submergence ratio decreases), flow velocity within the vegetated zone decreases while
velocity above the vegetation increases, particularly under ice-covered conditions. Under
ice-covered flow conditions, velocity profiles exhibit two distinct patterns: a pronounced
variation within the vegetation zone, dominated by the drag caused by the pool bed and
vegetation, and a mild fluctuation above the vegetation top under ice cover, where the
maximum velocity is observed in this zone. The velocity profile in the non-vegetated slope
sections of the pool adheres to the conventional logarithmic law, regardless of the presence
of vegetation in the deep pool section. However, vegetation on the pool bed alters flow
distribution, redirecting the main flow towards the water surface.
2) The entrance section of the pool, where the cross-section expands, plays a critical role in
shaping the flow and turbulence patterns within the vegetated pool. Results show that, in
the presence of vegetation in the deep pool section, high velocities are concentrated in the
deep pool section near the entrance slope. In contrast, lower velocities and increased
turbulence intensities are observed near the pool bed, particularly upstream of the pool
near the entrance section.
3) The presence of vegetation in the pool bed leads to increased streamwise TKE value within
the pool. Under the same water depth, as inflow rates increase, although the velocity across

189

the pool section rises, the TKE shows slight variation within the vegetation zone but
significantly increases at the top of the vegetation. The presence of vegetation in the pool
section increases streamwise TKE value. An ice cover on the water surface reduces the
TKE value near the vegetation patch in the pool section. However, it increases near the
end of the deep pool section, and more pronounced fluctuations of the TKE value are
observed under rough ice-cover flow conditions.
4) An analytical model has been developed to account for the impact of vegetation and ice
cover on the streamwise velocity in the vegetated pool section. This model incorporates
potential flow assumptions and a stream function to simulate velocity distribution
considering the presence of both vegetation in the pool bed and ice cover on the water
surface. The proposed equation, solved iteratively to address non-dimensional variables,
models vegetation drag as a loss term in the momentum equation. Validation against the
measured streamwise velocities in the vegetated pool in the downstream sandbox showed
strong alignment with experimental results (R² = 0.876), demonstrating the model's
effectiveness in simulating streamwise velocity distribution in the flow above the
submerged vegetation under ice cover, with potential applications for predicting flow
behavior in similar environments.
The use of rigid cylinders to simulate vegetation in flume experiments, though typical for
controlled and replicable results, can lead to deviations from natural conditions. Unlike the
uniform layout pattern of vegetation elements used in this study, natural vegetation varies in
stem diameter, flexibility, and spatial distribution, critically influencing flow dynamics,
turbulence, and sediment transport. The staggered configuration of vegetation elements used
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in this study can create preferential flow paths, which are unrepresentative of the random
distribution found in nature, potentially skewing drag force and turbulence estimates. While
laboratory experiments and computer simulations offer valuable insights, their applicability to
real-world scenarios requires cautious interpretation. More sophisticated models that
incorporate the natural variability of vegetation are essential for accurate predictions of flow
behavior in vegetated pools.

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6.

CHAPTER SIX: GENERAL CONCLUSIONS

This research, through comprehensive experimental studies conducted in a large-scale
flume and Flow-3D numerical simulation, provides an in-depth understanding of the complex
interactions between submerged spur dikes, submerged vegetation, and flow dynamics under
various conditions, including ice-covered and open-channel scenarios. The studies revealed
that both spur dikes' orientation and submergence levels and the morphology and arrangement
of submerged vegetation influence flow patterns, including velocity distributions, Turbulence
Kinetic Energy (TKE), bed deformation, and scouring processes. Notably, the presence of ice
cover further amplified the complexity of these interactions by altering flow structures and
intensifying local scouring around the spur dikes. The results indicate that the flow dynamics
notably differ between the open channel and ice-covered conditions. Reynolds shear stress and
turbulent events are more pronounced under ice cover, leading to more severe scouring around
the spur dikes. These findings provide critical insights into the design and implementation of
hydraulic structures in cold regions, contributing to enhanced river management and
engineering practices.

6.1 Synthesis
Chapter 3 investigates the local scour dynamics around submerged angled spur dikes
under ice cover. The research focuses on the effects of dike orientation and submergence levels
on flow patterns, including velocity distributions and Reynolds shear stress, under various icecovered conditions. The study reveals that ice cover alters the flow structure around spur dikes,
leading to more pronounced scouring and sediment transport than open channel conditions.
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The findings provide insights into the complex interactions between hydraulic structures and
ice cover, emphasizing the need for careful consideration in the design of spur dikes in cold
regions.
Chapter 4 builds upon the previous chapter by examining the turbulent flow around
submerged angled spur dikes under ice cover. This chapter delves into the detailed analysis of
flow velocity fields and turbulence characteristics, including identifying transverse flow
regions and recirculation zones induced by spur dikes. The quadrant analysis of turbulent
events reveals that ice cover amplifies the intensity of ejection and sweep events near the dike
tip, leading to increased turbulence and sediment mobilization. These results contribute to a
deeper understanding of how submerged spur dikes influence flow dynamics in ice-covered
rivers, with implications for flood management and sediment control.
Chapter 5 focuses on the hydrodynamic characteristics within pools containing leafless
vegetation under ice cover, representing a regional disturbance for the flow field rather than a
local disturbance such as spur dikes. The study explores how vegetation and ice cover
interaction affect flow velocity profiles and turbulence generation within pool structures. The
presence of vegetation mitigates flow velocity and enhances sediment deposition, while the ice
cover further modifies the flow patterns, leading to unique hydrodynamic conditions. This
research highlights the possible role of vegetation in riverbank restoration projects and
controlling sediment transport, particularly in cold climates where ice cover is a significant
factor.
These chapters comprehensively analyze the interactions between submerged hydraulic
structures, vegetation, and ice cover, offering valuable insights for river engineering and

193

management in cold regions. Collected data supporting these findings are provided in the
appendices, offering a detailed account of the experimental conditions and results across the
different flow scenarios.

6.2 Conclusions of Chapter Three
1) This study demonstrates that submerged angled spur dikes’ orientation and submergence
level influence local scour patterns under ice-covered conditions. The findings reveal that
as the angle of the spur dike increases beyond 90°, the extent of scour around the dike
decreases, highlighting the critical role of dike alignment in controlling sediment transport
and erosion. The ice cover intensifies the scouring process, particularly at higher
submergence levels, by altering the flow velocity and turbulence around the dike,
underscoring the importance of considering ice cover in designing and placing hydraulic
structures in cold regions.
2) The analysis showed that the Froude number (Fr) is critical in determining the severity of
local scour. Higher Froude numbers, indicative of more turbulent flow conditions,
correspond to increased scour depths around the dikes. The study also found that the
submergence ratio (S), which reflects the extent to which the dike is submerged, inversely
affects the scour depth. As the submergence ratio increases, the scour depth decreases,
suggesting that higher submergence provides some protection against scouring.
3) A modified empirical equation was proposed in this study to predict the maximum scour
depth around submerged angled spur dikes. This equation incorporates the hydraulic radius
(Rh) and other relevant factors, such as the roughness of the channel cover and the

194

overtopping ratio. The equation was validated against experimental data, accurately
predicting scour depths under various conditions. This new model offers a valuable tool
for engineers to estimate scour depths more reliably in environments with ice cover.
4) This research provides crucial insights into the interaction between submerged spur dikes
and ice-covered flow conditions. The study’s findings are particularly relevant for
designing and constructing hydraulic structures in cold regions, where ice cover can
significantly alter flow dynamics and exacerbate scouring. By incorporating the factors
identified in this research, engineers can better predict and mitigate the risks associated
with local scour, leading to more resilient infrastructure in these challenging environments.

6.3 Conclusions of Chapter Four
1) This study comprehensively analyzes the turbulent flow structure around submerged
angled spur dikes under various ice cover conditions, focusing on the effects of dike
orientation and submergence levels. The findings reveal that dike alignment angles greater
than 90°reduce streamwise velocity components near the dike, with a notable increase in
velocity magnitude observed at the dike tip, especially under ice-covered conditions. The
presence of ice cover, particularly rough ice, amplifies turbulence intensity and alters the
velocity field, pushing the maximum velocity closer to the channel bed.
2) The research demonstrates that the formation of transverse flow regions and recirculation
zones downstream of the dike is heavily influenced by the dike's orientation and the nature
of the ice cover. Quadrant analysis indicates that both ejection and sweep events dominate
turbulent interactions near the dike tip under ice-covered conditions, contrasting with open

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channel conditions where sweep events are more prevalent. These findings highlight the
significant impact of ice cover on flow dynamics around submerged spur dikes,
emphasizing the need for careful consideration of ice cover characteristics in hydraulic
structure design.
3) The study presents a detailed examination of Reynolds shear stress (RSS) distribution,
showing that RSS values are higher under ice-covered conditions, particularly with rough
ice cover, compared to open-channel conditions. The RSS variation is more pronounced
downstream of the dike due to the recirculation wake zone formed by flow separation. The
results underscore the importance of considering both dike orientation and ice cover
roughness in predicting and managing turbulent flow around submerged spur dikes.
4) Overall, this research advances the understanding of flow dynamics in cold regions,
providing valuable insights for designing and managing hydraulic structures in iceaffected rivers. Future work should explore the broader implications of these findings in
natural river systems and consider further integrating advanced measurement techniques
and numerical simulations to refine the understanding of turbulent flow around submerged
structures.

6.4 Conclusions of Chapter Five
1) This study has shown that submerged rigid leafless vegetation alters pool flow structure,
particularly under ice-covered conditions. The presence of vegetation in the pool bed
transforms the vertical distribution of flow velocity from a logarithmic shape to a quasi-S
shape within the vegetated zone. The results indicate that vegetation height and

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arrangement play a crucial role in redirecting flow towards the water surface, with
increased vegetation height leading to greater velocity near the water surface and reduced
flow within the vegetated zone. This reconfiguration of flow dynamics highlights the
importance of vegetation in modulating flow characteristics, especially in cold regions
where ice cover is present.
2) The research also demonstrated that vegetation and ice cover interactions affect the pool’s
turbulent kinetic energy (TKE) distribution. Under ice-covered flow conditions, TKE
values exhibit distinct peaks near the vegetation tops and the ice-water interface, forming
a mirrored “C” shape profile. The study found that the roughness of the ice cover further
amplifies turbulence near the pool bed and the water surface, contributing to more
pronounced variations in TKE compared to open channel conditions. These findings are
critical for understanding the complex flow-vegetation interactions in ice-covered rivers
and designing more effective flood control and river restoration strategies.
3) The study successfully used experimental data to validate the numerical simulation model
FLOW-3D, demonstrating the model's effectiveness in replicating flow characteristics in
vegetated pools under ice-covered conditions. The simulation results closely aligned with
the experimental measurements, particularly in capturing variations in streamwise velocity
and TKE across different vegetation heights and water surface conditions. This validation
highlights the potential of numerical models to predict flow behavior in complex
environments, offering a valuable tool for river management and ecological protection
efforts.
4) An analytical model was developed to simulate the streamwise velocity distribution above

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the vegetation zone under ice-covered conditions. This model incorporates the effects of
both vegetation drag and ice cover on the flow field, offering a practical approach for
predicting velocity profiles in vegetated pools. The model strongly agreed with the
experimental results, indicating its potential applicability in real-world scenarios where
vegetation and the influence of ice cover on flow dynamics.
5)

The research highlights the limitations of using rigid cylinders to simulate vegetation in
flume experiments, noting that natural vegetation's variability in stem diameter, flexibility,
and spatial distribution can lead to different flow dynamics. The staggered configuration
of vegetation elements used in this study may only represent special cases in nature,
suggesting the need for more sophisticated models that account for the natural variability
of vegetation in future studies.

6.5 Significance of This Study
This section synthesizes the contributions of the conclusions discussed in the previous
chapters and their broader applications. The findings from these studies offer valuable insights
into river management, particularly in cold regions where ice cover and hydraulic structures
play a critical role.
The research demonstrates the impacts of submerged angled spur dikes on flow dynamics,
scour formation, and turbulence under ice-covered conditions. The inverse relationship
between the spur dikes’ alignment angle and the scour’s depth suggests that strategically
orienting these structures can effectively mitigate erosion and protect riverbanks. This insight
is valuable and relevant for river managers and engineers designing hydraulic structures to

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withstand the challenges of ice cover and high-flow conditions. By optimizing the orientation
and submergence levels of spur dikes, the erosive potential of high-velocity flows can be
reduced, thereby minimizing damage to adjacent infrastructure and enhancing riverbank
stability.
The studies also highlight the role of vegetation in modulating flow characteristics within
pools, particularly under ice-covered scenarios. The transformation of flow velocity profiles
from a logarithmic to a quasi-S shape within vegetated zones underscores the importance of
vegetation in creating favorable habitats for aquatic organisms. By incorporating vegetation
into river restoration projects, river managers can enhance sediment retention, reduce flow
velocities, and promote the formation of sheltered zones that serve as refuges for fish and other
aquatic species. The ability of vegetation to modify turbulent kinetic energy profiles further
emphasizes its potential to improve water quality and stabilize riverbeds by limiting sediment
resuspension.
Moreover, the findings regarding the effects of rough ice cover on scour formation around
both vegetation and spur dikes provide critical guidance for managing river systems in cold
climates. The increased scour depths associated with rough ice cover conditions highlight the
need for careful consideration of ice cover roughness when designing and implementing river
management strategies. Protective measures, such as reinforcing vulnerable sections of the
riverbed and selecting vegetation and dike configurations that minimize turbulence, can
mitigate the adverse effects of ice cover on river morphology.
The development of numerical models further strengthens the applicability of these
findings. These models offer a reliable tool for predicting flow behavior and optimizing the

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design of aquatic habitat restoration projects, such as vegetation replantation and introduction
of wood debris, for building diverse habitat environments. Simulating complex interactions
between vegetation, ice cover, and channel bed under varying conditions enhances the
precision of river management interventions, contributing to more resilient and sustainable
river ecosystems.
In conclusion, the research comprehensively explains the interplay between hydraulic
structures, vegetation, and ice cover in shaping river dynamics. The practical applications of
these findings offer river managers and engineers the tools and knowledge necessary to design
more effective and ecologically sound river management strategies, particularly in cold regions
where ice cover significantly influences river behavior.

6.6 Limitation of the Current Study
The experimental studies and numerical simulations conducted in this research were
subject to several limitations despite efforts to minimize their impact. When interpreting the
results and applying the findings to real-world scenarios, these limitations should be considered.
One notable limitation arises from the ice cover conditions simulated in the experiments.
The study utilized Styrofoam panels to mimic smooth and rough ice cover, which, while useful
for controlled experimentation, may only partially replicate the complexities of natural ice
covers in rivers. The roughness of natural ice can vary significantly, and this variability may
influence flow and scour patterns in ways not fully captured by the experimental setup.
Additionally, the experimental setup itself posed certain constraints. The flume’s slope
and the fixed distance between the sandboxes introduced consistent variations in water depth

200

that may have influenced the flow and turbulence measurements. Additionally, using an
Acoustic Doppler Velocimeter (ADV) for velocity measurements had its limitations,
particularly in regions close to the water surface and near the channel bed, where signal
interference and noise can affect data accuracy.
Another limitation involves using rigid cylinders to model vegetation in the numerical
simulations. Although these provided consistency and repeatability, they fall short in
representing the natural variability of vegetation, such as differing stem flexibility, diameters,
and spatial distributions, potentially leading to deviations from actual flow dynamics and
sediment transport.
Moreover, the numerical simulations relied on the FLOW-3D software, which, although
effective in replicating flow characteristics, involves certain assumptions and simplifications
inherent to computational fluid dynamics models. For example, the RNG k-ε turbulence model
used in the simulations may not fully resolve all scales of turbulence, particularly in complex
flow conditions involving vegetation and ice cover. The model’s inability to account for plant
deformation under flow conditions further limits its accuracy in representing the dynamic
interactions between flow and flexible vegetation.
Finally, the study's scope was constrained by the controlled laboratory conditions and
experimental scale. While these conditions facilitate simplified analysis and reproducibility,
they do not entirely capture the intricacies of natural river systems, where diverse sediment
sizes, fluctuating water levels, and heterogeneous vegetation significantly influence flow
dynamics.
These limitations highlight the need for further research incorporating more diverse and

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flexible vegetation models, advanced turbulence models, and field studies to validate and
expand upon the findings. Such efforts would enhance the applicability of the results to natural
river systems and improve the accuracy of predictions in river management and restoration
projects.

6.7 Future Directions
6.7.1. Specialized Research in River Ice Hydraulics
Building on the conclusions of this thesis, several avenues for future research are proposed:
1) Advanced Study of Spur Dike Configurations: Future research could explore the effects
of varied spur dike configurations, such as multiple dike systems and their interactions
under different ice cover conditions. Investigating the impact of dike spacing, alignment
variations, and the use of flexible materials could provide a deeper understanding of how
to optimize dike design for effective erosion control and flow management. Additionally,
studies could focus on the long-term effects of spur dikes in natural rivers, considering
factors like sediment deposition, channel migration, and ice dynamics over multiple
seasons.
2) Further Integration with Numerical Simulations: Building upon the findings of this thesis,
future work could focus on integrating the experimental data with advanced numerical
simulations. Enhancing the accuracy of computational models like OpenFOAM and
FLUENT by incorporating more complex turbulence models or simulating the interaction
between spur dikes and varying ice roughness conditions could improve flow behavior
and scour pattern predictions. Such models could also be used to simulate scenarios not
202

easily replicated in laboratory settings, such as the effects of extreme weather events on
spur dike performance.
3) Field Validation and Long-Term Monitoring: While this thesis utilized controlled
laboratory experiments, field studies in natural rivers with existing spur dikes under ice
cover would provide valuable validation of the experimental results. Long-term
monitoring of these sites could offer insights into the real-world performance of spur dikes,
including their impact on local ecology, sediment transport, and river morphology over
time.
4) Interaction Between Spur Dikes and Vegetation: Further investigation could explore the
synergistic effects of spur dikes and submerged vegetation. Understanding how the
interactions between these two elements influence flow patterns, sediment deposition, and
erosion under ice-covered conditions could inform more holistic river management
strategies. For example, research could examine the potential of using vegetation to
enhance the stability and effectiveness of spur dikes in river systems.
5) Vegetation Dynamics and Flexibility: While this thesis focused on rigid, leafless
vegetation, future research could examine the dynamics of flexible vegetation, including
how it responds to varying flow conditions and ice cover. Studies could investigate
phenomena such as monami (the oscillatory motion of plants in water) and how vegetation
growth and seasonal changes influence flow dynamics and sediment transport. This could
lead to a better understanding of utilizing natural vegetation in river management and
restoration projects.
6) Climate Change Impacts: As climate change alters river environments, future research

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should investigate how changes in temperature, ice cover duration, and flow regimes affect
the interaction between spur dikes, vegetation, and river dynamics. Understanding these
impacts will be crucial for adapting river management practices to changing environmental
conditions.

6.7.2 Interdisciplinary River Science
The intersection of river hydraulics with stream ecology and fluvial geomorphology
continues to attract significant academic interest, particularly in understanding how channel
obstructions like spur dikes and vegetated pools influence flow dynamics, sediment transport,
and habitat formation. While these disciplines have traditionally operated in specialized silos,
addressing similar issues from different perspectives, the need for interdisciplinary
collaboration is increasingly recognized as essential for achieving more comprehensive
solutions.
Spur dikes and vegetated pools play critical roles in shaping river morphology and
improving aquatic habitats. Spur dikes, for instance, create stable pools and tributary regions
that offer refuge for aquatic organisms and enhance habitat diversity. Meanwhile, vegetated
pools modulate flow velocity and sediment deposition, contributing to the stability of
riverbanks and the health of aquatic ecosystems. Despite these benefits, research in these
areas remains discipline-specific, limiting the potential for cross-disciplinary innovation.
Future research must embrace interdisciplinary frameworks integrating hydraulic,
ecological, and geomorphological perspectives to advance understanding of these complex
interactions. Such collaboration will improve the design and implementation of river
204

management strategies and foster sustainable relationships between human activities and
natural systems. By bridging the gaps between disciplines, researchers can develop more
effective solutions for river restoration and conservation, benefiting both the scientific
community and the environment.

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BIBLIOGRAPHY
Abdolahpour, M., Ghisalberti, M., Mcmahon, K., & Lavery, P. (2020). Material Residence Time in Marine
Canopies Under Wave-Driven Flows.
Abeysingha, N., Singh, M., Sehgal, V., Khanna, M., Pathak, D. S., Jayakody, P., & Srinivasan, R. (2015).
Assessment of water yield and evapotranspiration over 1985 to 2010 in the Gomti River basin in
India using the SWAT model. Current Science, 108, 25–2015.
Abid, A. (2020). Analytical and numerical models for velocity profile in vegetated open-channel flows.
https://doi.org/10.13140/RG.2.2.35075.07207
Ackermann, N. L., Shen, H. T., & Olsson, p. (2002). Local Scour Around Circular Piers Under Ice Covers.
Proceedings of the 16th IAHR International Symposium on Ice. 16th IAHR International
Symposium on Ice, Dunedin. https://www.iahr.org/library/infor?pid=19865
Afzalimehr, H., & Rennie, C. D. (2009). Determination of bed shear stress in gravel-bed rivers using
boundary-layer
parameters.
Hydrological
Sciences
Journal,
54(1),
147–159.
https://doi.org/10.1623/hysj.54.1.147
Ahmad,

M.
(1953).
Experiments
On
Design
And
Behavior
Of
Spur
Dikes.
https://www.semanticscholar.org/paper/Experiments-On-Design-And-Behavior-Of-Spur-DikesAhmad/e9abf616e32a1a4b551ac1a6661bc9c77e948196#citing-papers

Alasadi, L., Alabedi, T., & Abdulabbas Hassan, F. (2023). Experimental investigation for the local scour
around V-shaped spur-dikes. Scientific Review Engineering and Environmental Studies (SREES),
32, 69–86. https://doi.org/10.22630/srees.4506
Alireza, K., Mehdi, V., & James, B. (2010). Experimental Study of the Effects of Submerged Dikes on the
Energy and Momentum Coefficients in Compound Channel. Engineering, 2010.
https://doi.org/10.4236/eng.2010.211108
Allan, J. D. (2004). Landscapes and Riverscapes: The Influence of Land Use on Stream Ecosystems. Annu.
Rev. Ecol. Evol. Syst, 35, 257–284. https://doi.org/10.1146/annurev.ecolsys.35.120202.110122
Allan, J. D., Castillo, M. M., & Capps, K. A. (2021). Fluvial Geomorphology. In J. D. Allan, M. M. Castillo,
& K. A. Capps (Eds.), Stream Ecology: Structure and Function of Running Waters (pp. 45–73).
Springer International Publishing. https://doi.org/10.1007/978-3-030-61286-3_3
Apsilidis, N., Diplas, P., Dancey, C., Vlachos, P., & Raben, S. (2010). Local Scour at Bridge Piers: The Role
of Reynolds Number on Horseshoe Vortex Dynamics. In Geotechnical Special Publication (p. 94).
https://doi.org/10.1061/41147(392)7
Aydogdu, M. (2023). Analysis of the effect of rigid vegetation patches on the hydraulics of an open channel

206

flow with Realizable k-ε and Reynolds stress turbulence models. Flow Measurement and
Instrumentation, 94, 102477. https://doi.org/10.1016/j.flowmeasinst.2023.102477
Bahrami-Yarahmadi, M., Pagliara, S., Yabarehpour, E., & Najafi, N. (2020). Study of Scour and Flow
Patterns around Triangular-Shaped Spur Dikes. KSCE Journal of Civil Engineering, 24(11), 3279–
3288. https://doi.org/10.1007/s12205-020-2261-x
Barahimi, M., & Sui, J. (2023). Effects of Submerged Vegetation Arrangement Patterns and Density on Flow
Structure. Water, 15(1), Article 1. https://doi.org/10.3390/w15010176
Barahimi, M., & Sui, J. (2024a). Deformation of vegetated channel bed under ice-covered flow conditions.
Journal of Hydrology, 636, 131280. https://doi.org/10.1016/j.jhydrol.2024.131280
Barahimi, M., & Sui, J. (2024b). Flow structure and shear stress in the presence of both ice cover on water
surface and leafless vegetation in channel bed. Journal of Hydrodynamics, 36(2), 340–354.
https://doi.org/10.1007/s42241-024-0021-y
Barbhuiya, A. K., & Dey, S. (2004). Measurement of turbulent flow field at a vertical semicircular cylinder
attached to the sidewall of a rectangular channel. Flow Measurement and Instrumentation, 15(2),
87–96. https://doi.org/10.1016/j.flowmeasinst.2003.11.002
BC Ministry of Agriculture and Lands. (2006). Winter Considerations—Ice formation, freezing index and
frost penetration (Fact Sheet 590.307-1; Livestock Watering, p. 4). BC Ministry of Agriculture and
Lands.
Beechie, T. J., Liermann, M., Beamer, E. M., & Henderson, R. (2005). A Classification of Habitat Types in
a Large River and Their Use by Juvenile Salmonids. Transactions of the American Fisheries Society,
134(3), 717–729. https://doi.org/10.1577/T04-062.1
Beltaos, S. (2008). Progress in the study and management of river ice jams. Cold Regions Science and
Technology, 51(1), 2–19. https://doi.org/10.1016/j.coldregions.2007.09.001
Beltaos, S., & Bonsal, B. (2021). Climate change impacts on Peace River ice thickness and implications to
ice-jam flooding of Peace-Athabasca Delta, Canada. Cold Regions Science and Technology, 186,
103279. https://doi.org/10.1016/j.coldregions.2021.103279
Bisson, P. A., Sullivan, K., & Nielsen, J. L. (1988). Channel Hydraulics, Habitat Use, and Body Form of
Juvenile Coho Salmon, Steelhead, and Cutthroat Trout in Streams. Transactions of the American
Fisheries
Society,
117(3),
262–273.
https://doi.org/10.1577/15488659(1988)117<0262:CHHUAB>2.3.CO;2
Blanckaert, K., Duarte, A., & Schleiss, A. J. (2010). Influence of shallowness, bank inclination and bank
roughness on the variability of flow patterns and boundary shear stress due to secondary currents in
straight
open-channels.
Advances
in
Water
Resources,
33(9),
1062–1074.

207

https://doi.org/10.1016/j.advwatres.2010.06.012
Boulange, J., Hanasaki, N., Yamazaki, D., & Pokhrel, Y. (2021). Role of dams in reducing global flood
exposure
under
climate
change.
Nature
Communications,
12(1),
417.
https://doi.org/10.1038/s41467-020-20704-0
Bouma, T. J., De Vries, M. B., Low, E., Peralta, G., Tánczos, I. C., van de Koppel, J., & Herman, P. M. J.
(2005). Trade-Offs Related to Ecosystem Engineering: A Case Study on Stiffness of Emerging
Macrophytes. Ecology, 86(8), 2187–2199. https://doi.org/10.1890/04-1588
Briganti, R., Musumeci, R. E., Bellotti, G., Brocchini, M., & Foti, E. (2004). Boussinesq modeling of
breaking waves: Description of turbulence. Journal of Geophysical Research: Oceans, 109(C7).
https://doi.org/10.1029/2003JC002065
Brookes, A. (1987). River channel adjustments downstream from channelization works in England and
Wales.
Earth
Surface
Processes
and
Landforms,
12(4),
337–351.
https://doi.org/10.1002/esp.3290120402
Brunner, G. (2016). HEC-RAS River Analysis System User’s Manual Version 5.0.4 (Computer Program
Documentation 0704–0188). Institute for Water Resource.
Buffington, J. M., Montgomery, D. R., & Greenberg, H. M. (2004). Basin-scale availability of salmonid
spawning gravel as influenced by channel type and hydraulic roughness in mountain catchments.
Canadian Journal of
Fisheries and Aquatic Sciences,
61(11), 2085–2096.
https://doi.org/10.1139/f04-141
Calderon, M. S., & An, K.-G. (2016). An influence of mesohabitat structures (pool, riffle, and run) and landuse pattern on the index of biological integrity in the Geum River watershed. Journal of Ecology
and Environment, 40(1), 13. https://doi.org/10.1186/s41610-016-0018-8
Carling, P. A. (1991). An appraisal of the velocity-reversal hypothesis for stable pool-riffle sequences in the
river severn, England. Earth Surface Processes and Landforms, 16(1), 19–31.
https://doi.org/10.1002/esp.3290160104
Carollo, F., Ferro, V., & Termini, D. (2002). Flow Velocity Measurements in Vegetated Channels. Journal of
Hydraulic Engineering-Asce - J HYDRAUL ENG-ASCE, 128. https://doi.org/10.1061/(ASCE)07339429(2002)128:7(664)
Caroppi, G., Västilä, K., Gualtieri, P., Järvelä, J., Giugni, M., & Rowiński, P. M. (2021). Comparison of
Flexible and Rigid Vegetation Induced Shear Layers in Partly Vegetated Channels. Water Resources
Research, 57(3), e2020WR028243. https://doi.org/10.1029/2020WR028243
Carr, M. L., & Tuthill, A. M. (2012). Modeling of Scour-Inducing Ice Effects at Melvin Price Lock and Dam.
Journal of Hydraulic Engineering, 138(1), 85–92. https://doi.org/10.1061/(ASCE)HY.1943-

208

7900.0000483
Çengel, Y. A., & Cimbala, J. M. (2014). Chapter Eight: Internal Flow. In Fluid Mechanics: Fundamentals
and
Applications
(3rd
ed.,
pp.
347–437).
McGraw-Hill
Education.
https://www.mheducation.ca/fluid-mechanics-fundamentals-and-applications-9781259696534can-group
Chabert, J., & Engelrndinger, P. (1956). Etude des affouillements autourdes piles de ponts [Study of scour
around bridge piers]. LaboratoriesNational d’Hydraulique.
Chanson, H. (2004). Physical Modelling of Hydraulics. In Hydraulics of Open Channel Flow: An
Introduction Basic Principles, Sediment Motion, Hydraulic Modelling, Design of Hydraulic
Structures
(2nd
ed.,
pp.
253–274).
https://www.sciencedirect.com/book/9780750659789/hydraulics-of-open-channel-flow
Chen, W., & Olden, J. D. (2017). Designing flows to resolve human and environmental water needs in a
dam-regulated river. Nature Communications, 8(1), 2158. https://doi.org/10.1038/s41467-01702226-4
Chen, Y.-C., Kao, S.-P., Lin, J.-Y., & Yang, H.-C. (2009). Retardance coefficient of vegetated channels
estimated by the Froude number. Ecological Engineering, 35(7), 1027–1035.
https://doi.org/10.1016/j.ecoleng.2009.03.002
Chen, Z., Zheng, X., & Shen, L. (2019, January 1). Numerical Study on Influence of Oriented Groin Angle
on Hydraulic Characteristics of Curved Water Flow. https://doi.org/10.2991/masta-19.2019.40
Chipongo, K., Khiadani, M., & Sookhak Lari, K. (2020). Comparison and verification of turbulence
Reynolds-averaged Navier–Stokes closures to model spatially varied flows. Scientific Reports,
10(1), 19059. https://doi.org/10.1038/s41598-020-76128-9
Conde-Frias, M., Ghisalberti, M., Lowe, R. J., Abdolahpour, M., & Etminan, V. (2023). The Near-Bed Flow
Structure and Bed Shear Stresses Within Emergent Vegetation. Water Resources Research, 59(4),
e2022WR032499. https://doi.org/10.1029/2022WR032499
Cui, H., Felder, S., & Kramer, M. (2023). Predicting flow resistance in open-channel flows with submerged
vegetation. Environmental Fluid Mechanics, 23(4), 757–778. https://doi.org/10.1007/s10652-02309929-x
Cui, J., & Neary, V. (2008). LES study of turbulent flows with submerged vegetation. Journal of Hydraulic
Research - J HYDRAUL RES, 46, 307–316. https://doi.org/10.3826/jhr.2008.3129
Cunha, D., & Veiga, L. (1970). Discussion of “Local Scour Around Bridge Piers.” Journal of the Hydraulics
Division, 96(8), 1742–1747. https://doi.org/10.1061/JYCEAJ.0002655

209

de Almeida, G. A. M., & Rodríguez, J. F. (2011). Understanding pool-riffle dynamics through continuous
morphological
simulations.
Water
Resources
Research,
47(1).
https://doi.org/10.1029/2010WR009170
de Lima, P. H. S., Janzen, J. G., & Nepf, H. M. (2015). Flow patterns around two neighboring patches of
emergent vegetation and possible implications for deposition and vegetation growth. Environmental
Fluid Mechanics, 15(4), 881–898. https://doi.org/10.1007/s10652-015-9395-2
Dehrashid, F. A., Heidari, M., Rahimi, H., Khoshkonesh, A., Yuan, S., Tang, X., Lu, C., & Wang, X. (2023).
CFD modeling the flow dynamics in an open channel with double-layered vegetation. Modeling
Earth Systems and Environment, 9(1), 543–555. https://doi.org/10.1007/s40808-022-01513-4
Dey, S., & Barbhuiya, A. K. (2005). Time Variation of Scour at Abutments. Journal of Hydraulic
Engineering, 131(1), 11–23. https://doi.org/10.1061/(ASCE)0733-9429(2005)131:1(11)
Dietrich, W. E., & Whiting, P. (1989). Boundary Shear Stress and Sediment Transport in River Meanders of
Sand and Gravel. In River Meandering (pp. 1–50). American Geophysical Union (AGU).
https://doi.org/10.1029/WM012p0001
Du, S., Wu, G., Zhu, D. Z., Wang, R., Lu, Y., & Liang, B. (2022). Experimental study of local scour around
submerged square piles in combined waves and current. Ocean Engineering, 266, 113176.
https://doi.org/10.1016/j.oceaneng.2022.113176
Duró, G., Crosato, A., Kleinhans, M. G., Roelvink, D., & Uijttewaal, W. S. J. (2020). Bank Erosion Processes
in Regulated Navigable Rivers. Journal of Geophysical Research: Earth Surface, 125(7),
e2019JF005441. https://doi.org/10.1029/2019JF005441
Ebersole, J. L., Liss, W. J., & Frissell, C. A. (2003). Cold Water Patches in Warm Streams: Physicochemical
Characteristics and the Influence of Shading. JAWRA Journal of the American Water Resources
Association, 39(2), 355–368. https://doi.org/10.1111/j.1752-1688.2003.tb04390.x
El‐Hakim, O., & Salama, M. M. (1992). Velocity Distribution Inside and Above Branched Flexible
Roughness. Journal of Irrigation and Drainage Engineering, 118(6), 914–927.
https://doi.org/10.1061/(ASCE)0733-9437(1992)118:6(914)
Environment Canada. (2013, February 27). Avadepth. https://www2.pac.dfo-mpo.gc.ca/index-eng.html
Eraky, O. M., Eltoukhy, M. A. R., Abdelmoaty, M. S., & Farouk, E. (2022). Effect of rigid, bank vegetation
on velocity distribution and water surface profile in open channel. Water Practice and Technology,
17(7), 1445–1457. https://doi.org/10.2166/wpt.2022.068
Errico, A., Lama, G. F. C., Francalanci, S., Chirico, G. B., Solari, L., & Preti, F. (2019). Flow dynamics and
turbulence patterns in a drainage channel colonized by common reed (Phragmites australis) under
different scenarios of vegetation management. Ecological Engineering, 133, 39–52.

210

https://doi.org/10.1016/j.ecoleng.2019.04.016
Ettema, R., Melville, B. W., & Barkdoll, B. (1998). Scale Effect in Pier-Scour Experiments. Journal of
Hydraulic
Engineering,
124(6),
639–642.
https://doi.org/10.1061/(ASCE)07339429(1998)124:6(639)
Farhadi, A., Mayrhofer, A., Tritthart, M., Glas, M., & Habersack, H. (2018). Accuracy and comparison of
standard k-ϵ with two variants of k-ω turbulence models in fluvial applications. Engineering
Applications
of
Computational
Fluid
Mechanics,
12(1),
216–235.
https://doi.org/10.1080/19942060.2017.1393006
Farshad, R., Kashefipour, S. M., Ghomeshi, M., & Oliveto, G. (2022). Temporal Scour Variations at
Permeable and Angled Spur Dikes under Steady and Unsteady Flows. Water, 14(20), Article 20.
https://doi.org/10.3390/w14203310
Feddersen, F., & Williams, A. J. (2007). Direct Estimation of the Reynolds Stress Vertical Structure in the
Nearshore. Journal of Atmospheric and Oceanic Technology, 24(1), 102–116.
https://doi.org/10.1175/JTECH1953.1
Federal Highway Administration. (2001). Evaluating Scour at Bridges (FHWA-NHI-01-001; Hydraulic
Engineering Circular No. 18). Federal Highway Administration.
Finotello, A., Ielpi, A., Lapôtre, M. G. A., Lazarus, E. D., Ghinassi, M., Carniello, L., Favaro, S., Tognin, D.,
& D’Alpaos, A. (2024). Vegetation enhances curvature-driven dynamics in meandering rivers.
Nature Communications, 15(1), 1968. https://doi.org/10.1038/s41467-024-46292-x
Flow Science, Inc. (2023). FLOW-3D® Version 2023R1 Users Manual. Flow Science, Inc.
https://www.flow3d.com/
Froehlich,
D.
C.
(1989).
Local
scour
https://pubs.er.usgs.gov/publication/70015379

at

bridge

abutments.

13–18.

Froehlich, D. C. (1991). Analysis of onsite measurements of scour at piers. Proceedings of the ASCE
National Hydraulic Engineering Conference. https://www.usgs.gov/publications/analysis-onsitemeasurements-scour-piers
Fu, H., Wang, D., Li, W., Ren, B., & Yang, K. (2021). Velocity and turbulence characteristics in an open
channel with multi-row staggered vegetation patches. Journal of Hydrodynamics, 33(5), 1035–1044.
https://doi.org/10.1007/s42241-021-0091-z
Fuller, J. (2018). Defining Ordinary and Natural Conditions for State Navigability Determinations.
Gadissa, E. (2017). Estimation of Open Channel Roughness by using Gradual Varied Flow Profiles. Civil
Engineering Research Journal, 1(1). https://doi.org/10.19080/CERJ.2017.01.555552

211

Gazi, A. H., & Afzal, M. S. (2020). A review on hydrodynamics of horseshoe vortex at a vertical cylinder
mounted on a flat bed and its implication to scour at a cylinder. Acta Geophysica, 68(3), 861–875.
https://doi.org/10.1007/s11600-020-00439-8
Giglou, A. N., Mccorquodale, J. A., & Solari, L. (2018). Numerical study on the effect of the spur dikes on
sedimentation
pattern.
Ain
Shams
Engineering
Journal,
9(4),
2057–2066.
https://doi.org/10.1016/j.asej.2017.02.007
Goring, D. G., & Nikora, V. I. (2002). Despiking Acoustic Doppler Velocimeter Data. Journal of Hydraulic
Engineering, 128(1), 117–126. https://doi.org/10.1061/(ASCE)0733-9429(2002)128:1(117)
Gray, W., & Miller, C. (2023). On the equations of open channel flow. Journal of Hydraulic Research, 61(1),
1–17. https://doi.org/10.1080/00221686.2022.2106597
Gretler, W., & Meile, W. (1997). Calculation of plane turbulent Couette-Poiseuille flows with a modified kε model. Fluid Dynamics Research, 21(4), 263–283. https://doi.org/10.1016/S01695983(97)00012-9
Guan, D., Xie, Y., Yao, Z., Chiew, Y.-M., Zhang, J., & Zheng, J. (2022). Local scour at offshore windfarm
monopile foundations: A review. Water Science and Engineering, 15(1), 29–39.
https://doi.org/10.1016/j.wse.2021.12.006
Gul, H., Ijaz, N., Vanicek, I., Rehman, Z. ur, Ijaz, Z., Hassan, G. Z., & Rahim, S. A. (2024). State-of-the-art
review on stability and serviceability of dikes as a flood infrastructure and their comprehensive
assessment in Indus Plain considering global climate change. Natural Hazards.
https://doi.org/10.1007/s11069-024-06836-2
Gurnell, A. M., Bertoldi, W., & Corenblit, D. (2012). Changing river channels: The roles of hydrological
processes, plants and pioneer fluvial landforms in humid temperate, mixed load, gravel bed rivers.
Earth-Science Reviews, 111(1), 129–141. https://doi.org/10.1016/j.earscirev.2011.11.005
Hains, D. B., & Zabilansky, L. J. (2012). Scour under Ice: Potential Contributing Factor in the Schoharie
Creek Bridge Collapse. 1–9. https://doi.org/10.1061/40836(210)17
Hains, D., & Zabilansky, L. (2004). Laboratory Test of Scour Under Ice: Data and Preliminary Results
(ERDC/CRREL TR-04-9; p. 182). U.S Army Engineer Research and Development Center, Cold
Regions Research and Engineering Laboratory.
Hains, M. D. B., & Zabilansky, L. (2005). The Effects of River Ice on Scour and Sediment Transport. 13th
Workshop on the Hydraulics of Ice Covered Rivers, Hanover, NH.
Halket, I. H., & Snelgrove, K. R. (2012). Implications of Pool and Riffle Sequences for Water Quality
Modeling. 1–12. https://doi.org/10.1061/40763(178)61

212

Han, D., Xiong, J., Xie, X., & Lin, Y. (2021). Effects of emergent and submerged rigid vegetation
configurations on gravity current dynamics. Environmental Fluid Mechanics, 21(5), 1165–1187.
https://doi.org/10.1007/s10652-021-09814-5
HAN, X., Lin, P., & Parker, G. (2019). 3D NUMERICAL STUDY ON LOCAL SCOUR AROUND SPUR
DIKES WITH DIFFERENT LAYOUT ANGLES (p. 1594). https://doi.org/10.3850/38WC0920190394
Han, X., Lin, P., & Parker, G. (2022). Influence of layout angles on river flow and local scour in grouped
spur dikes field. Journal of Hydrology, 614, 128502. https://doi.org/10.1016/j.jhydrol.2022.128502
Hao, S., Xia, Y., Xu, H., & Wen, Y.-C. (2013). Review of local scour around submerged spur-dike.
Harrison, L. R., Legleiter, C. J., Wydzga, M. A., & Dunne, T. (2011). Channel dynamics and habitat
development in a meandering, gravel bed river. Water Resources Research, 47(4).
https://doi.org/10.1029/2009WR008926
Hei, P., Chen, Z., & Ding, X. (2009). Sediment Carrying Capacity of Open Channel Flow Around Spur Dike.
In C. Zhang & H. Tang (Eds.), Advances in Water Resources and Hydraulic Engineering (pp. 928–
932). Springer. https://doi.org/10.1007/978-3-540-89465-0_163
Heller, V. (2011). Scale effects in physical hydraulic engineering models. Journal of Hydraulic Research,
49(3), 293–306. https://doi.org/10.1080/00221686.2011.578914
Hirt, C. W., & Nichols, B. D. (1981). Volume of fluid (VOF) method for the dynamics of free boundaries.
Journal of Computational Physics, 39(1), 201–225. https://doi.org/10.1016/0021-9991(81)90145-5
Hong, V., Zhang, G., Wang, X., & Li, A. (2019). Experimental Investigation on the Shape and Depth of Local
Scour Hole Downstream of the Release Structure. World Journal of Engineering and Technology,
8(1), Article 1. https://doi.org/10.4236/wjet.2020.81010
Horvat, Z., Isic, M., & Spasojevic, M. (2015). Two dimensional river flow and sediment transport model.
Environmental Fluid Mechanics, 15(3), 595–625. https://doi.org/10.1007/s10652-014-9375-y
Hsieh, P.-C., & Shiu, Y.-S. (2006). Analytical solutions for water flow passing over a vegetal area. Advances
in Water Resources, 29(9), 1257–1266. https://doi.org/10.1016/j.advwatres.2005.10.004
Hu, H., Wang, J., Cheng, T., Hou, Z., & Sui, J. (2022). Channel Bed Deformation and Ice Jam Evolution
around Bridge Piers. Water, 14(11), Article 11. https://doi.org/10.3390/w14111766
Huai, W., Zhang, J., Katul, G. G., Cheng, Y., Tang, X., & Wang, W. (2019). The structure of turbulent flow
through submerged flexible vegetation. Journal of Hydrodynamics, 31(2), 274–292.
https://doi.org/10.1007/s42241-019-0023-3

213

Huang, H., Zhang, H., Zhong, D., & Zhang, Y. J. (2019). Turbulent mechanisms in open channel sedimentladen flows.
International Journal of Sediment Research, 34(6), 550–563.
https://doi.org/10.1016/j.ijsrc.2019.06.002
Huang, T., Lu, Y., & Liu, H. (2019). Effects of Spur Dikes on Water Flow Diversity and Fish Aggregation.
Water, 11(9), Article 9. https://doi.org/10.3390/w11091822
Jafari, R., & Sui, J. (2021). Velocity Field and Turbulence Structure around Spur Dikes with Different Angles
of Orientation under Ice Covered Flow Conditions. Water, 13(13), Article 13.
https://doi.org/10.3390/w13131844
Jafari, R., & Sui, J. (2024). Channel deformation around non-submerged spur dikes with different alignment
angles under ice cover. Journal of Hydrology and Hydromechanics, 72.
https://doi.org/10.2478/johh-2024-0014
Jansen, P. P. (1979). Principles of River Engineering: The Non-tidal Alluvial River. Pitman.
Jing, S., Yang, W., & Chen, Y. (2019). Smooth Open Channel with Increasing Aspect Ratio: Influence on
Secondary Flow. Water, 11(9), Article 9. https://doi.org/10.3390/w11091872
Jing, S. (景思雨), Duan, Y. (段炎冲), & Li, D. (李丹勋). (2023). A quantitative study on the turbulent kinetic
energy redistribution in the near free-water-surface region of open channel flows. AIP Advances,
13(3), 035129. https://doi.org/10.1063/5.0138423
John, C. K., Pu, J. H., Guo, Y., Hanmaiahgari, P. R., & Pandey, M. (2023). Flow turbulence presented by
different vegetation spacing sizes within a submerged vegetation patch. Journal of Hydrodynamics,
35(6), 1131–1145. https://doi.org/10.1007/s42241-024-0083-x
Jordanova, A. A., & James, C. S. (2003). Experimental Study of Bed Load Transport through Emergent
Vegetation. Journal of Hydraulic Engineering, 129(6), 474. https://doi.org/10.1061/(ASCE)07339429(2003)129:6(474)
Julien, P. Y. (2018). Steady Flow in Rivers. In River Mechanics (2nd ed., pp. 116–152). Cambridge
University Press. https://doi.org/10.1017/9781316107072
Kang, D. G., Na, H., & Lee, C. Y. (2019). Detached eddy simulation of turbulent and thermal mixing in a Tjunction. Annals of Nuclear Energy, 124, 245–256. https://doi.org/10.1016/j.anucene.2018.10.006
Karadimou, D. P., Markatos, N.-C., Karadimou, D. P., & Markatos, N.-C. (2018). Study of the Numerical
Diffusion in Computational Calculations. In Numerical Simulations in Engineering and Science.
IntechOpen. https://doi.org/10.5772/intechopen.75660
Keshavarzi, A., Shrestha, C. K., Zahedani, M. R., Ball, J., & Khabbaz, H. (2018). Experimental study of
flow structure around two in-line bridge piers. Proceedings of the Institution of Civil Engineers -

214

Water Management, 171(6), 311–327. https://doi.org/10.1680/jwama.16.00104
Khan, M., Muzzammil, M., & Alam, J. (2016). Bridge Pier Scour: A review of mechanism, causes and
geotechnical aspects.
Khanarmuei, M., Akutina, Y., Dupuis, V., Eiff, O., Trevisson, M., Suara, K., & Brown, R. (2020, August 27).
Secondary Currents in Smooth Wall Open-Channel Flow.
Kim, S.-C., Friedrichs, C. T., Maa, J. P.-Y., & Wright, L. D. (2000). Estimating Bottom Stress in Tidal
Boundary Layer from Acoustic Doppler Velocimeter Data. Journal of Hydraulic Engineering,
126(6), 399–406. https://doi.org/10.1061/(ASCE)0733-9429(2000)126:6(399)
Kline, S. J., Reynolds, W. C., Schraub, F. A., & Runstadler, P. W. (1967). The structure of turbulent boundary
layers. Journal of Fluid Mechanics, 30(4), 741–773. https://doi.org/10.1017/S0022112067001740
Knight, D. W., & Macdonald, J. A. (1979). Open Channel Flow with Varying Bed Roughness. Journal of the
Hydraulics Division, 105(9), 1167–1183. https://doi.org/10.1061/JYCEAJ.0005274
Koftis, T., & Prinos, P. (2018). Reynolds stress modelling of flow in compound channels with vegetated
floodplains. Journal of Applied Water Engineering and Research, 6(1), 17–27.
https://doi.org/10.1080/23249676.2016.1209437
Kohyama, K. (神山 一貴), Sano, M. (佐野 雅己), & Tsukahara, T. (塚原 隆裕). (2022). Sidewall effect on
turbulent band in subcritical transition of high-aspect-ratio duct flow. Physics of Fluids, 34(8),
084112. https://doi.org/10.1063/5.0096626
Koken, M., & Constantinescu, G. (2008a). An investigation of the flow and scour mechanisms around
isolated spur dikes in a shallow open channel: 1. Conditions corresponding to the initiation of the
erosion
and
deposition
process.
Water
Resources
Research,
44(8).
https://doi.org/10.1029/2007WR006489
Koken, M., & Constantinescu, G. (2008b). An investigation of the flow and scour mechanisms around
isolated spur dikes in a shallow open channel: 2. Conditions corresponding to the final stages of the
erosion and deposition process. Water Resources Research - WATER RESOUR RES, 44.
https://doi.org/10.1029/2007WR006491
Koken, M., & Constantinescu, G. (2021). Flow structure inside and around a rectangular array of rigid
emerged cylinders located at the sidewall of an open channel. Journal of Fluid Mechanics, 910, A2.
https://doi.org/10.1017/jfm.2020.900
Koken, M., & Gogus, M. (2015). Effect of spur dike length on the horseshoe vortex system and the bed shear
stress
distribution.
Journal
of
Hydraulic
Research,
53(2),
196–206.
https://doi.org/10.1080/00221686.2014.967819

215

Kondolf, G. M. (1997). PROFILE: Hungry Water: Effects of Dams and Gravel Mining on River Channels.
Environmental Management, 21(4), 533–551. https://doi.org/10.1007/s002679900048
Kondziolka, J. M., & Nepf, H. M. (2014). Vegetation wakes and wake interaction shaping aquatic landscape
evolution. Limnology and Oceanography: Fluids and Environments, 4(1), 106–119.
https://doi.org/10.1215/21573689-2846314
Kothyari, U. C., & Ranga Raju, K. G. (2001). Scour around spur dikes and bridge abutments. Journal of
Hydraulic Research, 39(4), 367–374. https://doi.org/10.1080/00221680109499841
Kouwen, N., Unny, T. E., & Hill, H. M. (1969). Flow Retardance in Vegetated Channels. Journal of the
Irrigation and Drainage Division, 95(2), 329–342. https://doi.org/10.1061/JRCEA4.0000652
Kuhnle, R. A., Alonso, C. V., & Shields, F. D. (2002). Local Scour Associated with Angled Spur Dikes.
Journal of Hydraulic Engineering, 128(12), 1087–1093. https://doi.org/10.1061/(ASCE)07339429(2002)128:12(1087)
Kuhnle, R. A., Jia, Y., & Alonso, C. V. (2008). Measured and Simulated Flow near a Submerged Spur Dike.
Journal of Hydraulic Engineering, 134(7), 916–924. https://doi.org/10.1061/(ASCE)07339429(2008)134:7(916)
Kumar, A., & Ojha, C. S. P. (2021). Review on the Field Applications of River Training Structures for River
Bank Protection. In M. S. Chauhan & C. S. P. Ojha (Eds.), The Ganga River Basin: A
Hydrometeorological Approach (pp. 115–133). Springer International Publishing.
https://doi.org/10.1007/978-3-030-60869-9_8
Kumar, P., Kumar, A., & Sharma, A. (2024). Numerical modeling of turbulent flow interactions with
vegetation in channels with fixed beds. Modeling Earth Systems and Environment, 10(3), 4337–
4360. https://doi.org/10.1007/s40808-024-02025-z
Lama, G. F. C., Errico, A., Francalanci, S., Solari, L., Preti, F., & Chirico, G. B. (2020). Evaluation of Flow
Resistance Models Based on Field Experiments in a Partly Vegetated Reclamation Channel.
Geosciences (Switzerland), 10, 47. https://doi.org/10.3390/geosciences10020047
Laursen, E. M. (1963). An Analysis of Relief Bridge Scour. Journal of the Hydraulics Division, 89(3), 93–
118. https://doi.org/10.1061/JYCEAJ.0000896
Le Minor, M., Zimmer, M., Helfer, V., Gillis, L. G., & Huhn, K. (2021). Chapter 4—Flow and sediment
dynamics around structures in mangrove ecosystems—A modeling perspective. In F. Sidik & D. A.
Friess (Eds.), Dynamic Sedimentary Environments of Mangrove Coasts (pp. 83–120). Elsevier.
https://doi.org/10.1016/B978-0-12-816437-2.00012-4
Lee, H. C., & Wahab, A. K. A. (2019). Performance of different turbulence models in predicting flow
kinematics around an open offshore intake. SN Applied Sciences, 1(10), 1266.

216

https://doi.org/10.1007/s42452-019-1320-8
Lee, S. O., & Sturm, T. W. (2009). Effect of Sediment Size Scaling on Physical Modeling of Bridge Pier
Scour.
Journal
of
Hydraulic
Engineering,
135(10),
793–802.
https://doi.org/10.1061/(ASCE)HY.1943-7900.0000091
Lei, Y., Hassan, M. A., Viparelli, E., Chartrand, S. M., An, C., Fu, X., & Hu, C. (2023). The Effect of
Sediment Supply on Pool-Riffle Morphology. Water Resources Research, 59(11), e2023WR035983.
https://doi.org/10.1029/2023WR035983
Leopold, L. B., & Wolman, M. G. (1957). River channel patterns: Braided, meandering, and straight (USGS
Numbered Series 282; Professional Paper). U.S. Geological Survey; USGS Publications Warehouse.
10.3133/pp282B
Li, C. W., & Yu, L. H. (2010). Hybrid LES/RANS modelling of free surface flow through vegetation.
Computers & Fluids, 39(9), 1722–1732. https://doi.org/10.1016/j.compfluid.2010.06.009
Li, G., Lang, L., & Ning, J. (2013). 3D Numerical Simulation of Flow and Local Scour around a Spur Dike.
Li, G., Sui, J., Sediqi, S., & Dziedzic, M. (2023). Local scour around submerged angled spur dikes under ice
cover. International Journal of Sediment Research. https://doi.org/10.1016/j.ijsrc.2023.08.003
Li, J., He, C., Huang, Q., & Li, L. (2024). Spatiotemporal dynamics of flood regulation service under the
joint impacts of climate change and Urbanization: A case study in Baiyangdian Lake Basin, China.
Ecological Indicators, 158, 111318. https://doi.org/10.1016/j.ecolind.2023.111318
Li, S. S. (2012). Estimates of the Manning’s coefficient for ice-covered rivers. Proceedings of the Institution
of Civil Engineers - Water Management, 165(9), 495–505. https://doi.org/10.1680/wama.11.00017
Li, Y.-H., Xie, L., & Su, T. (2018). Resistance of Open-Channel Flow under the Effect of Bending
Deformation of Submerged Flexible Vegetation. Journal of Hydraulic Engineering, 144(3),
04017072. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001419
Li, Y.-T., Zhan, J.-M., & Wai, W.-H. O. (2024). A study of the effect of local scour on the flow field near the
spur
dike.
Theoretical
and
Applied
Mechanics
Letters,
14(2),
100510.
https://doi.org/10.1016/j.taml.2024.100510
Liao, C.-T., Yeh, K.-C., & Huang, M.-W. (2014). Development and application of 2-D mobile-bed model
with bedrock river evolution mechanism. Journal of Hydro-Environment Research, 8(3), 210–222.
https://doi.org/10.1016/j.jher.2013.03.001
Liao, C.-T., Yeh, K.-C., Lan, Y.-C., Jhong, R.-K., & Jia, Y. (2021). Improving the 2D Numerical Simulations
on
Local
Scour
Hole
around
Spur
Dikes.
Water,
13(11), Article
11.
https://doi.org/10.3390/w13111462

217

Lim, S.-Y. (1997). Equilibrium Clear-Water Scour around an Abutment. Journal of Hydraulic Engineering,
123(3), 237–243. https://doi.org/10.1061/(ASCE)0733-9429(1997)123:3(237)
Lisle, T. (1986). Stabilization of a gravel channel by large streamside obstructions and bedrock bends, Jacoby
Creek, northwestern California. GSA Bulletin, 97(8), 999–1011.
Lisle, T. E., & Hilton, S. (1992). The Volume of Fine Sediment in Pools: An Index of Sediment Supply in
Gravel-Bed Streams. JAWRA Journal of the American Water Resources Association, 28(2), 371–
383. https://doi.org/10.1111/j.1752-1688.1992.tb04003.x
Liu, D., Lv, S., & Li, C. (2024). Impact of Spur Dike Placement on Flow Dynamics in Curved River Channels:
A CFD Study on Pick Angle and River-Width-Narrowing Rate. Water, 16(16), Article 16.
https://doi.org/10.3390/w16162236
Lodhi, A., Jain, R. K., & Sharma, P. (2015). Influence of cohesion on scour around submerged dike founded
in clay–sand–gravel mixtures. ISH Journal of Hydraulic Engineering, 22, 1–18.
https://doi.org/10.1080/09715010.2015.1075916
Lou, S., Chen, M., Ma, G., Liu, S., & Wang, H. (2022). Sediment suspension affected by submerged rigid
vegetation under waves, currents and combined wave–current flows. Coastal Engineering, 173,
104082. https://doi.org/10.1016/j.coastaleng.2022.104082
Lu, S. S., & Willmarth, W. W. (1973). Measurements of the structure of the Reynolds stress in a turbulent
boundary
layer.
Journal
of
Fluid
Mechanics,
60(3),
481–511.
https://doi.org/10.1017/S0022112073000315
Lu, Y., Cheng, N., Wei, M., & Ancey, C. (2024, April 14). Vegetation Submergence Effects on Bedload
Transport Rate. EGU General Assembly 2024, Vienna, Austria. https://doi.org/10.5194/egusphereegu24-9559, 2024
Maji, S., Pal, D., Hanmaiahgari, P., & Gupta, U. (2017). Hydrodynamics and turbulence in emergent and
sparsely vegetated open channel flow. Environmental Fluid Mechanics, 17.
https://doi.org/10.1007/s10652-017-9531-2
Masjedi, A., & Foroushani, E. (2012). Investigation of hydrodynamics on local scour by shape of single spur
dike in river bend. IOP Conference Series: Earth and Environmental Science, 15, 2025.
https://doi.org/10.1088/1755-1315/15/5/052025
McCoy, A., Constantinescu, G., & Weber, L. (2007). A numerical investigation of coherent structures and
mass exchange processes in channel flow with two lateral submerged groynes. Water Resources
Research, 43(5). https://doi.org/10.1029/2006WR005267
Melville, B. W. (1997). Pier and Abutment Scour: Integrated Approach. Journal of Hydraulic Engineering,
123(2), 125–136. https://doi.org/10.1061/(ASCE)0733-9429(1997)123:2(125)

218

Melville, B. W., & Coleman, S. E. (2000). Bridge Scour. Water Resources Publications.
https://www.wrpllc.com/books/bsr.html
Meng, X., Zhou, Y., Sun, Z., Ding, K., & Chong, L. (2021). Hydraulic Characteristics of Emerged Rigid and
Submerged Flexible Vegetations in the Riparian Zone. Water, 13, 1057.
https://doi.org/10.3390/w13081057
Mia, M. F., & Nago, H. (2003). Design Method of Time-Dependent Local Scour at Circular Bridge Pier.
Journal of Hydraulic Engineering, 129(6), 420–427. https://doi.org/10.1061/(ASCE)07339429(2003)129:6(420)
Mironov, D., Terzhevik, A., Kirillin, G., Jonas, T., Malm, J., & Farmer, D. (2002). Radiatively driven
convection in ice-covered lakes: Observations, scaling, and a mixed layer model. Journal of
Geophysical Research: Oceans, 107(C4), 7–1. https://doi.org/10.1029/2001JC000892
Mofrad, M., Parvizi, P., Afzalimehr, H., & Sui, J. (2023). Turbulence Kinetic Energy and High-Order
Moments of Velocity Fluctuations of Flows in the Presence of Submerged Vegetation in Pools.
Water, 15, 2170. https://doi.org/10.3390/w15122170
Montgomery, D., Buffington, J., Smith, R., Schmidt, K., & Pess, G. (1995). Pool Spacing in Forest Channels.
Water Resources Research, 31(4), 1097–1105.
Mosselman, E. (2018). Modelling in Applied Hydraulics: More Accurate in Decision-Making Than in
Science? In P. Gourbesville, J. Cunge, & G. Caignaert (Eds.), Advances in Hydroinformatics (pp.
741–749). Springer. https://doi.org/10.1007/978-981-10-7218-5_53
Mulahasan, S., Saleh, M. S., & Muhsun, S. S. (2023). Simulation of flow around a permeable dike using
physical and 3D-CFD models. International Journal of River Basin Management, 21(1), 53–65.
https://doi.org/10.1080/15715124.2021.1901726
Munteanu, A. (2004). Scouring around a cylindrical bridge pier under partially ice-covered flow condition
[University of Ottawa (Canada)]. http://hdl.handle.net/10393/26722
Nadaoka, K., & Yagi, H. (1998). Shallow-Water Turbulence Modeling and Horizontal Large-Eddy
Computation of River Flow. Journal of Hydraulic Engineering, 124(5), 493–500.
https://doi.org/10.1061/(ASCE)0733-9429(1998)124:5(493)
Nagy, H. (2005). Hydraulic evaluation of emerged and submerged spur-dikes: Temporal bed evolution and
equilibrium state characteristics. 44.
Nakajima, T., Asaeda, T., Fujino, T., & Nanda, A. (2006). Leaf Litter Decomposition in Aquatic and
Terrestrial Realms of a Second-Order Forested Stream System. Journal of Freshwater Ecology,
21(2), 259–263. https://doi.org/10.1080/02705060.2006.9664994

219

Namaee, M. R., & Sui, J. (2019). Effects of Ice Cover on the Incipient Motion of Bed Material and Shear
Stress around Side-by-Side Bridge Piers. Cold Regions Science and Technology, 165(0).
https://trid.trb.org/view/1632064
Namaee, M. R., & Sui, J. (2020). Velocity profiles and turbulence intensities around side-by-side bridge
piers under ice-covered flow condition. Journal of Hydrology and Hydromechanics, 68(1), 70–82.
https://doi.org/10.2478/johh-2019-0029
Namaee, M. R., Sui, J., Wu, P., Namaee, M. R., Sui, J., & Wu, P. (2019). Experimental Study of Local Scour
around Side-by-Side Bridge Piers under Ice-Covered Flow Conditions. In Current Practice in
Fluvial
Geomorphology—Dynamics
and
Diversity.
IntechOpen.
https://doi.org/10.5772/intechopen.86369
Namaee, M. R., Sui, J., Wu, Y., & Linklater, N. (2021). Three-dimensional numerical simulation of local
scour around circular side-by-side bridge piers with ice cover. Canadian Journal of Civil
Engineering, 48(10), 1335–1353. https://doi.org/10.1139/cjce-2019-0360
Namaee, M., & Sui, J. (2020). Velocity profiles and turbulence intensities around side-by-side bridge piers
under ice-covered flow condition. Journal of Hydrology and Hydromechanics, 68, 70–82.
https://doi.org/10.2478/johh-2019-0029
Namaee, M., Wu, P., & Dziedzic, M. (2023). Numerical Modeling of Local Scour in the Vicinity of Bridge
Abutments When Covered with Ice. Water, 15, 3330. https://doi.org/10.3390/w15193330
Nasrollahi, A., Ghodsian, M., & Salehi Neyshabouri, S. A. A. (2008). Local Scour at Permeable Spur Dikes.
Journal of Applied Sciences, 8. https://doi.org/10.3923/jas.2008.3398.3406
National Academies of Sciences, E. (2021). Revised Clear-Water and Live-Bed Contraction Scour Analysis.
https://doi.org/10.17226/26198
Nepf, H. M. (1999). Drag, turbulence, and diffusion in flow through emergent vegetation. Water Resources
Research, 35(2), 479–489. https://doi.org/10.1029/1998WR900069
Nepf, H. M. (2012). Flow and Transport in Regions with Aquatic Vegetation. Annual Review of Fluid
Mechanics, 44(Volume 44, 2012), 123–142. https://doi.org/10.1146/annurev-fluid-120710-101048
Nepf, H., & Vivoni, E. (2000). Flow structure in depth-limited, vegetated flow. Journal of Geophysical
Research, 105, 28547–28558. https://doi.org/10.1029/2000JC900145
Neter, J., Wasserman, W., & Kutner, M. H. (1991). Applied linear statistical models: Regression, analysis of
variance, and experimental designs (3rd ed.). Irwin.
Nezu, I., & Onitsuka, K. (2001). Turbulent structures in partly vegetated open-channel flows with LDA and
PI
V
measurements.
Journal
of
Hydraulic
Research.

220

https://www.tandfonline.com/doi/abs/10.1080/00221686.2001.9628292
Nikora, V. (2010). Hydrodynamics of aquatic ecosystems: An interface between ecology, biomechanics and
environmental fluid mechanics. River Research and Applications, 26(4), 367–384.
https://doi.org/10.1002/rra.1291
Ning, J., Li, G., & Li, S. (2019). Numerical Simulation of the Influence of Spur Dikes Spacing on Local
Scour and Flow. Applied Sciences, 9(11), Article 11. https://doi.org/10.3390/app9112306
Northwest Hydraulic Consultants. (2013). Nechako River 2013 Sediment Transport Investigations. Prepared
for Ministry of Forests, Lands and Renewable Resources.
Nosrati, K., Afzalimehr, H., & Sui, J. (2022). Interaction of Irregular Distribution of Submerged Rigid
Vegetation and Flow within a Straight Pool. Water, 14(13), Article 13.
https://doi.org/10.3390/w14132036
Nosrati, K., Afzalimehr, H., Sui, J., & Raeisifar, H. R. (2024). Characteristics of turbulent flow in 3-D pools
in the presence of submerged rigid vegetation in channel bed. Journal of Hydrodynamics, 36.
https://doi.org/10.1007/s42241-024-0009-7
Oğuz, K., & Bor, A. (2022). Prediction of Local Scour around Bridge Piers Using Hierarchical Clustering
and Adaptive Genetic Programming. Applied Artificial Intelligence, 36(1), 2001734.
https://doi.org/10.1080/08839514.2021.2001734
Okamoto, T., Nezu, I., & Ikeda, H. (2012). Vertical mass and momentum transport in open-channel flows
with submerged vegetations. Journal of Hydro-Environment Research, 6(4), 287–297.
https://doi.org/10.1016/j.jher.2012.03.002
Oliveto, G., & Hager, W. H. (2002). Temporal Evolution of Clear-Water Pier and Abutment Scour. Journal
of
Hydraulic
Engineering,
128(9),
811–820.
https://doi.org/10.1061/(ASCE)07339429(2002)128:9(811)
O’Neill, P. L., Nicolaides, D., Honnery, D., & Soria, J. (2004). Autocorrelation Functions and the
Determination of Integral Length with Reference to Experimental and Numerical Data. Proceeding
of the 15th Australasian Fluid Mechanics Conference, 1.
Özyaman, C., Yerdelen, C., Eris, E., & Daneshfaraz, R. (2022). Experimental investigation of scouring
around a single spur under clear water conditions. Water Supply, 22(3), 3484–3497.
https://doi.org/10.2166/ws.2021.389
Pan, D., & Li, Y. (2022). Tidal Bore Scour around a Spur Dike. Journal of Marine Science and Engineering,
10(8), Article 8. https://doi.org/10.3390/jmse10081086
Pan, J., Guo, X., Shen, H., Wang, T., Fu, H., Yongxin, G., Li, J., & Chen, Y. (2023). Transverse flow

221

distributions in ice‐covered channels. River, 2. https://doi.org/10.1002/rvr2.41
Pan, J., & Shen, H. T. (2022). Modeling ice cover effect on river channel bank stability. Environmental Fluid
Mechanics, 22(5), 1121–1133. https://doi.org/10.1007/s10652-022-09881-2
Pandey, M., Ahmad, Z., & Sharma, P. K. (2018). Scour around impermeable spur dikes: A review. ISH
Journal of Hydraulic Engineering, 24(1), 25–44. https://doi.org/10.1080/09715010.2017.1342571
Park, H., & Hwang, J. H. (2021). A Standard Criterion for Measuring Turbulence Quantities Using the FourReceiver Acoustic
Doppler
Velocimetry.
Frontiers
in
Marine
Science,
8.
https://www.frontiersin.org/articles/10.3389/fmars.2021.681265
Patel, H., Arora, S., Lade, A., Kumar, B., & Azamathulla, H. (2022). Flow behavior concerning bank stability
in the presence of spur dike- A review. Water Science & Technology Water Supply, 23.
https://doi.org/10.2166/ws.2022.418
Patel, H. K., Arora, S., Lade, A. D., Kumar, B., & Azamathulla, H. Md. (2022). Flow behaviour concerning
bank stability in the presence of spur dike – A review. Water Supply, 23(1), 237–258.
https://doi.org/10.2166/ws.2022.418
Patel, H. kumar, & Kumar, B. (2024). Experimental study on the optimal spur dike shape under downward
seepage. Water Science, 38(1), 172–191. https://doi.org/10.1080/23570008.2024.2321423
Paul, M., Bouma, T., & Amos, C. (2012). Wave attenuation by submerged vegetation: Combining the effect
of organism traits and tidal current. Marine Ecology Progress Series, 444, 31–41.
https://doi.org/10.3354/meps09489
Peña, E., & Anta, J. (2021). Editorial—Physical Modelling in Hydraulics Engineering. Water, 13(17), Article
17. https://doi.org/10.3390/w13172317
Pfister, M., & Chanson, H. (2014). Two-phase air-water flows: Scale effects in physical modeling. Journal
of Hydrodynamics, 26(2), 291–298. https://doi.org/10.1016/S1001-6058(14)60032-9
Pizarro, A., Manfreda, S., & Tubaldi, E. (2020). The Science behind Scour at Bridge Foundations: A Review.
Water, 12(2), Article 2. https://doi.org/10.3390/w12020374
Prowse, T., & Culp, J. (2011). Ice breakup: A neglected factor in river ecology. Canadian Journal of Civil
Engineering, 30, 128–144. https://doi.org/10.1139/l02-040
Qi, H., Wang, J., Zou, W., Luo, W., Tian, W., & Li, J. (2024). Characteristics and mechanism of local scour
reduction around spur dike using the collar in clear water. Scientific Reports, 14(1), 12299.
https://doi.org/10.1038/s41598-024-63131-7
Qiu, H., Li, P., Wang, W., Shi, P., Zhang, J., & Chen, H. (2024). Impacts of emergent rigid vegetation patches

222

on flow characteristics of open channels. Journal of Hydroinformatics, jh2024009.
https://doi.org/10.2166/hydro.2024.009
Rahimi, H., Fael, C. M. S., Taborda, C. S. B., Yuan, S., Tang, X., Singh, P. K., Fardoost, E., & Santos, C. A.
V. (2023). Numerical Modelling of Turbulence Kinetic Energy in Open Channel Flows with MixedLayer Vegetation. Water, 15(14), Article 14. https://doi.org/10.3390/w15142544
Rahimi, H. R., Tang, X., Singh, P., Li, M., & Alaghmand, S. (2020). Open channel flow within and above a
layered vegetation: Experiments and first-order closure modeling. Advances in Water Resources,
137, 103527. https://doi.org/10.1016/j.advwatres.2020.103527
Raudkivi, A. J., & Ettema, R. (1985). Scour at Cylindrical Bridge Piers in Armored Beds. Journal of
Hydraulic
Engineering,
111(4),
713–731.
https://doi.org/10.1061/(ASCE)07339429(1985)111:4(713)
Rehmel, M. (2007). Application of Acoustic Doppler Velocimeters for Streamflow Measurements. Journal
of Hydraulic Engineering, 133(12), 1433–1438. https://doi.org/10.1061/(ASCE)07339429(2007)133:12(1433)
Rezaie, A., Afzalimehr, H., Sohrabi, S., Nazari-Sharabian, M., Karakouzian, M., & Ahmadi, R. (2023).
Reducing Scour around Semi-Elliptical Bridge Abutments: Application of Roughness Elements.
Fluids, 8(12), Article 12. https://doi.org/10.3390/fluids8120306
Richardson, E. V., & Simons, D. B. (1984). Use of Spurs and Guidebanks for Highway Crossings.
Transportation Research Record Number 950, 2, 184–193.
Richardson, E. V., Simons, D. B., & Julien, P. Y. (1990). Highways in the River Environment (Final Report
August 1985 - November 1989 FHWA HI-90-016). Federal Highway Administration, U.S.
Department
of
Transportation.
https://www.fhwa.dot.gov/engineering/hydraulics/library_arc.cfm?pub_number=62&id=56
Richardson, E. V., Stevens, M. A., & Simons, D. B. (1975). The design of spurs for river training. XVIth,
IAHR Congress, 382–388.
Rodríguez, J. F., García, C. M., & García, M. H. (2013). Three-dimensional flow in centered pool-riffle
sequences. Water Resources Research, 49(1), 202–215. https://doi.org/10.1029/2011WR011789
Rodríguez, J. F., & García, M. H. (2008). Laboratory measurements of 3-D flow patterns and turbulence in
straight open channel with rough bed. Journal of Hydraulic Research, 46(4), 454–465.
https://doi.org/10.3826/jhr.2008.2994
Ruonan, B., Liekai, C., Xingkui, W., & Danxun, L. (2016). Comparison of ADV and PIV Measurements in
Open
Channel
Flows.
Procedia
Engineering,
154,
995–1001.
https://doi.org/10.1016/j.proeng.2016.07.588

223

Sahu, S. N., Hossain, S., Sen, S., & Ghoshal, K. (2024). Sediment transport in ice-covered channel under
non-equilibrium
condition.
Environmental
Earth
Sciences,
83(10),
315.
https://doi.org/10.1007/s12665-024-11642-x
Sanjou, M. (2016). Turbulence Diffusion Mechanism in Submerged Vegetation Flows. In River Basin
Management. IntechOpen. https://doi.org/10.5772/63207
Sarkar, S. (2020). Large Eddy Simulation of Flows of Engineering Interest: A Review. In A. Runchal (Ed.),
50 Years of CFD in Engineering Sciences: A Commemorative Volume in Memory of D. Brian
Spalding (pp. 363–400). Springer. https://doi.org/10.1007/978-981-15-2670-1_11
Schwartz, J. S., Neff, K. J., Dworak, F. E., & Woockman, R. R. (2015). Restoring riffle-pool structure in an
incised, straightened urban stream channel using an ecohydraulic modeling approach. Ecological
Engineering, 78, 112–126. https://doi.org/10.1016/j.ecoleng.2014.06.002
Schweiger, G., Nilsson, H., Schoeggl, J., Birk, W., & Posch, A. (2020). Modeling and simulation of largescale systems: A systematic comparison of modeling paradigms. Applied Mathematics and
Computation, 365, 124713. https://doi.org/10.1016/j.amc.2019.124713
Sebilian Wittyngham, S., Moderan, J., & Boyer, K. E. (2019). Temperature and salinity effects on submerged
aquatic vegetation traits and susceptibility to grazing. Aquatic Botany, 158, 103119.
https://doi.org/10.1016/j.aquabot.2019.05.004
Sediqi, S., Sui, J., Li, G., & Dziedzic, M. (2024). Characteristics of turbulent flow around bridge abutments
in the presence of vegetation in channel bed under ice-covered flow conditions. Cold Regions
Science and Technology, 221, 104172. https://doi.org/10.1016/j.coldregions.2024.104172
Seo, D. C., & Wang, J. (2021). Canada’s natural river and navigation regulation. Volume 7: Polar and Arctic
Sciences and Technology, V007T07A011. https://doi.org/10.1115/OMAE2021-61419
Shahmohammadi, R., Afzalimehr, H., & Sui, J. (2021). Assessment of Critical Shear Stress and Threshold
Velocity in Shallow Flow with Sand Particles. Water, 13(7), Article 7.
https://doi.org/10.3390/w13070994
Shahmohammadi, R., Afzalimehr, H., & Sui, J. (2022). Estimation of Bed Shear Stress in Shallow
Transitional Flows under Condition of Incipient Motion of Sand Particles Using Turbulence
Characteristics. Water, 14(16), Article 16. https://doi.org/10.3390/w14162515
Shampa, Hasegawa, Y., Nakagawa, H., Takebayashi, H., & Kawaike, K. (2020). Three-Dimensional Flow
Characteristics in Slit-Type Permeable Spur Dike Fields: Efficacy in Riverbank Protection. Water,
12(4), Article 4. https://doi.org/10.3390/w12040964
Shan, Y., Liu, C., Luo, M., & Yang, K. (2016). A simple method for estimating bed shear stress in smooth
and vegetated compound channels. Journal of Hydrodynamics, 28(3), 497–505.

224

https://doi.org/10.1016/S1001-6058(16)60654-6
Shields, A. (1936). Application of similarity principles and turbulence research to bed-load movement.
CalTech Library. https://repository.tudelft.nl/islandora/object/uuid%3Aa66ea380-ffa3-449b-b59f38a35b2c6658
Shumilova, O. O., & Sukhodolov, A. N. (2023). Flow dynamics in rivers with riffle-pool morphology: A
dataset from case studies and field experiments. Scientific Data, 10(1), 494.
https://doi.org/10.1038/s41597-023-02370-1
Sirianni, D. A. B., Valela, C., Rennie, C. D., Nistor, I., & Almansour, H. (2022). Effects of developing ice
covers on bridge pier scour. Journal of Hydraulic Research, 60(4), 645–655.
https://doi.org/10.1080/00221686.2022.2041497
Smith, B. T., & Ettema, R. (1997). Flow Resistance in Ice-Covered Alluvial Channels. Journal of Hydraulic
Engineering, 123(7), 592–599. https://doi.org/10.1061/(ASCE)0733-9429(1997)123:7(592)
Smith, H. D., & Foster, D. L. (2005). Modeling of Flow Around a Cylinder Over a Scoured Bed. Journal of
Waterway,
Port,
Coastal,
and
Ocean
Engineering,
131(1),
14–24.
https://doi.org/10.1061/(ASCE)0733-950X(2005)131:1(14)
Smith, K., Cockburn, J. M. H., & Villard, P. V. (2023). Rivers under Ice: Evaluating Simulated
Morphodynamics through a Riffle-Pool Sequence. Water, 15(8), Article 8.
https://doi.org/10.3390/w15081604
SonTek/YSI, Inc. (2001). Acoustic Doppler Velocimeter Principles of Operation (SonTek/YSI
ADVField/Hydra Acoustic Doppler Velocimeter (Field) Technical Documentation, p. 6) [Technical
Notes]. SonTek/YSI, Inc.
Souliotis, D., & Prinos, P. (2011). Effect of a vegetation patch on turbulent channel flow. Journal of
Hydraulic Research, 49(2), 157–167. https://doi.org/10.1080/00221686.2011.557258
Stephan, U., & Gutknecht, D. (2002). Hydraulic resistance of submerged flexible vegetation. Journal of
Hydrology, 269, 27–43. https://doi.org/10.1016/S0022-1694(02)00192-0
Stoesser, T., Salvador, G. P., Rodi, W., & Diplas, P. (2009). Large Eddy Simulation of Turbulent Flow
Through Submerged Vegetation. Transport in Porous Media, 78(3), 347–365.
https://doi.org/10.1007/s11242-009-9371-8
Su, X. H., Li, C. W., & Chen, B. H. (2003). Three-dimensional large eddy simulation of free surface turbulent
flow in open channel within submerged vegetation domain. Journal of Hydrodynamics, 15(3), 35–
43.
Sui, J. (2023). Fluvial Hydraulics Affected by River Ice and Hydraulic Structures. Water, 15(7), Article 7.

225

https://doi.org/10.3390/w15071262
Sui, J., Faruque, M. A. A., & Balachandar, R. (2009). Local Scour Caused by Submerged Square Jets under
Model Ice Cover. Journal of Hydraulic Engineering, 135. https://doi.org/10.1061/(ASCE)07339429(2009)135:4(316)
Sui, J., Karney, B. W., & Fang, D. (2005). Variation in water level under ice-jammed condition – field
investigation
and
experimental
study.
Hydrology
Research,
36(1),
65–84.
https://doi.org/10.2166/nh.2005.0006
Sui, J., Karney, B. W., Sun, Z., & Wang, D. (2002). Field Investigation of Frazil Jam Evolution: A Case
Study. Journal of Hydraulic Engineering, 128(8), 781–787. https://doi.org/10.1061/(ASCE)07339429(2002)128:8(781)
Sui, J., Wang, J., He, Y., & Krol, F. (2010). Velocity profiles and incipient motion of frazil particles under
ice cover. International Journal of Sediment Research, 25(1), 39–51. https://doi.org/10.1016/S10016279(10)60026-1
Sun, X., & Sakai, M. (2015). Three-dimensional simulation of gas–solid–liquid flows using the DEM–VOF
method. Chemical Engineering Science, 134, 531–548. https://doi.org/10.1016/j.ces.2015.05.059
Tang, C., Yi, Y., & Zhang, S. (2023). Flow and turbulence in unevenly obstructed channels with rigid and
flexible
vegetation.
Journal
of
Environmental
Management,
326,
116736.
https://doi.org/10.1016/j.jenvman.2022.116736
Thompson, D. M. (2006). The role of vortex shedding in the scour of pools. Advances in Water Resources,
29(2), 121–129. https://doi.org/10.1016/j.advwatres.2005.03.015
Tinoco, R. O., San Juan, J. E., & Mullarney, J. C. (2020). Simplification bias: Lessons from laboratory and
field experiments on flow through aquatic vegetation. Earth Surface Processes and Landforms,
45(1), 121–143. https://doi.org/10.1002/esp.4743
Toda, Y., Zhou, Y., & Sakai, N. (2020). Modeling of riparian vegetation dynamics and its application to sandbed
river.
Journal
of
Hydro-Environment
Research,
30,
3–13.
https://doi.org/10.1016/j.jher.2019.09.003
Trimble, S. W. (1997). Contribution of Stream Channel Erosion to Sediment Yield from an Urbanizing
Watershed. Science, 278(5342), 1442–1444. https://doi.org/10.1126/science.278.5342.1442
Turcotte, B., Morse, B., Bergeron, N. E., & Roy, A. G. (2011). Sediment transport in ice-affected rivers.
Journal of Hydrology, 409(1), 561–577. https://doi.org/10.1016/j.jhydrol.2011.08.009
Ulu, A. E., Aydin, M. C., & Önen, F. (2023). Energy Dissipation Potentials of Grouped Spur Dikes in an
Open Channel. Water Resources Management, 37(11), 4491–4506. https://doi.org/10.1007/s11269-

226

023-03571-4
USACE. (n.d.). HEC-RAS Hydraulic Reference Manual. USACE Hydrologic Engineering Center. Retrieved
March 13, 2023, from https://www.hec.usace.army.mil/confluence/rasdocs/ras1dtechref/latest
USDA. (2021). Conservation Practice Standard Vegetative Barrier (Code 601) (601-CPS-1).
Vaghefi, M., Alavinezhad, M., & Akbari, M. (2016). The effect of submergence ratio on flow pattern around
short T-head spur dike in a mild bend with rigid bed using numerical model. Journal of the Chinese
Institute of Engineers, 39(6), 666–674. https://doi.org/10.1080/02533839.2016.1187084
Valela, C., Sirianni, D. A. B., Nistor, I., Rennie, C. D., & Almansour, H. (2021). Bridge Pier Scour under Ice
Cover. Water, 13(4), Article 4. https://doi.org/10.3390/w13040536
Van Appledorn, M., Baker, M. E., & Miller, A. J. (2019). River-valley morphology, basin size, and flowevent magnitude interact to produce wide variation in flooding dynamics. Ecosphere, 10(1), e02546.
https://doi.org/10.1002/ecs2.2546
van Denderen, R. P., Kater, E., Jans, L. H., & Schielen, R. M. J. (2022). Disentangling changes in the river
bed profile: The morphological impact of river interventions in a managed river. Geomorphology,
408, 108244. https://doi.org/10.1016/j.geomorph.2022.108244
van der Mark, C. F., Blom, A., & Hulscher, S. J. M. H. (2008). Quantification of variability in bedform
geometry.
Journal
of
Geophysical
Research:
Earth
Surface,
113(F3).
https://doi.org/10.1029/2007JF000940
Wahl, T. L. (2000). Analyzing ADV Data Using WinADV. 1–10. https://doi.org/10.1061/40517(2000)300
Wan Mohtar, W. H. M., Lee, J. W., Mohammad Azha, N. I., & Cheng, N.-S. (2020). Incipient sediment
motion based on turbulent fluctuations. International Journal of Sediment Research, 35(2), 125–
133. https://doi.org/10.1016/j.ijsrc.2019.10.008
Wang, B., & Xu, Y. J. (2018). Decadal-Scale Riverbed Deformation and Sand Budget of the Last 500 km of
the Mississippi River: Insights Into Natural and River Engineering Effects on a Large Alluvial River.
Journal
of
Geophysical
Research:
Earth
Surface,
123(5),
874–890.
https://doi.org/10.1029/2017JF004542
Wang, F., Huai, W., Guo, Y., & Liu, M. (2021). Turbulence Structure and Momentum Exchange in
Compound Channel Flows With Shore Ice Covered on the Floodplains. Water Resources Research,
57(4), e2020WR028621. https://doi.org/10.1029/2020WR028621
Wang, F., Huai, W., Liu, M., & Fu, X. (2020). Modeling depth-averaged streamwise velocity in straight
trapezoidal compound channels with ice cover. Journal of Hydrology, 585, 124336.
https://doi.org/10.1016/j.jhydrol.2019.124336

227

Wang, J., He, G., Huang, L., Dey, S., & Fang, H. (2023). Effects of Submerged Flexible Vegetation on Scalar
Transport in an Open-Channel Flow. Water Resources Research, 59(9), e2022WR034235.
https://doi.org/10.1029/2022WR034235
Wang, J., Sui, J., & Karney, B. W. (2008). Incipient Motion of Non-Cohesive Sediment under Ice Cover—
An Experimental Study. Journal of Hydrodynamics, 20(1), 117–124. https://doi.org/10.1016/S10016058(08)60036-0
Wang, Z., Zhang, H., Xu, W., Wang, H., & Huang, H. (2019). Effects of Emergent Vegetation Patterns on
Flow Velocity, Turbulence, and Erosion Around River Banks. Iranian Journal of Science and
Technology, Transactions of Civil Engineering, 43(3), 509–519. https://doi.org/10.1007/s40996018-0200-6
Watt, W. (2013). The national Flood Damage Reduction Program: 1976–1995. Canadian Water Resources
Journal
/
Revue
Canadienne
Des
Ressources
Hydriques,
20,
237–247.
https://doi.org/10.4296/cwrj2004237
Wei, X., Lu, Y., Wang, Z., Liu, X., & Mo, S. (2018). A Machine Learning Approach to Evaluating the
Damage
Level
of
Tooth-Shape
Spur
Dikes.
Water,
10(11), Article
11.
https://doi.org/10.3390/w10111680
Widén, Å., Malm Renöfält, B., Degerman, E., Wisaeus, D., & Jansson, R. (2022). Environmental Flow
Scenarios for a Regulated River System: Projecting Catchment-Wide Ecosystem Benefits and
Consequences for Hydroelectric Production. Water Resources Research, 58(1), e2021WR030297.
https://doi.org/10.1029/2021WR030297
Wilcox, A. C., & Wohl, E. E. (2006). Flow resistance dynamics in step-pool stream channels: 1. Large woody
debris and controls on total resistance. Water Resources Research, 42(5).
https://doi.org/10.1029/2005WR004277
Wu, P., Balachandar, R., & Sui, J. (2016). Local Scour around Bridge Piers under Ice-Covered Conditions.
Journal of Hydraulic Engineering, 142(1), 04015038. https://doi.org/10.1061/(ASCE)HY.19437900.0001063
Wu, P., Hirshfield, F., & Sui, J. (2013). ADV measurements of flow field around bridge abutment under ice
cover.
Wu, P., Hirshfield, F., & Sui, J. (2015). Armour Layer Analysis of Local Scour around Bridge Abutments
Under
Ice
Cover.
River
Research
and
Applications,
31(6),
736–746.
https://doi.org/10.1002/rra.2771
Wu, P., Hirshfield, F., Sui, J., Wang, J., & Chen, P. (2014). Impacts of ice cover on local scour around semicircular bridge abutment. Journal of Hydrodynamics, Ser. B, 26(1), 10–18.
https://doi.org/10.1016/S1001-6058(14)60002-0

228

Wu, W., Shields Jr., F. D., Bennett, S. J., & Wang, S. S. Y. (2005). A depth-averaged two-dimensional model
for flow, sediment transport, and bed topography in curved channels with riparian vegetation. Water
Resources Research, 41(3). https://doi.org/10.1029/2004WR003730
Wuebben, J. (1996). Physical Modelling. In A Primer on Hydraulics of Ice Covered Rivers. Canadian
Committee on River Ice Processes and the Environment.
Xu, H., Li, Y., Zhao, Z., Wang, X., & Zhang, F. (2023). Experimental Study on the Local Scour of Submerged
Spur Dike Heads under the Protection of Soft Mattress in Plain Sand-Bed Rivers. Water, 15(3),
Article 3. https://doi.org/10.3390/w15030413
Xu, Y. J., Wang, B., Xu, W., Tang, M., Tsai, F. T.-C., & Smith, L. C. (2021). Four-decades of bed elevation
changes in the heavily regulated upper Atchafalaya River, Louisiana, USA. Geomorphology, 386,
107748. https://doi.org/10.1016/j.geomorph.2021.107748
Xu, Y., Li, D., & Nepf, H. (2022). Sediment Pickup Rate in Bare and Vegetated Channels. Geophysical
Research Letters, 49(21), e2022GL101279. https://doi.org/10.1029/2022GL101279
Xu, Y., & Nepf, H. (2020). Measured and Predicted Turbulent Kinetic Energy in Flow Through Emergent
Vegetation With Real Plant Morphology. Water Resources Research, 56(12), e2020WR027892.
https://doi.org/10.1029/2020WR027892
Xue, Z., Zhou, L., & Liu, D. (2023). Accurate Numerical Modeling for 1D Open-Channel Flow with Varying
Topography. Water, 15(16), Article 16. https://doi.org/10.3390/w15162893
Yakhot, V., Orszag, S. A., Thangam, S., Gatski, T. B., & Speziale, C. G. (1992). Development of turbulence
models for shear flows by a double expansion technique. Physics of Fluids A: Fluid Dynamics, 4(7),
1510–1520. https://doi.org/10.1063/1.858424
Yamasaki, T. N., Jiang, B., Janzen, J. G., & Nepf, H. M. (2021). Feedback between vegetation, flow, and
deposition: A study of artificial vegetation patch development. Journal of Hydrology, 598, 126232.
https://doi.org/10.1016/j.jhydrol.2021.126232
Yan, C., Nepf, H. M., Huang, W.-X., & Cui, G.-X. (2017). Large eddy simulation of flow and scalar transport
in
a
vegetated
channel.
Environmental
Fluid
Mechanics,
17(3),
497–519.
https://doi.org/10.1007/s10652-016-9503-y
Yang, C. T. (2003). Sediment Transport: Theory and Practice. Krieger Pub.
Yang, H. F., Yang, S. L., Xu, K. H., Wu, H., Shi, B. W., Zhu, Q., Zhang, W. X., & Yang, Z. (2017). Erosion
potential of the Yangtze Delta under sediment starvation and climate change. Scientific Reports,
7(1), 10535. https://doi.org/10.1038/s41598-017-10958-y
Yang, L., Fang, H., Yang, Z., & Huai, W. (2023). Longitudinal dispersive coefficient in channels with aquatic

229

vegetation: A review. Journal of Hydrodynamics, 35(3), 379–395. https://doi.org/10.1007/s42241023-0038-7
Yang, S.-Q., Tan, S. K., & Wang, X.-K. (2012). Mechanism of secondary currents in open channel flows.
Journal of Geophysical Research: Earth Surface, 117(F4). https://doi.org/10.1029/2012JF002510
Yazdi, J., Sarkardeh, H., Azamathulla, H. Md., & Ghani, A. Ab. (2010). 3D simulation of flow around a
single spur dike with free-surface flow. International Journal of River Basin Management, 8(1),
55–62. https://doi.org/10.1080/15715121003715107
Yochum, S. (2018). Flow Resistance Coefficient Selection in Natural Channels: A Spreadsheet Tool.
Zabilansky, L., & White, K. (2005). Ice Cover Effects on Scour in Narrow Rivers (Ice Engineering, April
2005). 7.
Zeng, C., Bai, Y., Zhou, J., Qiu, F., Ding, S., Hu, Y., & Wang, L. (2022). Large Eddy Simulation of Compound
Open Channel Flows with Floodplain Vegetation. Water, 14(23), Article 23.
https://doi.org/10.3390/w14233951
Zhang, J., Wang, W., Li, Z., Li, Q., Zhong, Y., Xia, Z., & Qiu, H. (2021). Analytical Models of Velocity,
Reynolds Stress and Turbulence Intensity in Ice-Covered Channels. Water, 13(8), Article 8.
https://doi.org/10.3390/w13081107
Zhang, J., Wang, W.-J., Shi, H., Wang, W., Li, Z., Tang, X., & Xia, Z. (2021). An analytical two-layer model
for velocity distribution in open-channel flows with submerged flexible canopies considering
multiply
fluids
mechanics.
Journal
of
Hydrology,
603,
127102.
https://doi.org/10.1016/j.jhydrol.2021.127102
Zhang, L., Wang, P., Yang, W., Zuo, W., Gu, X., & Yang, X. (2018). Geometric Characteristics of Spur Dike
Scour
under
Clear-Water
Scour
Conditions.
Water,
10(6),
Article
6.
https://doi.org/10.3390/w10060680
Zhang, M., Hao, Z., Zhang, Y., & Wu, W. (2013). Numerical simulation of solitary and random wave
propagation through vegetation based on VOF method. Acta Oceanologica Sinica, 32(7), 38–46.
https://doi.org/10.1007/s13131-013-0330-4
Zhang, S., & Liu, X. (2023). Theoretical, experimental, and numerical studies of flow field characteristics
and incipient scouring erosion for slope with rigid vegetations. Journal of Hydrology, 622, 129638.
https://doi.org/10.1016/j.jhydrol.2023.129638
Zhang, W., Uh Zapata, M., Bai, X., Pham-Van-Bang, D., & Nguyen, K. D. (2020). Three-dimensional
simulation of horseshoe vortex and local scour around a vertical cylinder using an unstructured
finite-volume technique. International Journal of Sediment Research, 35(3), 295–306.
https://doi.org/10.1016/j.ijsrc.2019.09.001

230

Zhang, X.-F., Yang, W.-T., & Xia, J.-Q. (2016). Bed shear stress in non-uniform flow. Environmental Fluid
Mechanics, 16(4), 777–792. https://doi.org/10.1007/s10652-016-9448-1
Zhang, Y., Wang, P., Cheng, J., Wang, W.-J., Zeng, L., & Wang, B. (2020). Drag Coefficient of Emergent
Flexible Vegetation in Steady Nonuniform Flow. Water Resources Research, 56(8),
e2020WR027613. https://doi.org/10.1029/2020WR027613
Zhao, T., & Nepf, H. M. (2021). Turbulence Dictates Bedload Transport in Vegetated Channels Without
Dependence on Stem Diameter and Arrangement. Geophysical Research Letters, 48(21),
e2021GL095316. https://doi.org/10.1029/2021GL095316
Zhao, X., Zhang, H., Wei, K., Wang, P., Ren, Q., & Zhang, D. (2021). Flow Field Fitting Method and
Acoustic Doppler Velocity Measurement: A New Approach for Detecting Leakage Pathways in
Concrete-Face Rockfill Dams. Earth and Space Science, 8(11), e2021EA001875.
https://doi.org/10.1029/2021EA001875
Zheng, S., Luo, H., Zhang, J., Cheng, H., Li, Z., Ma, Y., Wu, S., & Liu, E. (2022). Sediment budget and
riverbed deformation in the uppermost part of the lower Yangtze River, China. International Journal
of Sediment Research, 37(4), 484–492. https://doi.org/10.1016/j.ijsrc.2022.02.004
Zhuang, T., Ren, J., Dai, J., Zhang, H., Wang, J., Ma, Z., Xu, S., Chen, K., Guo, H., & Zhai, Y. (2023). The
influence of hyporheic exchange with spur dikes: Laboratory experiments. Journal of Hydrology,
622, 129754. https://doi.org/10.1016/j.jhydrol.2023.129754

231

APPENDIX I. TERRAIN ELEVATION SHANGE CONTOURS

d50 = 0.58 mm

227
Note: In these contour maps, units for x and y axis are cm, whereas the contour unit is mm. In the experiment serial
numbers, H, L, and A denotes the dike height (including buried in the sands, cm), design length (cm), and alignment angles
(°). O, S, R indicate the cover conditions (open channel smooth cover, and rough cover respectively.

d50 = 0.58 mm

228
Note: In these contour maps, units for x and y axis are cm, whereas the contour unit is mm. In the experiment serial
numbers, H, L, and A denotes the dike height (including buried in the sands, cm), design length (cm), and alignment angles
(°). O, S, R indicate the cover conditions (open channel smooth cover, and rough cover respectively.

229
Note: In these contour maps, units for x and y axis are cm, whereas the contour unit is mm. In the experiment serial
numbers, H, L, and A denotes the dike height (including buried in the sands, cm), design length (cm), and alignment angles
(°). O, S, R indicate the cover conditions (open channel smooth cover, and rough cover respectively.

230
Note: In these contour maps, units for x and y axis are cm, whereas the contour unit is mm. In the experiment serial
numbers, H, L, and A denotes the dike height (including buried in the sands, cm), design length (cm), and alignment angles
(°). O, S, R indicate the cover conditions (open channel smooth cover, and rough cover respectively.

231
Note: In these contour maps, units for x and y axis are cm, whereas the contour unit is mm. In the experiment serial
numbers, H, L, and A denotes the dike height (including buried in the sands, cm), design length (cm), and alignment angles
(°). O, S, R indicate the cover conditions (open channel smooth cover, and rough cover respectively.

232
Note: In these contour maps, units for x and y axis are cm, whereas the contour unit is mm. In the experiment serial
numbers, H, L, and A denotes the dike height (including buried in the sands, cm), design length (cm), and alignment angles
(°). O, S, R indicate the cover conditions (open channel smooth cover, and rough cover respectively.

233
Note: In these contour maps, units for x and y axis are cm, whereas the contour unit is mm. In the experiment serial
numbers, H, L, and A denotes the dike height (including buried in the sands, cm), design length (cm), and alignment angles
(°). O, S, R indicate the cover conditions (open channel smooth cover, and rough cover respectively.

234
Note: In these contour maps, units for x and y axis are cm, whereas the contour unit is mm. In the experiment serial
numbers, H, L, and A denotes the dike height (including buried in the sands, cm), design length (cm), and alignment angles
(°). O, S, R indicate the cover conditions (open channel smooth cover, and rough cover respectively.

235
Note: In these contour maps, units for x and y axis are cm, whereas the contour unit is mm. In the experiment serial
numbers, H, L, and A denotes the dike height (including buried in the sands, cm), design length (cm), and alignment angles
(°). O, S, R indicate the cover conditions (open channel smooth cover, and rough cover respectively.

236
Note: In these contour maps, units for x and y axis are cm, whereas the contour unit is mm. In the experiment serial
numbers, H, L, and A denotes the dike height (including buried in the sands, cm), design length (cm), and alignment angles
(°). O, S, R indicate the cover conditions (open channel smooth cover, and rough cover respectively.

237
Note: In these contour maps, units for x and y axis are cm, whereas the contour unit is mm. In the experiment serial
numbers, H, L, and A denotes the dike height (including buried in the sands, cm), design length (cm), and alignment angles
(°). O, S, R indicate the cover conditions (open channel smooth cover, and rough cover respectively.

238
Note: In these contour maps, units for x and y axis are cm, whereas the contour unit is mm. In the experiment serial
numbers, H, L, and A denotes the dike height (including buried in the sands, cm), design length (cm), and alignment angles
(°). O, S, R indicate the cover conditions (open channel smooth cover, and rough cover respectively.

239
Note: In these contour maps, units for x and y axis are cm, whereas the contour unit is mm. In the experiment serial
numbers, H, L, and A denotes the dike height (including buried in the sands, cm), design length (cm), and alignment angles
(°). O, S, R indicate the cover conditions (open channel smooth cover, and rough cover respectively.

240
Note: In these contour maps, units for x and y axis are cm, whereas the contour unit is mm. In the experiment serial
numbers, H, L, and A denotes the dike height (including buried in the sands, cm), design length (cm), and alignment angles
(°). O, S, R indicate the cover conditions (open channel smooth cover, and rough cover respectively.

241
Note: In these contour maps, units for x and y axis are cm, whereas the contour unit is mm. In the experiment serial
numbers, H, L, and A denotes the dike height (including buried in the sands, cm), design length (cm), and alignment angles
(°). O, S, R indicate the cover conditions (open channel smooth cover, and rough cover respectively.

242
Note: In these contour maps, units for x and y axis are cm, whereas the contour unit is mm. In the experiment serial
numbers, H, L, and A denotes the dike height (including buried in the sands, cm), design length (cm), and alignment angles
(°). O, S, R indicate the cover conditions (open channel smooth cover, and rough cover respectively.

243
Note: In these contour maps, units for x and y axis are cm, whereas the contour unit is mm. In the experiment serial
numbers, H, L, and A denotes the dike height (including buried in the sands, cm), design length (cm), and alignment angles
(°). O, S, R indicate the cover conditions (open channel smooth cover, and rough cover respectively.

244
Note: In these contour maps, units for x and y axis are cm, whereas the contour unit is mm. In the experiment serial
numbers, H, L, and A denotes the dike height (including buried in the sands, cm), design length (cm), and alignment angles
(°). O, S, R indicate the cover conditions (open channel smooth cover, and rough cover respectively.

245
Note: In these contour maps, units for x and y axis are cm, whereas the contour unit is mm. In the experiment serial
numbers, H, L, and A denotes the dike height (including buried in the sands, cm), design length (cm), and alignment angles
(°). O, S, R indicate the cover conditions (open channel smooth cover, and rough cover respectively.

246
Note: In these contour maps, units for x and y axis are cm, whereas the contour unit is mm. In the experiment serial
numbers, H, L, and A denotes the dike height (including buried in the sands, cm), design length (cm), and alignment angles
(°). O, S, R indicate the cover conditions (open channel smooth cover, and rough cover respectively.

N.B.: The following few experimental conditions were to determine whether the width will
influence the maximum scour depth. The widths in previous trials were 5 cm.

247
Note: In these contour maps, units for x and y axis are cm, whereas the contour unit is mm. In the experiment serial
numbers, H, L, and A denotes the dike height (including buried in the sands, cm), design length (cm), and alignment angles
(°). O, S, R indicate the cover conditions (open channel smooth cover, and rough cover respectively.

248
Note: In these contour maps, units for x and y axis are cm, whereas the contour unit is mm. In the experiment serial
numbers, H, L, and A denotes the dike height (including buried in the sands, cm), design length (cm), and alignment angles
(°). O, S, R indicate the cover conditions (open channel smooth cover, and rough cover respectively.

249
Note: In these contour maps, units for x and y axis are cm, whereas the contour unit is mm. In the experiment serial
numbers, H, L, and A denotes the dike height (including buried in the sands, cm), design length (cm), and alignment angles
(°). O, S, R indicate the cover conditions (open channel smooth cover, and rough cover respectively.

250
Note: In these contour maps, units for x and y axis are cm, whereas the contour unit is mm. In the experiment serial
numbers, H, L, and A denotes the dike height (including buried in the sands, cm), design length (cm), and alignment angles
(°). O, S, R indicate the cover conditions (open channel smooth cover, and rough cover respectively.

251
Note: In these contour maps, units for x and y axis are cm, whereas the contour unit is mm. In the experiment serial
numbers, H, L, and A denotes the dike height (including buried in the sands, cm), design length (cm), and alignment angles
(°). O, S, R indicate the cover conditions (open channel smooth cover, and rough cover respectively.

252
Note: In these contour maps, units for x and y axis are cm, whereas the contour unit is mm. In the experiment serial
numbers, H, L, and A denotes the dike height (including buried in the sands, cm), design length (cm), and alignment angles
(°). O, S, R indicate the cover conditions (open channel smooth cover, and rough cover respectively.

ds/h
0.410243
0.446387
0.466346
0.55954
0.630833
0.235725
0.260693
0.272307
0.293819
0.30931
0.410665
0.43363
0.474587
0.489567
0.595311
0.329387
0.339142
0.394481
0.450577
0.489698
0.483267
0.500467
0.561006
0.641939
0.656942
0.344072
0.385559

L/h
1.707317
1.715686
2.439024
2.415459
2.45098
2.439024
2.475248
1.732673
2.45098
1.724138
1.707317
1.682692
1.690821
2.403846
2.392344
2.439024
1.707317
2.415459
2.403846
2.403846
1.643192
1.650943
2.347418
2.347418
2.347418
1.666667
1.674641

Frd
4.822445
4.860219
4.87281
4.986131
5.07427
4.608394
4.646168
4.646168
4.721715
4.809854
4.583212
4.608394
4.620985
4.646168
4.721715
4.066971
4.205474
4.293613
4.432117
4.444708
3.966241
3.991423
4.004015
4.230657
4.268431
3.827737
3.865511
1.02
1.045
1.025
1.04
1.065
1.4
1.366667
1.346667
1.386667
1.36
1.065
1.02
1.06
1.035
1.04
1.366667
1.366667
1.393333
1.413333
1.346667
1.025
1.065
1.035
1.065
1.04
1.353333
1.38

S

sin α
0.866025
1
0.707107
0.866025
1
1
0.707107
0.866025
0.866025
1
0.866025
0.866025
1
0.707107
0.866025
0.707107
1
0.866025
1
1
0.866025
1
0.707107
1
0.866025
0.866025
1

n0
0.018645
0.018645
0.018645
0.018645
0.018645
0.018645
0.018645
0.018645
0.018645
0.018645
0.014649
0.014649
0.014649
0.014649
0.014649
0.014649
0.014649
0.014649
0.014649
0.014649
0.01984
0.01984
0.01984
0.01984
0.01984
0.01984
0.01984

Fr
0.270659
0.272779
0.273486
0.279846
0.284793
0.258645
0.260766
0.260766
0.265006
0.269952
0.257232
0.258645
0.259352
0.260766
0.265006
0.228258
0.236032
0.240978
0.248752
0.249459
0.222605
0.224018
0.224725
0.237445
0.239565
0.214831
0.216951
253

ln(ds/h)
-0.89101
-0.80657
-0.76283
-0.58064
-0.46071
-1.44509
-1.34441
-1.30083
-1.22479
-1.17341
-0.88998
-0.83556
-0.74531
-0.71423
-0.51867
-1.11052
-1.08134
-0.93018
-0.79723
-0.71397
-0.72719
-0.69221
-0.57802
-0.44326
-0.42016
-1.06691
-0.95306

ln(L/h)
0.534923
0.539813
0.891598
0.881889
0.896488
0.891598
0.90634
0.549665
0.896488
0.544727
0.534923
0.520395
0.525214
0.87707
0.872274
0.891598
0.534923
0.881889
0.87707
0.87707
0.496641
0.501347
0.853316
0.853316
0.853316
0.510826
0.515599

ln(Frd)
1.573281
1.581083
1.583671
1.60666
1.624183
1.527879
1.536043
1.536043
1.552172
1.570667
1.5224
1.527879
1.530608
1.536043
1.552172
1.402898
1.436387
1.457129
1.488877
1.491714
1.377819
1.384148
1.387297
1.442357
1.451246
1.342274
1.352094

ln(S)
0.019803
0.044017
0.024693
0.039221
0.062975
0.336472
0.312375
0.297632
0.326903
0.307485
0.062975
0.019803
0.058269
0.034401
0.039221
0.312375
0.312375
0.331699
0.345951
0.297632
0.024693
0.062975
0.034401
0.062975
0.039221
0.302571
0.322083

ln(sinα)
-0.14384
0
-0.34657
-0.14384
0
0
-0.34657
-0.14384
-0.14384
0
-0.14384
-0.14384
0
-0.34657
-0.14384
-0.34657
0
-0.14384
0
0
-0.14384
0
-0.34657
0
-0.14384
-0.14384
0

ln(n0)
-3.98219
-3.98219
-3.98219
-3.98219
-3.98219
-3.98219
-3.98219
-3.98219
-3.98219
-3.98219
-4.22342
-4.22342
-4.22342
-4.22342
-4.22342
-4.22342
-4.22342
-4.22342
-4.22342
-4.22342
-3.92006
-3.92006
-3.92006
-3.92006
-3.92006
-3.92006
-3.92006

Table A.II.1 Linear regression data worksheet for the derivation of the empirical equation of local scour around the submerged spur dike (upstream sandbox)

APPENDIX II. LINEAR REGRESSION DATA WORKSHEET
(B-Lsina)/B
0.852142004
0.828431373
0.827534931
0.79081512
0.754901961
0.756097561
0.824973569
0.849946093
0.787738872
0.827586207
0.852142004
0.854274571
0.830917874
0.830022408
0.792816889
0.827534931
0.829268293
0.79081512
0.759615385
0.759615385
0.857695356
0.83490566
0.834012493
0.765258216
0.796707652
0.855662433
0.832535885

ds/h
0.398406
0.458569
0.488024

L/h
2.392344
2.347418
2.358491

Table A.II.1 Cont’d

Frd
3.890693
3.915876
3.928467

S
1.366667
1.393333
1.42

sin α
0.707107
0.866025
1

n0
0.01984
0.01984
0.01984

Fr
0.218365
0.219778
0.220485

254

ln(ds/h)
-0.92028
-0.77964
-0.71739

ln(L/h)
0.872274
0.853316
0.858022

ln(Frd)
1.358587
1.365039
1.368249

ln(S)
0.312375
0.331699
0.350657

ln(sinα)
-0.34657
-0.14384
0

ln(n0)
-3.92006
-3.92006
-3.92006

(B-Lsina)/B
0.830835698
0.796707652
0.764150943

35

35

50
50
35
35

50
50

50
50
35
35
50

50

35
50
35
50
50

50

35
50
35
50
35

50

35
50

93.04

149.06
122.76
75.84
88.19603

81.65063
99.24108

108.8998
71.64406
115
95.13
150.28

122.76

81.99
92.04249
84.03
103.2582
113.3916

76.58674

128.2872
156.0143
95.09409
153.6826
90.55

93.23225

87.38284
101.127

L

ds(mm)
113.7

α
90

90
120

135

90
120
120
90
120

135

120
135
90
120
90

120

90
135
90
120
90

135
120

90
120
120
90

120

h

24.7
24.9

30.375

24.8
24.8
25.3
25.4
20.48

25.4

20.24
30.625
24.6
24.7
25

25.2

24.9
25.7
24.7
25
25.2

30.75
24.7

24.6
25.1
20.48
24.6

24.6

24.4

0.249665
0.233543

0.263701

0.366535
0.3603
0.313729
0.307365
0.298738

0.21662

0.270497
0.260335
0.240086
0.238465
0.226783

0.283502

0.2178
0.20264
0.328571
0.313848
0.30056

0.230943
0.229187

0.29812
0.283502
0.250207
0.251989

0.306952

ds/(Lsinα)
0.324857

0.705714
0.498

0.6075

0.708571
0.496
0.722857
0.508
0.585143

0.508

0.578286
0.6125
0.702857
0.494
0.5

0.504

0.498
0.514
0.705714
0.714286
0.504

0.615
0.494

0.492
0.502
0.585143
0.702857

0.702857

d/L
0.697143

5.058859
4.677437

5.075488

4.686811
4.674036
4.261541
4.070359
3.533704

4.061629

4.163101
5.245543
4.995823
4.888393
4.616669

4.235304

4.849182
4.468853
4.918514
4.373226
4.31087

5.062406
4.900173

4.378641
4.251737
3.938633
5.136734

4.82304

Frd
4.945625

255

1.235
1.245

1.215

0.992
0.992
1.012
1.016
1.024

1.27

1.012
1.225
1.23
1.235
1.25

1.008

1.245
1.285
0.988
1
1.008

1.23
1.235

0.984
1.004
1.024
1.23

0.984

S=h/T
0.976

0.019016
0.019016

0.019016

0.019016
0.019016
0.019016
0.019016
0.019016

0.013683

0.013683
0.013683
0.013683
0.013683
0.013683

0.013683

0.016922
0.016922
0.013683
0.013683
0.013683

0.016922
0.016922

0.016922
0.016922
0.016922
0.016922

0.016922

n0
0.016922

0.353777
0.406133

0.306937

0.517287
0.62909
0.375866
0.60505
0.442139

0.301523

0.405089
0.300547
0.341585
0.41805
0.453566

0.487143

0.437349
0.278771
0.465587
0.38052
0.596349

0.265531
0.401786

0.605935
0.489084
0.370313
0.35852

0.378211

ds/d
0.465984

1.417004
2.008032

1.646091

1.41129
2.016129
1.383399
1.968504
1.708984

1.968504

1.729249
1.632653
1.422764
2.024291
2

1.984127

2.008032
1.945525
1.417004
1.4
1.984127

1.626016
2.024291

2.03252
1.992032
1.708984
1.422764

1.422764

L/d
1.434426

0.283928
0.262521

0.284861

0.263047
0.26233
0.239178
0.228448
0.198329

0.227958

0.233653
0.294405
0.28039
0.27436
0.25911

0.237706

0.27216
0.250814
0.276051
0.245447
0.241947

0.284127
0.275022

0.245751
0.238628
0.221055
0.288298

0.270692

Fr
0.277573

0.253944
0.336578

0.213714

0.433959
0.522119
0.415348
0.697154
0.659114

0.348681

0.560071
0.211114
0.278951
0.341927
0.415268

0.620986

0.373202
0.278645
0.433068
0.439005
0.693219

0.21199
0.327108

0.694935
0.599348
0.567903
0.256373

0.377947

Cal. ds/d
0.426661

Table A.II.2 Validation worksheet of the derived local scour around submerged angled spur dikes using data collected from the downstream sandbox.

0.353777
0.406133

0.306937

0.517287
0.62909
0.375866
0.60505
0.442139

0.301523

0.405089
0.300547
0.341585
0.41805
0.453566

0.487143

0.437349
0.278771
0.465587
0.38052
0.596349

0.265531
0.401786

0.605935
0.489084
0.370313
0.35852

0.378211

Mea. ds/d
0.465984

L
50

50

ds(mm)
116.0705

78.19894

Table A.II.2 Cont’d

135

α
90
25.7

h
25.7
0.22118

ds/(Lsinα)
0.232141
0.514

d/L
0.514
4.271117

Frd
4.521583

256

1.285

S=h/T
1.285
0.019016

n0
0.019016
0.304276

ds/d
0.451636
1.945525

L/d
1.945525
0.239716

Fr
0.253773
0.292688

Cal. ds/d
0.372987

0.304276

Mea. ds/d
0.451636

257

Figure A.III.1 FLOW-3D simulation log for running at the same time as experimental vegetated pool conditions (118 days, not realistic for multiple simulations)

APPENDIX III. NUMERICAL SIMULATION RUNNING TIME OPTIMIZATION

time.

258

Figure A.III.2 FLOW-3D tips on steady solution time (approximately 800 seconds). The simulation duration was set as 1000 seconds for each case to save computational

259

APPENDIX IV. SEDIMENT SIZE DISTRIBUTION IN NECHOKO RIVER