EFFECTS OF VEGETATION DENSITY, ARRANGEMENT, AND MORPHOLOGY
ON FLOW STRUCTURE UNDER ICE-COVERED CONDITION

by

Mahboubeh Barahimi Varnousfaderani
B.Sc., Isfahan University of Technology, Iran, 2009
M.Sc., Isfahan University of Technology, Iran, 2014

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

UNIVERSITY OF NORTHERN BRITISH COLUMBIA
August 2023
© Mahboubeh Barahimi Varnousfaderani

Abstract
Aquatic vegetation appears very often in rivers and floodplains, which significantly
affects the flow structure. On the other hand, a common feature of cold regions is the presence
of river ice on water surfaces. Ice cover imposes an additional boundary layer on water surface
which leads to significant change in flow structure and bed deformation. It also causes a
decreasing trend of velocity profile near the cover. Because of vegetation’s positive impacts
on water quality, habitat, and channel stability, researchers now advocate replanting and
restoring projects in rivers, especially in agricultural waterways, floodways, and emergency
spillways. The expansion of vegetation in fluvial systems may worsen the flood impact since
highly dense vegetation in a channel reduces its flow capacity due to the increase in flow
resistance and decrease in the channel width. Therefore, an accurate and critical assessment of
the vegetation density and distribution pattern through reduction of bulk velocity is crucial in
sustainable restoration projects.
To the author's knowledge, no studies have been conducted to investigate the impacts of
both ice cover and vegetation on flow resistance and channel bed deformation. It is thus
necessary to examine the connection between vegetation and ice covers thoroughly in order to
guarantee successful restoration projects. Most of research projects on submerged vegetation
have been done in small-scale laboratory flume and specifically under the open channel flow
condition. Besides, most of reported research uses uniform sediment which is not an
appropriate representative of natural river systems.
In the present study, deflected and non-bending model vegetation elements arranged in
both square and staggered configurations with different density in the channel bed with three
different non-uniform sands under different cover conditions of water surface including open
channel flow and ice-covered flow conditions were used. In order to simulate the ice cover
ii

condition, smooth and rough ice covers made of Styrofoam panels were created to investigate
the impacts of ice cover roughness on channel bed deformation. To represent non-uniform
sediment condition, three different bed materials with median particle size (D50) of 0.50 mm,
0.60 mm, 0.98 mm were used.
Results showed that the most significant variable influencing the depth of scour holes under
ice-covered flow conditions is the ratio of the ice cover roughness to the bed roughness and in
open channel flow conditions, the flow Froude number is determining. In the conducted
experiments, it was consistently observed that the maximum scour depths occurred at the
upstream, front face of the vegetation elements. It was found that the scour holes were deeper
and longer under ice-covered flow. In the presence of vegetation in the bed under ice-covered
flow conditions, the velocity profiles exhibit a distinct pattern characterized by two peak
values. The study revealed an inverse relationship between canopy density and the dimensions
of the wake zone. As the spacing distance between deflected vegetation elements decreases,
the streamwise velocity experiences significant retardation slightly below the inflection point.
With a sparser vegetation canopy, the inflectional region tends to diminish or disappear.
Furthermore, the study observed that the inflection point was not observed in non-bending
vegetation. Additionally, velocity profiles showed more pronounced inflection points in the
case of a staggered arrangement of vegetation elements compared to a square arrangement.
Results of this study will provide vital information for river management, channel
restoration, and rehabilitation of fluvial environments through understanding the effect of
various vegetation densities, arrangement patterns and morphology, as well as the
revitalization of cold-weather river ecosystems.

iii

PREFACE
In terms of co-authorship, I was the primary investigator responsible for designing the
experimental plan, collecting and processing data, and interpreting the results. I took the lead
in writing the manuscripts and incorporating reviewers' comments and feedback into the final
versions of the dissertation. However, I acknowledge the contribution of Dr. Sui in the
finalization of the manuscripts, supervision of the experimental design, and data analysis for
the research. As a result of Dr. Sui's significant contributions, I have included him as a coauthor in all corresponding publications.
This Ph.D. dissertation yielded one published manuscript for Chapter 3, while the
manuscripts for Chapters 4 and Chapter 5 are currently under review. Publication and
authorships from this dissertation were stated as follows (Published or under review).

1) Barahimi, M., & Sui, J. (2023). Effects of Submerged Vegetation Arrangement
Patterns and Density on Flow Structure. Water, 15(1), 176. 23 pages,
http://dx.doi.org/10.3390/w15010176.
2) Barahimi, M., & Sui, J. (2023). Deformation of vegetated channel bed under icecovered flow conditions. Journal of Hydrology (under review).
3) Barahimi, M., & Sui, J. (2023). Flow structure and shear stress in the presence of both
ice cover on water surface and leafless vegetation in channel bed. Journal of
Hydrodynamics (under review).

iv

Contents
Abstract ................................................................................................................................................. ii
PREFACE ............................................................................................................................................ iv
ACKNOWLEDGEMENT ................................................................................................................ xiii
1.

CHAPTER ONE: INTRODUCTION AND LITERATURE REVIEW .................................. 1
1.1 Vegetation.................................................................................................................................... 1
1.1.1 Increasing bank stability and controlling floods .............................................................. 4
1.1.2 Improving water quality and decreasing turbidity .......................................................... 5
1.1.3 Habitat .................................................................................................................................. 6
1.1.4 Carbon storage..................................................................................................................... 6
1.1.5 Control of sediment movement .......................................................................................... 6
1.2 Ice cover....................................................................................................................................... 7
1.3 Division of flow based on Froude number and Reynolds number ....................................... 11
1.4 Vegetation induced turbulence ................................................................................................ 13
1.5 Boundary layer theory ............................................................................................................. 16
1.6 Incipient motion ........................................................................................................................ 19
1.7 Flow resistance and shields diagram ...................................................................................... 20
1.8 Hypothesis ................................................................................................................................. 23
1.9 Objectives .................................................................................................................................. 25
1.10

2.

Thesis Structure .................................................................................................................. 28

CHAPTER TWO: MATERIALS AND METHODS .............................................................. 30
2.1 Flume, ADV and SonTek IQ used for this study ................................................................... 31
2.2 Vegetation settings .................................................................................................................... 34
2.3 Sediment used in experiments ................................................................................................. 39
2.4 Ice cover conditions .................................................................................................................. 40
2.5 Research Innovation................................................................................................................. 41
2.6 Bibliography.............................................................................................................................. 42

3. Effects of submerged vegetation arrangement patterns and density on flow structure .......... 55
3.1 Introduction .............................................................................................................................. 55
3.2 Materials and Methods ............................................................................................................ 57
3.2.1 Flume, ADV and SonTek IQ used for this study ............................................................ 57
3.2.2 Sediment used in experiments .......................................................................................... 59
3.2.3 Vegetation settings ............................................................................................................. 60
3.3 Results and discussions ............................................................................................................ 63
3.3.1 Velocity ............................................................................................................................... 63
v

3.3.1.1 Effects of vegetation density on streamwise velocity ............................................... 65
3.3.1.2 Effects of water depth of streamwise velocity .......................................................... 67
3.3.1.3 Effects of square arrangement on velocity profile ................................................... 69
3.3.1.4 Effects of staggered arrangement on velocity profile .............................................. 70
3.3.1.5 Velocity contours in square arrangement ................................................................. 71
3.3.2 Turbulence Kinetic Energy (TKE) .................................................................................. 73
3.3.3 Shear Stress ........................................................................................................................ 77
3.4 Conclusions ............................................................................................................................... 82
3.5 Bibliography.............................................................................................................................. 85
4. Deformation of vegetated channel bed under ice-covered flow conditions ............................... 90
4.1 Introduction .............................................................................................................................. 90
4.1.1 Ice and sediment concentration ........................................................................................ 91
4.1.2 Presence of ice cover and vegetation in rivers................................................................. 92
4.2 Material and methods .............................................................................................................. 94
4.2.1 Equipment for Experiments ............................................................................................. 94
4.2.2 Vegetation settings ............................................................................................................. 94
4.2.3 Sediment used in experiments .......................................................................................... 97
4.2.4 Ice cover conditions ........................................................................................................... 98
4.3 Results........................................................................................................................................ 99
4.3.1 Manning’s coefficient ........................................................................................................ 99
4.3.2 Scour and deposition patterns and armour layer ......................................................... 103
4.3.3 Equations for calculating the maximum scour depth (y S) ........................................... 108
4.3.3.1 The maximum relative scour depth (yS/H) vs. Froude number (Fr) .................... 108
4.3.3.2

The maximum relative scour depth (yS/H) vs. roughness of ice cover (ni/nb) .. 109

4.3.3.3 The maximum relative scour depth (yS/H) vs. the vegetation density λ ............... 110
4.3.3.4 Equations for determining the maximum relative scour depth (yS/H) ................ 111
4.4 Conclusions ............................................................................................................................. 114
4.5 Bibliography............................................................................................................................ 116
5. Flow structure and shear stress in the presence of both ice cover on water surface and leafless
vegetation in channel bed................................................................................................................. 122
5.1 Introduction ............................................................................................................................ 122
5.2 Material and methods ............................................................................................................ 123
5.2.1 Facilities for experiments ................................................................................................ 123
5.2.2 Vegetation settings ........................................................................................................... 124
5.2.3 Sediment used in experiments ........................................................................................ 126
vi

5.2.4 Ice cover conditions ......................................................................................................... 126
5.3 Results...................................................................................................................................... 127
5.3.1 Velocity profiles ............................................................................................................... 127
5.3.2 Shear Stress ...................................................................................................................... 133
5.3.3 Turbulent kinetic energy (TKE) .................................................................................... 136
5.3.4 Quadrant analysis ............................................................................................................ 139
5.4 Conclusions ............................................................................................................................. 143
5.5 Bibliography............................................................................................................................ 145
6. GENERAL CONCLUSIONS ...................................................................................................... 149
6.1 Synthesis .................................................................................................................................. 149
6.2 Conclusions of chapter 3 ........................................................................................................ 150
6.3 Conclusions of chapter 4 ........................................................................................................ 153
6.4 Conclusions of chapter 5 ........................................................................................................ 156
6.5 Significance of Study .............................................................................................................. 159
6.6 Limitation of the current study ............................................................................................. 161
6.7 Future directions .................................................................................................................... 161
APPENDIX ....................................................................................................................................... 164

vii

List of Tables
Table 1.1: Division of flow based on shear Reynolds number ............................................................. 12
Table 2.1: Vegetation density parameters in this study ........................................................................ 37
Table 3.1: Some data for the flow depth of 20 cm ............................................................................... 63
Table 4.1: Vegetation density parameters in this study ........................................................................ 95
Table 4.2: Some of hydraulic data for canopy density of λ = ah=0.624............................................... 97
Table 4.3: Manning’s coefficient using three methods for different bed materials and different ice
cover conditions ................................................................................................................................. 102
Table 4.4: Median grain size of armour layer inside scour holes and at the surface of deposition dunes
(sand bed material: D50=0.50mm, rough ice-covered flow) ............................................................... 104
Table 4.5: Median grain size of armour layer inside scour holes and at the surface of deposition dunes
(sand bed material: D50=0.60mm, rough ice-covered flow) .............................................................. 104
Table 4.6: Median grain size of armour layer inside scour holes and at the surface of deposition dunes
(sand bed material:D50=0.98mm, rough ice-covered flow) ................................................................ 105
Table 5.1: Vegetation density parameters in this study ...................................................................... 125
Table I.1: Experimental data collected for D50=0.98 mm ................................................................. 164
Table I.2: Experimental data collected for D50=0.60 mm ................................................................. 166
Table I.3: Experimental data collected for D50=0.50 mm ................................................................. 168

viii

List of Figures

Figure 1.1: A two-layer velocity profile in a river section covered with ice .......................................... 9
Figure 1.2: Ice jam flood during 2008 breakup on the Hay River, NWT. This photo was taken looking
upstream along the ice jam and shows the flooding in the adjacent old village of the Kátl`odeeche
First Nation. (Photo by F. Hicks.) ........................................................................................................ 11
Figure 1.3: Flow within and above a submerged canopy of height h in water depth H. Profiles of
mean velocity (solid line) and turbulent stress (dashed line). The canopy- induced shear layer
generates shear-scale vortices that penetrate a distance δe into the canopy (Nepf & Ghisalberti, 2008)
.............................................................................................................................................................. 15
Figure 1.4: Comparison of (a) free shear layer (FSL) and (b) canopy shear layer (CSL) vortices. The
vortices translate with speed Uv, which is defined by the time required, T, for the vortex center to
move distance L downstream, Uv = L/T. (a) In a FSL the vortex is symmetric about the inflection
point, zi . The translation speed of the vortex matches the velocity of the inflection point, Uv = Ui. (b)
In a CSL the inflection point corresponds roughly with the top of the canopy, z i = h. The vortex center
is displaced upward relative to the inflection point, and the vortex travels faster than the velocity at
the inflection point, which occurs at the top of the canopy, Uv > Uh = Ui = 〈 〉 (z) = h (Nepf &
Ghisalberti, 2008). ................................................................................................................................ 16
Figure 1.5: Basic characteristics of all laminar and turbulent boundary layers developing flow over a
flat plate (Krishnan et al., 2017) ........................................................................................................... 18
Figure 1.6: Overview of forces acting on a sediment particle .............................................................. 19
Figure 1.7: The Shield's Diagram (Cao et al., 2006) ............................................................................ 22
Figure 2.1: The layout of the experimental flume (vertical and plan views)........................................ 32
Figure 2.2: The holding tank with a volume of 90 m3 .......................................................................... 32
Figure 2.3: Schematic top view of a vegetative zone in the flume. Black pronged shape shows the
positions of individual vegetation elements. Black circles are ADV measurement locations in the
wake of each vegetation element. Red circles show the ADV location between two vegetation
elements, and green circles show the ADV location in the center of four vegetation elements which
have been placed in a square pattern. The spacing distance between adjacent vegetation elements is
shown in the figure. .............................................................................................................................. 35
Figure 2.4: Grain size distribution of bed materials ............................................................................. 39
Figure 2.5: Attached Styrofoam cubes to simulate rough ice cover in the presence of deflected
vegetation, (b) simple Styrofoam as smooth ice cover in the presence of non-bending vegetation ..... 40

Figure 3.1: Apparatus used in the study (a) ADV (b) Sontek IQ ......................................................... 58
Figure 3.2: Grain size distribution of bed materials ............................................................................. 59
Figure 3.3: Schematic top view of a vegetative zone in the flume. Black pronged shape shows the
positions of individual vegetation elements. Black circles are ADV measurement locations in the
wake of each vegetation element. Red circles show the ADV location between two vegetation
elements, and green circles show the ADV location in the center of four vegetation elements which
have been placed in a square pattern. The spacing distance between adjacent vegetation elements is
shown in the figure. .............................................................................................................................. 60

ix

Figure 3.4: ADV position between two vegetation elements in (a) non-bending vegetation setting (b)
deflected vegetation setting .................................................................................................................. 62
Figure 3.5: One sample of fitting Logarithmic Law distribution on the upper layer of velocity profile
in a deflected and non-bending vegetation (staggered arrangement, flow depth: 30 cm) .................... 65
Figure 3.6: Velocity profiles with high vegetation density (a=0.624 m − 1) and lower vegetation
density (a=0.256 m − 1) (a) deflected vegetation (b) non-bending vegetation (Water depth: 20 cm and
square arrangement of vegetation in the wake behind vegetation (black circles in Figure 3.3) ........... 67
Figure 3.7: Comparison of velocity profiles in the wake zone behind vegetation elements arranged in
a square configuration, (a) water depth = 20 cm (b) water depth = 30 cm ........................................... 68
Figure 3.8: Dimensionless time-averaged streamwise velocity distribution in the presence of square
vegetation configuration with a vegetation density of a=0.624 m − 1. ADV locations: between two
vegetation elements (red circles in Figure 3.3) and in the center of four vegetation elements (green
circles in Figure 3.3) (a) water depth = 20 cm (b) water depth=30 cm. ............................................... 70
Figure 3.9: Velocity profiles in the wake zone behind non-bending vegetation elements deflected
vegetation elements which arranged in the staggered configuration in flow with the depths of 20 cm
and 30 cm ............................................................................................................................................. 71
Figure 3.10: Contours and 3D velocity graphs in vegetation with density of λ=0.09 at (a) near the bed
at the depth of z/H=0.1 (b) top of deflected vegetation at the depth of z/H=0.4 .................................. 72
Figure 3.11: Comparison of Turbulence Kinetic Energy (TKE) between deflected vegetation
morphology and non-bending vegetation morphology at different positions (a) higher vegetation
density (a=0.624 m-1) (b) lower vegetation density (a=0.256 m-1) ....................................................... 76
Figure 3.12: Contour of Turbulence Kinetic Energy (TKE) for deflected vegetation case having a
square configuration (λ=0.04, water depth = 30 cm). (a) around the top of vegetation z/H=0.4 (b) near
the bed z/H=0 ....................................................................................................................................... 77
Figure 3.13: Normalized Reynolds Shear Stress (flow depth = 20 cm) (a) Square configuration of
deflected vegetation in the wake zone of vegetation, between two vegetation elements and in the
center of four vegetation elements with λ=0.09 (b) Square configuration of non-bending vegetation in
the wake zone of vegetation, between two vegetation elements and in the center of four vegetation
elements with λ=0.12 (c) Staggered configuration of deflected vegetation in wake of three random
vegetation elements with λ=0.17 (d) Staggered configuration of non-bending vegetation in wake of
three random vegetation elements with λ=0.23 .................................................................................... 80
Figure 3.14: Normalized Reynolds Shear Stress in (water depth = 20 cm) (a) Square configuration of
deflected vegetation in the wake of vegetation, between two vegetation elements and in the center of
four vegetation elements with λ=0.04 (b) Square configuration of non-bending vegetation in the wake
of vegetation, between two vegetation elements and in the center of four vegetation elements with
λ=0.05 (c) Staggered configuration of deflected vegetation in wake of three random vegetation
elements with λ=0.07 (d) Staggered configuration of non-bending vegetation in wake of three random
vegetation elements with λ=0.1 ............................................................................................................ 81

Figure 4.1: Schematic top view of a vegetation zone in sand boxes. Black pronged shape shows the
positions of individual vegetation elements. Circles represent locations of ADV measurement in the
wake of vegetation elements. Star shapes depict the ADV location between two vegetation elements,
and diamond shapes show the ADV location in the center of four vegetation elements which have
been placed in a squared-configuration pattern. The spacing distance between adjacent vegetation
elements is shown in the figure. ........................................................................................................... 95
Figure 4.2: Grain size distribution of bed materials ............................................................................. 98
x

Figure 4.3: An example of linear regression for the rough ice cover using the law of the wall
approximation..................................................................................................................................... 101
Figure 4.4: Grain size distribution of the sediment particles under rough ice-covered flow condition
(a) armour layer inside scour holes, and (b) deposition dunes ........................................................... 106
Figure 4.5: . Images describing scour and deposition in the presence of vegetation under rough ice
cover condition: (a) square configuration of vegetation (b) staggered configuration of vegetation .. 107
Figure 4.6: Relation between the maximum relative scour depth (ys/H) and Froude number (Fr) ... 109
Figure 4.7: Relation between the maximum relative scour depth (yS/H) with the relative Manning’s
coefficient (ni/nb) .............................................................................................................................. 110
Figure 4.8: Relation between the maximum relative scour depth (yS/H) with the vegetation density (λ)
............................................................................................................................................................ 110
Figure 4.9: Comparison of calculated relative scour depth (ys/H) to those observed from experiments
(a) under ice-covered flow conditions (b) open flow conditions ........................................................ 113

Figure 5.1: The layout of the experimental flume (vertical and plan views)...................................... 124
Figure 5.2: Schematic top view of a vegetation zone in sand boxes. Black pronged shape shows the
positions of individual vegetation elements. Circles represent locations of ADV measurement in the
wake of vegetation elements. Star shapes depict the ADV location between two vegetation elements,
and diamond shapes show the ADV location in the center of four vegetation elements which have
been placed in a square pattern. The spacing distance between adjacent vegetation elements is shown
in the figure. ....................................................................................................................................... 125
Figure 5.3: Grain size distribution of bed materials ........................................................................... 126
Figure 5.4: Streamwise velocity under different surface condtions behind vegetation with the
vegetation density of λ=0.09 and water depth = 30 cm: (a) D50=0.50 mm (b) D50=0.60 mm and (c)
D50=0.98 mm ...................................................................................................................................... 130
Figure 5.5: Streamwise velocity under different surface condtions in a bare channel (water depth = 30
cm): (a) D50=0.50 mm (b) D50=0.60 mm and (c) D50=0.98 mm ......................................................... 132
Figure 5.6: Streamwise velocity profiles behind vegetation under different cover condtions with the
vegetation density λ=0.09, water depth =20 cm: (a) D50=0.50 mm (b) D50=0.60 mm and (c) D50=0.98
mm ...................................................................................................................................................... 132
Figure 5.7: Streamwise velocity profiles under different surface condtions without vegetation in the
channel bed, water depth = 20 cm: (a) D50=0.50 mm (b) D50=0.60 mm and (c) D50=0.98 mm ......... 132
Figure 5.8: Streamwise velocity profiles behind vegetation with density of 0.17 in staggered
configuration of vegetation elements (water depth= 30 cm): (a) D50=0.50 mm (b) D50=0.60 mm and
(c) D50=0.98 mm................................................................................................................................. 133
Figure 5.9: Normalized Reynolds Shear Stress downstream of vegetation elements under different
surface cover conditions (flow depth = 30 cm): (a) D50=0.50 mm (b) D50=0.60 mm (c) D50=0.98 mm
............................................................................................................................................................ 136
Figure 5.10: Normalized Reynolds Shear Stress downstream of vegetation elements under different
surface cover conditions (flow depth = 20 cm): (a) D50=0.50 mm (b) D50=0.60 mm (c) D50=0.98 mm
............................................................................................................................................................ 136
Figure 5.11: Comparison of Turbulent Kinetic Energy (TKE) behind dense (λ=0.9) deflected
vegetation in square configuration under different surface cover conditions, (a) D50=0.50 mm (b)
D50=0.60 mm and (c) D50=0.98 mm ................................................................................................... 138
Figure 5.12: Comparison of Turbulent Kinetic Energy (TKE) behind dense (λ=0.17) deflected
vegetation in staggered configuration, (a) D50=0.50 mm (b) D50=0.60 mm and (c) D50=0.98 mm .... 139
xi

Figure 5.13: Percentage of velocity fluctuations (u' and w') for each quadrant behind vegetation
elements (a) open channel flow, (b) smooth covered flow (c) rough covered flow. .......................... 142

xii

ACKNOWLEDGEMENT

I wanted to express my heartfelt gratitude to my supervisor Dr. Jueyi Sui throughout my
Ph.D. study and research. His unwavering support, patience, motivation, and extensive
knowledge have been invaluable to me. His feedback and constructive criticism have helped
me refine my ideas and improve the quality of my dissertation. His mentorship has extended
beyond the academic realm, and I am truly fortunate to have had him as my advisor.
I would like to extend my gratitude to each of my committee members: Dr. Faran Ali,
Dr. Liang Chen, Dr. Wenbo Zheng for their invaluable contributions. Their insightful
comments have been instrumental in shaping the outcome of my research.
I would like to express my deepest gratitude to Dr. Ellen Petticrew and Dr. Phil Owens
for the resources and facilities they have provided at Quesnel River Research Center (QRRC)
that significantly contributed to the quality and depth of my research. I am forever grateful for
the time, kindness, and support of Todd French. I deeply appreciate the guidance and support
of my dear friend Rahim Jafari, who continuously motivated and encouraged me throughout
my studies.
Lastly, I want to declare heartfelt gratitude to my beloved husband, Reza, and my parents.
Their constant love, encouragement, and sacrifices have been the foundation of my success.
And finally, to my precious son, Barbod, even though he is too young, his presence brings
immense joy to our family. I am grateful for the happiness and love he has brought into our
live.

xiii

1. CHAPTER ONE: INTRODUCTION AND LITERATURE REVIEW
The motivation behind this research study stems from the recognition of the significant
influence of both vegetation and ice cover on flow dynamics in fluvial systems. Despite the
individual understanding of vegetation and ice cover effects, no research has been conducted
to investigate their combined impacts on flow resistance and channel bed deformation. This
research study aimed to bridge this knowledge gap by examining the connection between
vegetation and ice covers comprehensively. By considering different vegetation densities,
arrangement patterns, and morphology, as well as the influence of ice cover roughness, the
study sought to provide a critical assessment of the vegetation density and distribution pattern's
impact on flow resistance and channel bed deformation.
Understanding these combined effects is crucial for sustainable restoration projects, river
management, and the rehabilitation of fluvial environments. It can inform decision-making
processes related to vegetation replanting, channel restoration, and the revitalization of coldweather river ecosystems. Additionally, the findings contribute to the development of accurate
and critical assessment methods that can be employed in future restoration projects to mitigate
flood impacts and ensure long-term channel stability.
1.1 Vegetation
Human civilizations (such as ancient civilizations in Mesopotamia, China, and Egypt)
was initiated along rivers because of the importance of water in human life. Fresh water in
rivers account for 0.0001 percent of the total water on the planet but nevertheless plays a very
important role in the physical, chemical and biological processes of our planet.

1

Aquatic vegetation in rivers, streams, lakes, and coastal regions offers a broad range of
advantages to the environment, including improving water quality, providing protection for
economically valuable fish species, and maintaining a stable riverbed (Barbier et al., 2011;
Costanza et al., 1997; Kemp et al., 2000). River floodplains and nearby wetlands play an
essential ecological role in river ecosystems (Newson, 1992; Ward et al., 2001). Plants grow
in a diverse and heterogeneous mix of herbs, shrubs, and trees, which play a crucial role in
determining how water, sediment, nutrients, and pollutants move through them (Nepf &
Vivoni, 2000). In floodplains and streams, vegetation alters hydrodynamics and flood flow
responses, which is critical for flood management. During flooding, woody plants' stems and
leaves increase turbulence, reduce flow velocity, and increase drag within vegetation patches,
and increase velocity outside vegetation patches (Luhar & Nepf, 2011; Nepf, 1999; Yager &
Schmeeckle, 2013).
Two types of vegetation are usually defined based on flexibility as stiff (typically woody
or arborescent plants) and flexible (herbaceous plants). In contrast to rigid vegetation, flexible
vegetation bends when water flows. Because bending degree varies with flow velocity,
resistance varies as a result of different degrees of bending. Flexible vegetation can adopt their
posture in response to the flow and reduce drag (Rominger & Nepf, 2014), thus preventing
uprooting during periods of strong currents and extreme waves (Albayrak et al., 2012; Vogel,
1984). Flexibility reduces drag in current-dominated conditions, resulting in velocity
attenuation inside the canopy (Nepf, 2012a, 2012b), and therefore a weaker shear layer at the
top of the canopy (Ghisalberti & Nepf, 2006). Hydrodynamic drag forces in stiff canopies have
been shown to be three times higher than that in canopies with flexible leaves (Bouma et al.,
2005). In a study, researchers discovered that the relationship between the drag coefficient and

2

Reynolds number is influenced by the flexibility and morphology of vegetation (Houser et al.,
2015). They observed that more flexible vegetation leads to a greater reduction in the drag
coefficient. They also noted that flexible vegetation generally has a lower drag coefficient
compared to rigid vegetation. Furthermore, they found that the prediction of the drag
coefficient can vary depending on the methodology and the specific morphology of the
vegetation. Therefore, canopy flexibility has been observed to greatly affect wave attenuation
(Houser et al., 2015; Paul et al., 2012). Flexibility has also been shown to positively influence
nutrient uptake and the efflux of dissolved oxygen from canopy elements (Huang et al., 2011;
Mass et al., 2010).
Both density and blade length can influence flow processes. Hansen & Reidenbach, 2012
did an experimental study and reported that at Site 2, which had a mid-density of 390 ± 80
shoots m-2, the greatest reduction in flow within the canopy compared to above the canopy was
observed along the density gradient ranging from 150 to 560 shoots m–2. Interestingly, the
eelgrass at this site exhibited significantly higher mean (28 cm) and maximum blade length
(51 cm) compared to the other Z. marina sites. While seagrass density has been identified as a
significant factor in flow reduction (Ackerman & Okubo, 1993), blade length also plays a
crucial role in modifying canopy friction (Fonseca & Fisher, 1986), thereby leading to a
proportional decrease in fluid velocity. Site 3, which had the lowest eelgrass density and
smallest average blade length, exhibited the smallest flow reduction within the canopy.
Historically, aquatic vegetation in streams was seen as flow resistance and was often
removed to facilitate the passage of water and reduce flooding. Despite this, vegetation also
contributes ecological services to coastal and river systems, which makes it an integral part of
them. With the goal of better understanding and protecting these systems, vegetation

3

hydrodynamics has become intertwined with other disciplines (Nepf, 2012b), such as biology
(e.g. Huang et al., 2011), fluvial geomorphology (Bennett et al., 2002), landscape ecology
(Larsen & Harvey, 2011), and geochemistry (Clarke, 2002). Here some of the advantages of
vegetation in rivers and streams have been highlighted.
1.1.1 Increasing bank stability and controlling floods
It has been demonstrated that riparian vegetation contributes to the cohesion of river
banks and significantly affects channel geometry in riverine environments and overbank
deposition patterns (Braudrick et al., 2009; Perignon et al., 2013; Tal & Paola, 2007). Water
erosion can be reduced by vegetation by dampening waves on coastal lines and riverbanks
(Türker et al., 2006). Vegetation drag reduces wave energy and canopy velocity, creating
aquatic ecological habitats (Kobayashi et al., 1993; Sánchez-González et al., 2011).
The ability of vegetation to enhance channel stability has now been clearly demonstrated
(Afzalimehr & Dey, 2009; Li & Millar, 2011) and reduce sediment loading from bank erosion
(Lawler, 2008). Vegetation can be used to stabilize banks and this can influence meandering,
create single-thread channels, decrease the number of branches in a river or stream, and reduce
the width of the channel (Allmendinger et al., 2005; Micheli & Kirchner, 2002; Tal & Paola,
2007). Based on modeling studies, it has been determined that wave energy attenuation is
positively correlated with shoot density, as stated by Chen et al., 2007. However, the extent of
flow reduction caused by the vegetation can also depend on factors such as the distance from
the vegetation edge and the average depth at which the seagrass is located beneath the water
surface, as noted by (Fonseca & Fisher, 1986).

4

1.1.2 Improving water quality and decreasing turbidity
Water quality in rivers and streams is deteriorating due to rapid urbanization and
industrialization. A major societal research concern is how to restore such degraded or
damaged ecosystems and effectively control the deteriorating water quality (Richardson et al.,
2007; Huang et al., 2011). It is common for shallow water systems to have submerged
vegetation, and the presence of vegetation is often associated with clear water conditions,
whereas its absence is generally associated with turbid water conditions (Hauxwell et al.,
2004). Sufficiently dense vegetation plays a crucial role in preserving the clarity of water by
minimizing resuspension (Moore, 2004). The uptake of nutrients and production of oxygen
improves water quality (Wilcock et al., 1999). The uptake of nutrients by submerged
vegetation is influenced by the local current and wave velocity (Koch, 1994; Weitzman et al.,
2013), which in turn are affected by the density of vegetation (Ghisalberti & Nepf, 2002; Lowe
et al., 2005). Turbulence patterns created by vegetation lead to a rise in the interchange of
chemicals and nutrients, and modifies range of sediment grain size, geochemical composition
and turbidity (Koch, 2001; Madsen et al., 2001; Sand-jensen, 1998). Numerous studies have
examined the impact of the specific morphology of coral canopies on both the flow structure
within the canopy (e.g., Chamberlain & Graus, 1975) and the rate at which scalar quantities,
such as dissolved nutrients, are transported to the organism's tissue (e.g., Helmuth, et al., 1997).
Some researchers advocate widespread planting in waterways as a means of removing nitrogen
and phosphorous (Mars et al., 1999; Moore, 2004). Enhancing our understanding of turbulence
within submerged meadows can lead to improved predictions of sediment mobilization.

5

1.1.3 Habitat
Aquatic plants are commonly found in both freshwater and saltwater environments. They
provide food and habitat for fish and other aquatic creatures (Irlandi & Peterson, 1991; Nedjimi
et al., 2012; Yi et al., 2017). Vegetation in river channels helps to increase biodiversity by
forming different habitats with various levels of velocity (Kemp et al., 2000). The magnitude
of flow through vegetation impacts the growth of them and aquatic species. For example,
reduced flow affects the food availability (Boström et al., 2006; Waycott et al., 2005),
providing shelter (Costanza et al., 1997) for fish and aquatic invertebrates.
1.1.4 Carbon storage
Many ecosystem services are provided by vegetation, such as the production and storage
of carbon (Greiner et al., 2013; Tang et al., 2018). Ocean vegetation can play a crucial role in
carbon storage and release in marine ecosystems, changing sea levels and sediment supplies
affect carbon storage and release in sediment plant systems (Fourqurean et al., 2012; Mcleod
et al., 2011; Nepf, 2012a).
1.1.5 Control of sediment movement
Channel vegetation alters flow structure, increases bed roughness, and results in lower
flow velocity, thereby affecting sediment and solute transport. Some researches shows that the
vegetation density (Bouma et al., 2007; Leonard & Croft, 2006), height (Nepf & Vivoni, 2000;
Shi et al., 1996), morphology (Morris et al., 2002), and flexibility (Ghisalberti & Nepf, 2006)
affect sediment transport and concentration.
Vegetation influences hydraulics, sediment erosion and deposition and channel
morphology (Bouma et al., 2007; Gran & Paola, 2001; López & García, 1998; Nepf, 2012a;
Simon & Collison, 2002). Vegetation in rivers and tidal environments is patchy by nature, and

6

it is the distribution of patches and density of plants within those patches that controls the
morphodynamical evolution of vegetated sedimentary environments (Le Bouteiller & Venditti,
2014). They found that the sediment transport capacity is reduced in the plants and that the bed
adjusts by increasing its slope to pass the supply through the plant patch. Vegetation
contributes to a range of ecosystem services like retention of suspended sediment by reducing
the near bed velocity of water close to the bottom (Fonseca & Fisher, 1986; Granata et al.,
2001). This retention of particles within vegetated regions can influence nutrient and
contaminant cycling, and carbon sequestration (Luettich et al., 1990).
1.2 Ice cover
River ice is an integral and important component of the high-latitude and high-altitude
flow regime in cold-regions environments. It can significantly affect many of the hydrologic,
geomorphic, and chemical characteristics of a river (Prowse, 2001).
Generally, ice action creates habitat heterogeneity, which favors riverine species
diversity (Lind et al., 2014). Some frost tolerant plants can survive for several months under
an ice cover. Their ability to survive under an ice cover gives them an advantage over annual
plants, as they will occupy the habitat once it melts (Renman, 1989). The erosive power of
moving ice floes in rivers favours vegetatively reproducing plants with budding parts
underground, plants with abundant seeds, or sturdy plants, for example those with widespread
root systems. Plants with combinations of these traits have a higher chance of overwintering
survival (Engström et al., 2011). Furthermore, an ice cover on water surface may also benefit
biota by providing insulation against extreme weather events (Andrews et al., 2019, 2020) and
acting as a stable substrate for colonization in turbulent or scouring conditions (Katz et al.,
2015; Twiss et al., 2012). However, during an ice covered period, snowpack on the top of ice
7

cover can decrease benthic light availability in rivers of all sizes, thereby reducing the
availability of suitable habitat for photosynthetic organisms or visual predators (Sharma et al.,
2020).
There is more sediment transport near the bed than throughout the entire column of water
under ice cover, based on the clarity of the water under ice cover, since most of the suspended
sediment is trapped in ice cover (Lawson et al., 1986; Sui et al., 2000). They found that after
river breakup, sediment transport and aggregation happens. In contrast, during ice-covered
period, due to freezing and decreasing discharge, sediment transport decreases and degradation
occurs (Lawson et al., 1986). The presence of an ice cover on water surface may change the
position and width of thalwegs, erode and deposit bed materials, weaken riverbank stability
(Sui et al., 2000). Based on field data of sediment concentration collected along a 70-km long
Hequ Reach of the Yellow River, it is reported that, during the formation of ice jams and breakup periods, the suspended load carried by the flow is coarser, as finer sediments from land
sources are reduced and finer sediments are entangled in ice, resulting in a predominant source
of sediment being the coarser material of the riverbed (Sui et al., 2000). Consequently,
sediment concentrations are more likely to increase during the dynamic transient phase of ice
breakup than that during stable ice-covered period. Under an ice jammed flow condition, water
level will be increased significantly (Sui et al., 2002, 2005, 2008). These impacts reduce
riverbank resistance to erosion and increase the local supply of sediment to the channel
(Ettema, 2002; Sui et al., 2006). The roughness of the ice jam – whether it contains loose or
dense slush or solid-ice blocks – as well as its thickness, determines its resistance to flow and
is therefore important for the flooding potential (Beltaos, 2008).

8

There has traditionally been a two-layer model for flow under an ice cover (see Figure
1.1). With an increasing distance from the underside of an ice cover, flow velocity increases
monotonically, reaches its maximum, then decreases toward the riverbed. Whether the channel
bed or ice cover has lower roughness and lower resistance, the maximum velocity will be closer
to that solid surface (Uzuner, 1975). In Figure 1.1, the maximum velocity occurs at yi that has
the lowest resistance. Ks is the roughness of the ice cover. The presence of an ice cover on
water surface increases the total wetted perimeter of the cross-section that is in contact with
water. In channels with a high width-to-depth ratio, having an ice cover can literally double
this wetted perimeter (Hicks, 2016).

Figure 1.1: A two-layer velocity profile in a river section covered with ice (Li, S. S. 2012)

River ice makes the design and implementation of a study across the continuum
challenging and expensive. The dynamics of ice cover in larger rivers can now be quantified
from space (Kääb et al., 2019; Yang et al., 2020), but sampling them during a winter period
without expensive equipment can be difficult and dangerous by using specialized equipment
such as snowmobiles or air boats, thereby limiting the capacity to obtain more ecological

9

information. Although it is simpler to get to smaller rivers and streams for ecological sampling
using everyday methods (e.g., going on foot or by car; excepting those in high mountain areas
or particularly isolated locations), it is hard to recognize large-scale disparities in ice dynamics
in small rivers (Thellman et al., 2021).
Thellman et al. (2021) found that ice loss patterns varied based on whether rivers flowed
north-south or east-west and that the importance of winter to annual productivity was greatest
in the smallest rivers. They demonstrated that north-south oriented rivers were more likely to
experience a reduction in surface air temperature gradient from headwaters to river mouth,
which led to a reduced ice duration gradient along the river profile.
The damage caused by ice jams is much greater than the damage caused by open-water
flooding (see Figure 1.2). Among these damages are flooding, structural damage, erosion and
scouring of beds and banks, failure of ripraps, failure of bridge pier, increased flood fighting
and assistance costs, and environmental degradation (Beltaos & Tang, 2013; NyantekyiKwakye et al., 2018; White et al., 2007). It was vegetation-covered bars and terrace margins
that were most vulnerable to erosion caused by impacting ice floes. In contrast, banks adjoining
floodplain surfaces and partially protected by vegetation roots and ice rubble walls were less
susceptible (Beltaos & Burrell, 2021). A variety of human activities have altered riparian and
aquatic habitats in high-latitude and high-altitude regions, such as impoundments, flow
regulation, mining, channelization, agriculturalization, and water pollution (Dynesius &
Nilsson, 1994; Nilsson et al., 2005; Ranzi et al., 2002; Takács et al., 2013; Walling, 2006). It
is common for large rivers with high energy potential to be regulated and fragmented for
hydropower production (Jansson et al., 2000; Prowse, 1994). The most direct effect on ice
conditions has likely been caused by hydroelectric development and channelization. These

10

changes have altered the environments of rivers and streams in ways that some species cannot
adapt to (Rood et al., 2007). Furthermore, due to water regulation, these waterways are
particularly susceptible to climate change, especially in northern regions (Woo et al., 2008).

Figure 1.2: Ice jam flood during 2008 breakup on the Hay River, NWT. This photo was taken looking upstream
along the ice jam and shows the flooding in the adjacent old village of the Kátl`odeeche First Nation. (Photo by
F. Hicks.)

1.3 Division of flow based on Froude number and Reynolds number
At any point of the flow field, the velocity vector is obtained by deriving the location
vector and is defined as follows:
⃗ = ⃗+ ⃗+

⃗=

⃗+

⃗+

⃗

1.1

Vectors of velocity and their components in the x, y, and z directions have specific values
at different points and times. In the current study, the direction of the flow in the x direction
and its corresponding velocity is u, while the direction perpendicular to the bottom of the
channel is z and its corresponding velocity is w, and the transverse direction of the flow y and
its corresponding velocity v will be studied.
In uniform flow at a given instant, the water depth in x direction remains unchanged with
distance along the flow path. In this regime, the channel slope is parallel to the water surface
slope. However, in non-uniform flow, water depth in cross sectional area varies along the flow.
11

The presence of vegetation in a flow path, various bed forms, changes in the flow width,
longitudinal and transverse slopes of the path, ice cover surface, and roughness characteristics
of channel bed are different factors for changing uniform flow to non-uniform flow.
(t=constant)

=0

uniform flow

1.2

(t=constant)

≠0

non-uniform flow

1.3

where, t is a time period. Most open channel flows are turbulent. There are three types of
turbulent flows: smooth, transition and fully rough. Each type of turbulent flow can be
distinguished as a function of the shear Reynolds number defined as:
∗ =

1.4

∗

where, ks is the average roughness height,

∗ is shear velocity and

is the kinematic viscosity

of water (Henderson, 1995): p. 95–96). For turbulent flows, the transition between smooth
turbulence and fully rough turbulence is approximately defined as (Chanson, 2004):
Table 1.1: Division of flow based on shear Reynolds number
Flow situation

Open channel flow (Henderson, 1966)

Smooth turbulent

∗ <4

Transition

4<

Fully rough turbulent

∗ < 100

∗ > 100

Hydraulic radius is defined as (Chanson, 2004):
=

1.5

=

Another dimensionless number that describes the fluid flow regime under the
simultaneous influence of acceleration and gravity forces is Froude number:
1.6

=

12

where, U is the mean steam-wise velocity of the fluid, g is the acceleration of gravity, and H
is the water depth. In the classification of flow types based on Froude number, critical flow is
defined as a flow whose Froude number is equal to one.
Based on this definition, two other types of flow are also introduced:
Super-critical flow: It is a flow whose Froude number is greater than one (Fr>1).
Subcritical flow: It is a flow whose Froude number is less than one (Fr<1)

1.4 Vegetation induced turbulence
Vegetation increases chemical and nutrient exchange rates due to vegetation-induced
turbulence (J. D. Madsen et al., 2001). Turbulence caused by vegetation can increase the
absorption of nutrients by vegetation (Cornacchia et al., 2018). Vegetation with specific
density has been seen to cause turbulence which increases sediment resuspension and bed load
transport, leading to sediment mobilization at a lower velocity than that without the presence
of vegetation (Tinoco & Coco, 2016). Vegetation density and morphology have a significant
influence on mixing rates and turbulent kinetic energy (TKE) (Widdows et al., 2008;
Worcester, 1995).
The interaction between flow and plants introduces supplementary mechanisms for
converting energy from the mean flow to turbulence. This phenomenon becomes evident
through the localized increase of spectral energy. This turbulent energy production occurs in a
range of frequencies, which is likely controlled by vegetation flexibility, arrangement, and
morphology of the patch elements, as well as the velocity field (Siniscalchi et al., 2012).
Vegetation-generated turbulence may be the only water motion turbulence of the right scale to
enhance nutrient uptake and exchange gases and solutes (Anderson & Charters, 1982). In high
stem density, however, the canopy dampens and dissipates mean current, a process known as
13

sheltering. By combining reduced velocity and reduced eddy-scale, (Nepf, 1999) defined
sheltering or dampening as a reduction in the in-emergent canopy macroscale diffusion. Some
researchers (e.g. Neumeier, 2007; Neumeier & Amos, 2006) found a reduction in turbulence
near the bed, resulting in an enhancement of sediment deposition and protection of the bed
against subsequent erosion. Research has shown that marsh canopies experience less
turbulence than neighboring channels, which is thought to be caused by increased deposition
(Leonard & Croft, 2006; Neumeier, 2007). Pujol et al., 2010 conducted experiments using an
oscillating grid in still water and observed that both rigid and flexible meadows provided
protection to the bed by reducing the turbulence generated above the meadow. This resulted in
a significant reduction of up to 60% in near-bed turbulent kinetic energy (TKE) compared to
bare-bed conditions. The damping effect was further enhanced by reducing stem diameter and
increasing stem density.
The resistance caused by vegetation elements diminishes the velocity within the
vegetation (z < h) relative to the non-vegetated area (z > h). The interface of vegetation and
non-vegetated layer (z = h) is a region of strong shear resembling a free-shear-layer.
Turbulence is also damped within the canopy, as shown in Figure 1.3, it is important to note
that a shear-layer is generated only when the momentum absorption by the vegetation is
sufficient to produce an inflection point in the velocity profile, which is needed to trigger the
Kelvin–Helmholtz (KH) instability. Only vegetation with CDah > ≈ 0.1 provide sufficient
resistance to generate an inflection point (Dunn, et al., 1996; Poggi et al., 2004). Note that CD
is vegetation drag, a is vegetation density and h is the bending height of vegetation. In both
terrestrial and aquatic canopies, the vortices dominate the exchange of mass and momentum
between the canopy and the overlying flow (Finnigan, 2000). In contrast, turbulence in the

14

lower canopy (z < h – ) is generated in the wakes of individual vegetation elements, therefore,
has significantly smaller scale, set by the stem diameters and spacing. The penetration depth
( =

) is defined as the point into the canopy that shear stress decays to its 10% of the

maximum value (Nepf & Ghisalberti, 2008). As canopy density increases (CDah > 0.2), the
penetration depth decreases (Aberle & Järvelä, 2015).

Figure 1.3: Flow within and above a submerged canopy of height h in water depth H. Profiles of mean velocity
(solid line) and turbulent stress (dashed line). The canopy- induced shear layer generates shear-scale vortices that
penetrate a distance δe into the canopy (Nepf & Ghisalberti, 2008)

Canopies in the natural environment are flexible and move according to the mean and
turbulent flow fields. Specifically, KH vortices passing over a flexible canopy can cause
progressive waving called monami. The waving has been observed extensively in the field
(e.g., Ackerman and Okubo, 1993; Fonseca and Kenworthy, 1987). The frequency of the
monami matches the frequency of vortex passage, which in turn matches the frequency of the
KH instability. Figure 1.4 shows a schematic passing of a vortex and bending of the vegetation
in accordance with it (Nepf & Ghisalberti, 2008).

15

Figure 1.4: Comparison of (a) free shear layer (FSL) and (b) canopy shear layer (CSL) vortices. The vortices
translate with speed Uv, which is defined by the time required, T, for the vortex center to move distance L
downstream, Uv = L/T. (a) In a FSL the vortex is symmetric about the inflection point, zi . The translation speed
of the vortex matches the velocity of the inflection point, Uv = Ui. (b) In a CSL the inflection point corresponds
roughly with the top of the canopy, zi = h. The vortex center is displaced upward relative to the inflection point,
and the vortex travels faster than the velocity at the inflection point, which occurs at the top of the canopy, Uv >
Uh = Ui = 〈 〉 (z) = h (Nepf & Ghisalberti, 2008).

1.5 Boundary layer theory
The motion of a real fluid is effectively affected by the solid boundary. The concept of
the boundary layer was introduced by Prandtl in 1904. He theorized that the effect of friction
was caused the fluid immediately adjacent to the surface to stick to the surface. In other words,
he assumed the no-slip condition at the surface and that frictional effects were experienced
only in the boundary layer, a thin region near the surface that slows down the movement.
Outside the boundary, the flow is essentially inviscid (Anderson, 2005). In the shallow currents
of rivers, the boundary layer continues up to the water level.
In this study, the values of shear velocity ( ∗ ) was obtained using the boundary layer
method (Afzalimehr & Rennie, 2009).

16

∗

=

( ∗

1.7

)
∗

where, umax is the maximum streamlined velocity, C is an empirical constant that was found
to be equal to 4.4 in laboratory experiments (Afzalimehr & Rennie, 2009). The parameter δ* is
boundary layer displacement thickness and indicates the distance by which the external
streamlines are shifted owing to the formation of the boundary layer. It is impossible to present
a boundary-layer thickness in an unambiguous way because the effect of viscosity in the
boundary layer decreases asymptotically outwards (Schlichting & Gersten, 2000). In order to
avoid utilization of an arbitrary boundary layer thickness, it is necessary to consider the
boundary layer displacement thickness, δ* (Clauser, 1956):
∗ =∫

1.8

1−

where, u is the mean point velocity at a distance z measured from the reference level.
Furthermore, the momentum thickness (θ) in Equation 1.7 indicates the loss of momentum in
the boundary layer as compared with potential flow and is defined as:
=∫

1.9

1−

The exact values of δ* and θ depend upon the distribution of downstream velocity in the
cross section normal to the flow.
When the flow hits a horizontal plate (such as the channel bed), the boundary layer is
formed on it. As the distance from the beginning of the solid surface increases, the boundary
layer thickness increases. In this area, the shape of the velocity profiles changes along the
channel. The further along the channel, the boundary layer thickness increases along the flow
depth until it reaches a flow depth from which the shape of the velocity profile remains constant
in the longitudinal direction. The flow in this area is called fully developed flow. The rougher

17

the channel bed, the fully developed flow is formed at a closer distance from the beginning of
the channel. The Reynolds number in these cases is defined as follows:
1.10

=

In which, x is the distance from the beginning of the solid bed. for small Reynolds numbers
(

=5×10 ), the boundary layer is laminar, and if Reynolds numbers is more than (

=

5 × 10 ), the boundary layer becomes a turbulent boundary layer, so at a distance from the
beginning of the bed (leading edge) the flow inside the boundary layer becomes turbulent.
There is distance between the laminar and turbulent boundary layer named the transition zone.
In the laminar boundary layer flow, viscosity is a determining factor in how velocity changes,
but in the turbulent boundary layer, the parallel flow lines do not remain, and the movement
of the particles takes place randomly, and the effect viscosity decreases. In the case of turbulent
boundary layer, a very thin layer is formed near the bed where viscosity is still the determining
factor, which is called the viscous sublayer (Schlichting & Gersten, 2000). Figure 1.5 shows a
boundary along the channel bed.

Figure 1.5: Basic characteristics of all laminar and turbulent boundary layers developing flow over a flat plate
(Krishnan et al., 2017)

18

1.6 Incipient motion
In general, as showed in Figure 1.6, the theoretical prediction of the critical condition for
the incipient motion of bed material is based on both force or momentum balance between the
destabilizing hydrodynamic drag (FD) and lift forces (FL) against the resisting gravitational
force (W) and frictional force (FR). Sediment particle will be initiated to move if the applied
forces overcome the resistance force. Under the condition of the threshold of movement, the
applied forces are just in balance with the resisting forces (Chang, 1992). In other words, a
particle is at a state of incipient motion when the following conditions have been satisfied:

Figure 1.6: Overview of forces acting on a sediment particle

=

1.11

=

1.12

=

−

= (

1.13

− )

where, D50A is the particle size in the armor layer,
is the specific weight of water,

is the specific weight of the sediment, γ

is the submerged weight of the particle and

is the

buoyancy force applied on the sediment particle. An object partially or fully immersed in water
will experience buoyancy as a result of a fluid exerting a force against its weight. As the weight

19

of the overlying fluid increases with depth in a column of fluid, pressure increases with depth.
As a result of the pressure difference, the object experiences a net upward force.
To preciously predict the incipient motion of a sand particle, it is necessary to know the
hydrodynamic drag (FD) and lift force (FL) acting on a particle in addition to its geometry,
exposure, the cohesive forces acting between particles and geometry. By using Yang’s criteria
(2003) for the incipient motion, the drag force can be expressed as (Yang, 2003):
=

1.14

=

1.15

=

1.16

where, CD is the drag coefficient at the velocity of Vs which is the local velocity at a distance
of s above the bed; and CL is the lift coefficient at velocity Vs.

1.7 Flow resistance and shields diagram
River engineering, fluvial geomorphology, ecohydrology, environmental management,
and hazard prediction all rely heavily on the prediction of sediment transport (Recking, 2009).
It is believed that almost all sediment-related problems in water, such as water quality and
pollution, scouring, deposition, and problems related to construction and management of
reservoirs and canals, as well as the restoration of wetlands, are related to sediment motion
(Ghose-Hajra et al., 2015; Venditti et al., 2006; Zhang & Yu, 2017). In natural rivers, it is
difficult to assess the threshold motion of sediment since the bed material is not uniform.
Knowing the threshold velocity is useful for understanding the scouring process around bridge
piers, defining stable channels and calculating the permitted slope and water depth, calculating
the roughness coefficient of stable channels, and studying sedimentation in reservoirs.

20

Wang et al. (2008) speculated that the incipient motion of sediment under ice-covered
flow conditions is different from that under open channel flow conditions since the maximum
flow velocity is forced to move closer to the channel bed. Besides, they found that the deeper
the flow depth under an ice cover, the higher the flow velocity needed for the incipient motion
of bed material. Streams with non-uniform bed materials are typically protected by an armor
layer in the bed. The phenomenon is caused mainly by selective erosion processes in which
the bed shear stress on finer sediment particles exceeds the critical shear stress for movement
during the erosion process. Consequently, finer sediment particles are transported, and coarser
sediment particles are left behind. Flow exposure within the scour hole zone is also reduced
due to the development of the armour layer (Sui et al., 2010). There is an association between
the incipient motion of sediment particle and the development of an armour layer around bridge
piers and vegetation stems. For the same bed material, it found that the scour depth around
bridge piers with an armour layer is less than that without armour layer under both open
channel and ice-covered flow conditions (Dey and Raikar, 2007; Namaee and Sui, 2019b; Wu
et al., 2014). For any bed material having the same grain size, with the increase in the particle
size of armour-layer, scour depth will decrease (Namaee & Sui, 2019).
The Shields diagram is widely used in practice to study the incipient motion of noncohesive sediment particles. The graph (Figure 1.7) is based on the Shields parameter
(θc)/Shields criterion/ Shields number /dimensionless shear stress ( ∗ ) against the grain
Reynolds number

∗ , which defines the transition between hydraulic smooth and rough

conditions for which grains protrude into the flow above the laminar sublayer (
al., 1977).

21

∗ ) (Miller et

Figure 1.7: The Shield's Diagram (Cao et al., 2006)

The conditions necessary for an impending sediment entrainment can be determined by
comparing the critical Shields value ( ∗ ) and the boundary shear Reynolds number (

∗ ). The

latter is expressed as:
∗ =

1.17

∗

where, ν is the kinetic viscosity of fluid, and

∗ is shear velocity. The shear velocity ( ∗ ) in

Equation 1.17 can be determined as follows:
1.18

∗ =

Where, S is the channel slope. The dimensionless shear stress is used to calculate the initiation
of sediment motion in a fluid flow (Madsen, 1991). The critical dimensionless shear stress ( ∗ )
is defined as follows:

22

∗

=(

1.19

∗

)

In which, ρs and ρ are the mass density of sediment and water, respectively, and

∗

is the

critical shear velocity that initializes the motion of the particles. The function of the

∗

equals to critical bed shear stress (

).

If the shear stress is higher than the critical shear stress, but less than the critical shear
stress for initiation of suspended particles, the sediments will begin to move, known as bedload
transport. Transport of bedload takes the form of traction (rolling and sliding) or saltation
(hopping). However, if the shear stress is higher than the critical shear stress for initiation of
suspended particle, the sediment starts to move in suspension (Hassanzadeh, 2012).
The Shields diagram usually requires an iterative procedure to determine the critical bed
shear stress due to the presence of Reynolds numbers (

∗ ) on both axes. The following

dimensionless sediment size parameter has been proposed by some researchers (Yalin, 1972)
to avoid the trial and error solutions:
∗ =

Where,

(

1.20

)

represents the specific weight of sediment particle. It introduces a new parameter

into the Shields diagram on the horizontal axis instead of the shear Reynolds number, called
the sediment-fluid parameter. After that, empirical threshold curves for non-cohesive
sediments were developed on the basis of Shields' study (Cao et al., 2006).
1.8 Hypothesis
A comprehensive insight into the effects of various variables on flow structure will be
achieved in the present study using a variety of variables found in nature with different
diversity. These variables include vegetation morphology including deflected and non-

23

bending, submergence ratio of the vegetation, vegetation density, vegetation arrangement such
as square and staggered arrangement patterns, different flow depths, three different sands and
three different surface cover conditions including smooth ice-covered, rough ice-covered and
open channel flow conditions.
Many studies have been conducted on the effects of these variables separately. For
example, it is known that ice cover surface decreases the bulk velocity and shifts the maximum
velocity closer to the bed. However, the interaction of the mentioned variables has not been
studied yet. The hypothesis of the present study is that the presence of vegetation in different
densities, submergence ratio and densities complicate the prediction of the flow structure in
the presence of an ice cover on water surface.
In addition, it is known that the depth of scour holes under an ice-covered flow condition
is deeper compared to that under an open flow condition. However, the presence of vegetation
makes it complicated to predict how would be the scour pattern when different factors are
present. One of the present hypotheses is that the contribution of the vegetation density on bed
deformation and velocity profiles is the highest among other variables.
The following hypothesis suggests that "the presence of vegetation with different
densities, submergence ratios, and arrangements, in combination with different cover
conditions of water surface (including smooth ice-covered, rough ice-covered, and open
channel flow conditions), complicates the prediction of flow structure. Additionally, the
interaction of these factors affects the scour pattern around vegetation elements under cecovered flow conditions."

24

1.9 Objectives
Through the processes described above, aquatic vegetation provides ecosystem services
with an estimated annual value of over ten trillion dollars (Costanza et al., 1997). This includes
reducing flood damage (Narayan et al., 2017) and removing polluted particles in water (Jenkins
et al., 2010). These services are all influenced in some way by the flow field existing within
and around the vegetated region (Nepf, 2012b).
Knowing how vegetation and ice cover affects the amount of sediment transport and
channel bed deformation will increase our ability to benefit the water system and prevent
erosion rate in vegetated areas.
The following list is the objectives of the present study:
I.

Effects of vegetation morphology including deflected and non-bending vegetation
(chapter 3)
The morphology, or physical form of submerged vegetation can have a
significant impact on aquatic environments. Two common types of morphology are
deflected and non-bending vegetation that cause different submergence ratios.
Deflected vegetation refers to submerged vegetation that is bent over or tilted by the
current of flowing water. Non-bending vegetation, on the other hand, refers to
submerged vegetation that is standing upright in the water column.

II.

The impact of non-uniformity of sediment on local scour around vegetation stems
(chapter 4)
The uniform sediment used in experiments for investigating the channel bed
deformation and local scour can result in overly conservative design values for scour,
as bed materials in natural rivers are non-uniform.

25

To address this issue, in this study, three non-uniform bed materials with
different median particle sizes (D50) of 0.50 mm, 0.60 mm , and 0.98 mm, are used
to present study to reasonably represent the sediment conditions in natural rivers. By
analyzing the scour depths and bed deformation of these different sediments, the study
can provide insights into how sediment characteristics can impact bed deformation
around vegetation elements.
III.

Effects of different arrangement patterns of submerged vegetation including square
and staggered layouts on flow structure (chapter 3,4,5)
Research results have shown that the arrangement pattern of vegetation can
influence flow structure. For example, a square layout of submerged vegetation
elements can produce a more uniform flow structure, with water flowing more evenly
around the vegetation patch. In contrast, a staggered layout of submerged vegetation
elements can produce more complex flow patterns, with eddies and vortices forming
between vegetation elements.
Understanding the impact of the arrangement patterns of submerged vegetation
on velocity profiles, Reynolds shear stress, and TKE is important for a range of
applications, including ecological restoration and the design of aquatic habitats for
fish and other aquatic species. By carefully considering the arrangement of submerged
vegetation, it may be possible to create optimal flow conditions for these applications.

IV.

Effects of submerged vegetation density on flow structure (chapter 3,4,5)
Different vegetation densities have different effects on flow structure. As the
density of vegetation increases, the resistance to flow also increases, leading to
changes in flow velocity, turbulence, and sediment transport. One of the primary

26

effects caused by increasing vegetation density is the decrease in flow velocity. This
is because the vegetation creates a barrier to flow, which causes water to slow down
as it moves through the vegetation patch. This decrease in velocity can result in the
formation of eddies and vortices.
In the present study, a critical range of vegetation density including dense,
transition and sparse vegetation density will be used to find the impacts of the
difference in vegetation density on sediment transport and flow structure.
V.

The impact of hydraulic condition on local scour around vegetation elements under
ice-covered and open-channel flow condition (chapter 3,4,5)
In the present study, incorporating different combinations of flow velocity and
flow depth to create a wide range of flow Froude numbers can provide valuable
insights into the impact of flow conditions on aquatic environments. The Froude
number is a dimensionless parameter that describes the relative importance of inertial
forces to gravitational forces in a fluid system, and can be used to predict flow
behavior and sediment transport in rivers and other aquatic environments.
By studying the impact of Froude numbers on aquatic environments,
researchers can gain insights into how flow conditions affect some fluvial processes
such as sediment transport, nutrient transport, and the distribution and growth of
aquatic vegetation. This information can be useful for a range of applications,
including ecological restoration, water resource management, channelization, and the
design of aquatic habitats for fish and other aquatic species.

27

VI.

Effects of different cover conditions of water surface like open channel, smooth icecovered and rough ice- covered flow condition on channel bed deformation and flow
characteristics (chapter 4,5)
Velocity distribution under an ice cover is different from that of an open
channel. When there is an ice cover on water surface, a new boundary is added to the
surface of the water, and this causes the velocity to decrease near the ice cover and
the channel bed due to the no-slip boundary condition. This leads to a parabola-shaped
velocity profile, as has been observed in previous studies. In addition, the maximum
velocity under ice-covered conditions occurs between the bed and the bottom surface
of ice cover, and this depends on the relative roughness of the ice cover and the
channel bed (Ettema & Daly, 2004; Muste et al., 2000; Prowse, 1994).
The main objective of this study is to compare and analyze the velocity profile
distribution under open channel flow, smooth and rough ice-covered flow conditions.
This will provide valuable insights into the behavior of water flow in these different
scenarios and may have important implications for various practical applications, such
as water resource management, flood control, and environmental protection.

1.10 Thesis Structure
Chapter Two serves as an introduction to the materials and methods employed in this
experimental study. This chapter provides a comprehensive overview of the various
components involved, including the characteristics of the flume, the apparatus utilized, the
application of artificial vegetation, the presence of ice cover, and the composition of the sand.
Each of these elements will be thoroughly demonstrated and elaborated upon in Chapter Two,
ensuring a clear understanding of their roles and significance within the study. Chapter Three
28

primarily investigates the impact of vegetation characteristics, including density, arrangement,
and morphology, on flow structure. The chapter aims to uncover the specific effects of these
parameters on flow velocity, turbulence, and Turbulent Kinetic Energy (TKE). The findings
will contribute to our understanding of the role of vegetation in hydraulic processes and have
practical implications in areas such as river management and environmental engineering.
Chapter Four examines the effects of vegetation and ice cover on scouring and bed
deformation. It investigates how different vegetation densities and arrangements influence bed
deformation in the presence of ice cover. The findings contribute to our understanding of how
vegetation mitigates ice-induced scouring and affects sediment redistribution, providing
valuable insights for river engineering and environmental management. Chapter Five
investigates the interaction between vegetation and different surface conditions: rough ice
cover, smooth ice cover, and open flow. It explores how vegetation affects flow dynamics,
turbulence, and Reynolds shear stress in each condition. The findings enhance our
understanding of vegetation's response to diverse surface conditions and have practical
implications for river management and environmental engineering. In Chapter Six, the study
concludes with a comprehensive summary of the findings and outcomes. It provides an
overview of the key insights gained from the research, highlighting the significant
contributions and implications of the study's results. Additionally, Chapter Six addresses the
limitations of the current research. It acknowledges any constraints, challenges, or potential
sources of error that may have influenced the study's outcomes. Moreover, this chapter outlines
potential directions for future research. It discusses areas that require further investigation and
suggests avenues for expanding upon the current study.

29

2. CHAPTER TWO: MATERIALS AND METHODS
In Chapter Two, special attention is given to ensuring that the composition of the
materials and methods used in the experimental study closely resembles the natural conditions
found in rivers. This chapter introduces fundamental aspects of the experimental study,
focusing specifically on the materials and methods utilized.
The first component discussed is the flume. A comprehensive overview of its
characteristics is presented, highlighting its dimensions, slope, and functionality. The flume's
size, shape, and configuration are carefully described, emphasizing how these factors
contribute to the experimental setup.
Next, the apparatus employed in the experimental study is introduced and detailed. This
section delineates the various instruments used to measure and monitor the turbulent flow. The
purpose, specifications, and data filtration methods for each apparatus are explained, enabling
readers to grasp their significance in gathering accurate and reliable data throughout the study.
Artificial submerged vegetation, a vital component of the experimental setup, is
extensively covered here. The chapter introduces the characteristics of the artificial vegetation,
including factors such as height, density, flexibility, arrangement, and morphology which
contribute to its influence on flow patterns and sediment transport.
Another essential aspect discussed is the composition of the sand used in the
experimental study is thoroughly examined. The chapter presents a detailed analysis of the
sand properties, such as grain size distribution and standard deviation which influence
sediment transport processes.

30

Lastly the chapter provides insights into simulate smooth and rough ice cover within the
flume.
2.1 Flume, ADV and SonTek IQ used for this study
Experiments have been carried out in a large-scale outdoor flume. This flume is 38-m
long, 2.0-m wide, and 1.3-m deep, as showed in Figure 2.1. The longitudinal slope of the flume
bed is 0.2%. Two water depths of 20 cm and 30 cm have been used for this experimental study
by adjusting the tailgates at the end of the flume. These water depths were chosen based on a
real situation in nature since the submerged vegetation typically grows in shallow regions of
rivers. Flowing water was supplied by a pump and three valves that feed the upstream holding
tank. The water in the holding tank upstream of the main channel was maintained a constant
water level. The desired constant flow rate, which is 100 cm3/s in this study, was obtained by
adjusting these three valves. The holding tank has a volume of 90 m3 to keep a constant water
level during each experimental run (Figure 2.2).
The aspect ratio W/H is defined as the ratio of the flume width to water depth. For both
water depths of 20 cm and 30 cm used in this experimental study, the flume is classified as a
wide flume since the aspect ratio is greater than 5 to 10. This means that in this flume, the
effects of the side walls of the channel and the secondary currents can be ignored in the center
zone of the flume (Chow, 2009)
There were two sandboxes which are spaced 10.2 meters from each other. The upstream
sandbox is 5.60-m long, 2.00-m wide, and 0.30-m deep, while the downstream one is 5.80-m
long, 2.00-m wide, and 0.30-m deep. A transparent viewing window made of plexiglass is
constructed inside each of the sand boxes which makes it possible to observe the process of
scouring and deposition around vegetation elements.

31

Figure 2.1: The layout of the experimental flume (vertical and plan views)

Figure 2.2: The holding tank with a volume of 90 m 3

In this experimental study, a down-looking Acoustic Doppler Velocimeter (ADV) 10MHz developed by Nortek, was used to measure the instantaneous three-dimensional velocity

32

components with a sampling rate of 25 Hz and a sampling volume of 0.25 cc. The duration of
each measurement was 2 min, acquiring 3000 instantaneous velocity data at each measurement
point. The vertical intervals between two consecutive points for each velocity profile were 10
mm. The signal-to-noise ratio (SNR) was recorded in the ADV file and used for assessing the
strength of the received acoustic signal against the ambient electronic noise level of the ADV
(Sontek, A.D.V., 1997) . To obtain high-quality data from the ADV, SNR values should be
greater than 5 dB for measurements of the mean flow velocity and greater than 15 dB for the
instantaneous velocity or turbulence quantities. The filtering method of (Goring & Nikora,
2002) and (Wahl, 2003) was selected in this study. The WinADV software was used for data
filtering. One of the real-time outputs provided by the ADV is a statistical correlation to assess
the quality of the velocity measurements. If the average correlation was less than or equal to
70%, the measured velocity data were filtered out.
After removing spikes using the WinADV software, velocity fluctuation in the
longitudinal (x), lateral (y), and vertical (z) directions were calculated as follows:
=

−

=

−

=

−

2.1

Where, u, v, and w are the time-averaged velocities that correspond to the directions x, y, and
z, respectively;

,

, and

are the instantaneous velocity components that correspond to the

directions x, y, and z, respectively. The x axis is aligned with the direction of the mean flow (or
stream-wise direction). The y axis is the spanwise direction, and the z axis is vertical, with z =
0 at the channel bed, and positive upward.
The equilibrium state of the scour process in vegetated channels will achieve after 48
hours (Nabaei et al., 2021). To make sure that the exact flow rate has been obtained over the

33

duration of 48 hours, a SonTek-IQ Plus was used. This precise and robust apparatuse was also
used to measure the average velocity and water depth with advanced post-processing functions
(SonTek-IQ Series, 2017). The SonTek IQ is a semi-rectangular shape designed to mount on
the channel bottom. Because of the sleek shape of the SonTek IQ, its impact on flow is
minimal. The surface slope

⁄

was measured using a staff gauge installed in the middle

of the sandbox to verify the water depth manually.

2.2 Vegetation settings
The model flexible vegetation elements used in this study are made of plastic material.
The selected artificial vegetation flexibility is commensurate with the geometry and flexural
rigidity of typical aquatic vegetation growing in natural rivers. Each vegetation element
consisted of five blades attached to it. Every vegetation element was attached to a grid mesh
panel with the spacing distances respectively of 15 cm and 25 cm in a square configuration,
and 10.61 cm and 17.68 cm in a staggered configuration. Then, the grid mesh panel with
vegetation elements was placed and buried 10 cm below the sand bed surface. Afterward, the
surface of the sandbox with vegetation was carefully leveled. By doing so, the vegetation
elements were fully stabilized in the sand bed, representing a natural situation with roots in
channel bed.
Figure 2.3 shows the positions for measurement using an ADV (called as the “ADV
positions”) in channel bed with two different vegetation arrangement patterns, namely, the
square and staggered configurations. Measurements at 24 ADV positions around vegetation
elements provide robust information for detecting flow structure and turbulence. To determine
the wake structure behind each vegetation element, the velocity profile was taken at three
points in the wakes of some vegetation elements, as shown in Figure 2.3.
34

Figure 2.3: Schematic top view of a vegetative zone in the flume. Black pronged shape shows the positions of
individual vegetation elements. Black circles are ADV measurement locations in the wake of each vegetation
element. Red circles show the ADV location between two vegetation elements, and green circles show the ADV
location in the center of four vegetation elements which have been placed in a square pattern. The spacing distance
between adjacent vegetation elements is shown in the figure.

The flowing water from upstream passes through the submerged vegetation patch. After
a certain distance from the upstream edge of the submerged vegetation patch, the flow will be
fully developed. Upstream of submerged vegetation, flow follows boundary layer conditions.
Once the flow approaches submerged vegetation, this condition turns into a mixing layer. In
the mixing layer flow, the shear layer known as Kelvin Helmholtz vortices will be developed
and reach an equilibrium in size depending on the vegetation density and submergence ratio
(Huai et al., 2019). The flow within the submerged vegetation is fully developed when the
equilibrium is achieved. In this study, all velocity profiles are collected using the ADV in the
fully developed flow inside of the vegetation patch, which is different from the fully developed
flow in channels without the presence of vegetation.
In the presence of a finite vegetation patch, channel resistance and conveyance are
modified, at least locally, resulting in a deviation from uniform flow conditions (Siniscalchi et
al., 2012). In addition, the channel has a longitudinal slope of 0.2% and the bed material is
nonuniform sand, which leads to non-uniform flow in the experiment.

35

To investigate the influence of vegetation density on flow structure, artificial vegetation
with densities of 16, 32, 36, 72 stems/

were used in this study. It may be sufficient to

parameterize vegetation based on stem diameter, density, and the number of plants per area for
flow without leaf and non-bending vegetation (Nepf, 1999; Petryk S & Bosmajian G, 1975).
The vegetation density a (

) was determined by dividing the projected vegetation area

by the vegetation volume (Equation 2.2) as (Nezu & Sanjou, 2008):
=

=

̅

2.2

where, n is the amount of vegetation in the area of (W * L), W is the channel width, ̅ is the
mean frontal vegetal area, h is the vegetation bending height, and L is the length of channel in
which n was counted. Considering five blades per vegetation element, the vegetation density
a varies from 0.256 m-1 to 1.2 m-1. Finally, a non-dimensional measure of the canopy density
= ℎ, known as the roughness density was calculated. The frontal area of vegetation was
determined using an image analysis software. This software was designed to distinguish
between black and white zones to calculate the silhouette of the vegetation. According to
(Belcher et al., 2003), there is a scale to distinguish sparse and dense vegetation. In a sparse
regime (λ= ah < 0.1), the vegetation drag is small compared to the bed roughness. Therefore,
flow velocity acts following the boundary layer profile. In this regime, the turbulence near the
bed will increase as the stem density increases. On the other hand, in dense vegetation regime
(λ= ah > 0.1), the vegetation drag is clearly high compared to the bed stress. An increase in
the vegetation density will lead to a decreased turbulence near-bed and increased deposition.
The vegetation density in this study is summarized in Table 2.1. One can see from Table 2.1,
the range of the canopy density λ=ah is 0.04 < λ ≈<0.23. Some researchers found that, for 0.1<
λ ≈<0.2, the eddies in the mixing layer penetrate toward the bed. In this study, the vortices
36

(eddies) in the middle layer of the flow named mixing layer penetrate toward the bed and are
responsible for turbulence patterns across the vegetation and benefits the resuspension of
sediment (Huai et al., 2021; Nepf & Ghisalberti, 2008). As a result, no penetration depth needs
to be calculated in the present study because the eddies reach the bed.
Table 2.1: Vegetation density parameters in this study
Configuration of vegetation
elements
Square non-bending,
Square deflected

Vegetation density
a(
0.624

Staggered non-bending

1.2

Staggered deflected
Square non-bending
Square deflected
Staggered non-bending
Staggered deflected

0.256
0.506

)

Canopy density
(λ= ah)
0.12
0.09
0.23
0.17
0.05
0.04
0.1
0.07

Some researchers used the inflexible and idealized cylinders to represent vegetation to
investigate the complicated flow structure caused by vegetation, it is unable to fully predict the
behavior of natural vegetation due to its differences in roughness, flexibility, and drag
coefficient. Besides, flow structure around a single cylinder or vegetation element cannot be
generalized for a vegetation patch since a group of cylinders or vegetation elements interact
with each other and on flow structure through sheltering effect, blocking effects and flow
separation. Compared to a single cylinder, turbulent fluctuations in the wakes of upstream
elements introduce additional kinetic energy to the boundary layer of each element, delaying
separation and reducing drag coefficient (Etminan et al., 2017; Nepf, 1999). Therefore,
properly characterizing morphological properties of vegetation is essential for studying the
hydrodynamics of vegetated streams. To investigate the effect of the flexibility and height of
37

vegetation on flow, both deflected and non-bending morphology of vegetation were used in
this study. In one of these vegetation settings, all vegetation elements were placed in a fully
non-bending setting to represent the stiff and rigid vegetation patch. In this way, the vegetation
exhibits no deformation during the experiments, representing the real situation of reeds and
sedges in natural rivers. In another setting, all vegetation elements were deflected, representing
the flexible vegetation in streams. The height of non-bending and deflected vegetation
elements in 20-cm water depth was 12.6 cm and 8 cm, respectively and 19 cm and 12 cm in
the 30-cm water depth. As you saw in Figure 2.1, the length of each sandbox is around 5.5 m.
The 3-m long vegetation region was located in the middle of the sandbox. The vegetation has
a certain degree of flexibility and can swing under flow, but it does not deform. The
morphological properties of the vegetation such as the vegetation deflected height are related
to some other hydraulic properties of flow such as flow depth and velocity.
The ratio of the flow depth to the vegetation bending height is defined as the degree of
submergence (

=

/ℎ) (Nepf, 2012a). In this study, the degree of submergence was selected

as 1.58 for non-bending and 2.5 for deflected vegetation arrangement, respectively.
Each vegetation element has the width of 10 mm at the bottom and 22 mm at the top,
respectively. Thus, the average width of each element was considered as 16 mm. In the present
study, for the case of the densest vegetation configuration, the ratio of the total vegetation
thickness to the channel width, D/W, was smaller than 0.5; therefore, the effect of channel
blockage on the wake structure can be negligible.
The vegetation Reynolds number associated is defined as:
2.3

=
where,

= mean flow velocity, d = stem diameter, and

38

= kinematic viscosity of water.

To start each experimental run, one valve with the low discharge (5 L/s) was gradually
opened while the tailgates downstream were closed to avoid sediment being washed away.
From the holding tank, water was gently discharged through the spillway into the flume. To
maintain the desired flow rate, all three valves were fully opened once the desired water depth
was reached.
2.3 Sediment used in experiments
The sandboxes are filled with three different non-uniform sediment with a median
particle size (
⁄

) of 0.50 mm, 0.60 mm and 0.98 mm. The standard deviation ( =

) used to analyze the uniformity of the distributions where

16% finer particle diameters, respectively. The smaller the value of

and

are 84% and

, the well-sorted the

sediment is (Blott & Pye, 2001). The standard deviation for the sand with median grain size of
0.50 mm, 0.60 mm and 0.98 mm in this study are 1.97, 2.39, and 1.41 respectively . Based on
that, the sand size used in this experiment is poorly sorted sand. The grain size distribution was
obtained using a mechanical shaker and seven different-sized sieves. The grain size distribution
of the three non-uniform sediments are shown in Figure 2.4.

Figure 2.4: Grain size distribution of bed materials

39

2.4 Ice cover conditions
To simulate ice cover, Styrofoam panels were used. While the experiment was running,
Styrofoam was floated on the surface of the water with a density of 0.026

⁄

. Two types

of ice cover are used in the present study, namely smooth and rough. Styrofoam panels make
up the smooth ice cover, while small Styrofoam cubes are attached to the smooth ice cover's
bottom to make the rough ice cover (Figure 2.5). A Styrofoam cube has dimensions of 25 mm
x 25 mm x 25 mm, and each one is spaced 35 mm apart. The roughness of the ice jam – whether
it contains loose or dense slush or solid-ice blocks – as well as its thickness, determines its
resistance to flow and is therefore important for the flooding potential (Beltaos, 2008).
The hydraulic radius (R) is different in the case of ice-covered flow, since an additional
boundary is added to the water surface. As a result, an empirical equation introduced by (Tang,
& Davar, 1985) which is for the estimation of the hydraulic radius has been adopted for a
variety of covered flow regimes, from open water to fully covered. Equation 1.5 can be stated
as follows for rectangular channels in presence of ice cover:
=

(

2.4

)

Where, H is the flow depth, W is the channel width, and a is the percentage.

Figure 2.5: Attached Styrofoam cubes to simulate rough ice cover in the presence of deflected vegetation, (b)
simple Styrofoam as smooth ice cover in the presence of non-bending vegetation

40

2.5 Research Innovation
The present study is a comprehensive experimental research project that aims to
investigate the effects of different vegetation arrangements, densities, and morphologies, as
well as different ice covers on flow structure and bed deformation. The experiment was
conducted in a large-scale outdoor flume that closely resembles a real stream, with dimensions
of 2 meters wide, 1.3 meters deep, and 38 meters long.
The study applied various vegetation densities (including sparse, transition and dense
vegetation), and used both square and staggered vegetation arrangements with different
morphologies (such as non-bending and deflected vegetation). Two different water depths
were used to represent flow in shallow streams. The present study also compared results under
an open channel flow to those of smooth and rough ice-covered flow conditions, examining
the resulting resistance and sediment transport.
Additionally, the study applied three different non-uniform sands to investigate the local
scouring around vegetation elements in the presence of an ice cover. The study aimed to
investigate various parameters simultaneously, such as velocity profiles, Reynolds shear stress,
turbulent kinetic energy (TKE), bed deformation, and scouring around vegetation elements.
Collected data have been attached in appendix.
The results of the study would provide valuable insights and outcomes related to the
combined impacts of vegetation and ice cover on flow resistance and channel bed deformation.
The study would reveal the relationship between ice cover roughness, bed roughness, and the
depth of scour holes. It would identify the most significant variable influencing scour hole
formation under ice-covered flow conditions. This information can help in predicting and
managing channel bed erosion in cold regions, improving the design of structures and

41

interventions to mitigate the impacts of ice cover. Additionally, the research would provide
insights into the flow characteristics in the presence of vegetation and ice cover. It would
identify the influence of vegetation density, arrangement patterns, and ice cover roughness on
the velocity profiles. Understanding the flow patterns and changes in velocity distribution can
aid in predicting sediment transport, pollutant dispersion, and habitat suitability.
The study would also investigate the relationship between canopy density and the
dimensions of the wake zone behind vegetation elements. It would reveal how spacing distance
between vegetation elements affects streamwise velocity retardation and the presence of
inflection points in velocity profiles. This information can be useful for assessing the hydraulic
impacts of vegetation arrangements on flow resistance and designing restoration projects
accordingly. Furthermore, the study would compare the impacts of deflected and non-bending
vegetation on flow resistance and channel bed deformation. It would evaluate the differences
in scour depths, wake zone dimensions, and flow characteristics between these vegetation
types. This comparison can inform decisions regarding the selection of appropriate vegetation
species and forms for restoration projects.
According to the author's knowledge, no research work has been previously conducted
considering all these parameters and flow conditions simultaneously. Therefore, this study is
significant in advancing the understanding of the effects of vegetation and ice covers on flow
structure and bed deformation.
2.6 Bibliography
Aberle, J., & Järvelä, J. (2015). Hydrodynamics of Vegetated Channels. In P. Rowiński & A.
Radecki-Pawlik (Eds.), Rivers – Physical, Fluvial and Environmental Processes (pp. 519–
541). Springer International Publishing. https://doi.org/10.1007/978-3-319-17719-9_21
Ackerman, J. D., & Okubo, A. (1993). Reduced Mixing in a Marine Macrophyte Canopy. Functional
Ecology, 7(3), 305. https://doi.org/10.2307/2390209
42

Afzalimehr, H., & Dey, S. (2009). Influence of bank vegetation and gravel bed on velocity and
Reynolds stress distributions. International Journal of Sediment Research, 24(2), 236–246.
https://doi.org/10.1016/S1001-6279(09)60030-5
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
Albayrak, I., Nikora, V., Miler, O., & O’Hare, M. (2012). Flow-plant interactions at a leaf scale:
Effects of leaf shape, serration, roughness and flexural rigidity. Aquatic Sciences, 74(2), 267–
286. https://doi.org/10.1007/s00027-011-0220-9
Allmendinger, N. E., Pizzuto, J. E., Potter, N., Johnson, T. E., & Hession, W. C. (2005). The
influence of riparian vegetation on stream width, eastern Pennsylvania, USA. Geological
Society of America Bulletin, 117(1), 229. https://doi.org/10.1130/B25447.1
Anderson, J. (2005). Ludwig Prandtl’s boundary layer. 1;58(12): 1,58 (12), 42–48.
Anderson, S. M., & Charters, A. C. (1982). A fluid dynamics study of seawater flow through
Gelidium nudifrons 1: Gelidium fluid dynamics. Limnology and Oceanography, 27(3), 399–
412. https://doi.org/10.4319/lo.1982.27.3.0399
Andrews, S. N., Buhariwalla, C. F., Fleet-Pardy, B., Dadswell, M. J., Linnansaari, T., & Curry, R. A.
(2019). Left out in the cold: The understudied overwintering ecology of striped bass in
Canada. Environmental Biology of Fishes, 102(3), 499–518. https://doi.org/10.1007/s10641019-0847-2
Andrews, S. N., O’Sullivan, A. M., Helminen, J., Arluison, D. F., Samways, K. M., Linnansaari, T.,
& Curry, R. A. (2020). Development of Active Numerating Side-scan for a High-Density
Overwintering Location for Endemic Shortnose Sturgeon (Acipenser brevirostrum) in the
Saint John River, New Brunswick. Diversity, 12(1), 23. https://doi.org/10.3390/d12010023
Barbier, E. B., Hacker, S. D., Kennedy, C., Koch, E. W., Stier, A. C., & Silliman, B. R. (2011). The
value of estuarine and coastal ecosystem services. Ecological Monographs, 81(2), 169–193.
https://doi.org/10.1890/10-1510.1
Belcher, S. E., Jerram, N., & Hunt, J. C. R. (2003). Adjustment of a turbulent boundary layer to a
canopy of roughness elements. Journal of Fluid Mechanics, 488, 369–398.
https://doi.org/10.1017/S0022112003005019
Beltaos, S. (2008). Progress in the study and management of river ice jams. 51, 2–19.
Beltaos, S., & Burrell, B. C. (2021). Effects of River-Ice Breakup on Sediment Transport and
Implications to Stream Environments: A Review. Water, 13(18), 2541.
https://doi.org/10.3390/w13182541
Beltaos, S., & Tang, P. (2013). Applying HEC-RAS to simulate river ice jams: Snags and practical
hints. Proc. 17th Workshop on River Ice, Edmonton, Alberta, Canada.

43

Bennett, S. J., Pirim, T., & Barkdoll, B. D. (2002). Using simulated emergent vegetation to alter
stream flow direction within a straight experimental channel. Geomorphology, 44(1–2), 115–
126. https://doi.org/10.1016/S0169-555X(01)00148-9
Blott, S. J., & Pye, K. (2001). GRADISTAT: A grain size distribution and statistics package for the
analysis of unconsolidated sediments. Earth Surface Processes and Landforms, 26(11),
1237–1248. https://doi.org/10.1002/esp.261
Boström, C., Jackson, E. L., & Simenstad, C. A. (2006). Seagrass landscapes and their effects on
associated fauna: A review. Estuarine, Coastal and Shelf Science, 68(3–4), 383–403.
https://doi.org/10.1016/j.ecss.2006.01.026
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
Bouma, T. J., van Duren, L. A., Temmerman, S., Claverie, T., Blanco-Garcia, A., Ysebaert, T., &
Herman, P. M. J. (2007). Spatial flow and sedimentation patterns within patches of epibenthic
structures: Combining field, flume and modelling experiments. Continental Shelf Research,
27(8), 1020–1045. https://doi.org/10.1016/j.csr.2005.12.019
Braudrick, C. A., Dietrich, W. E., Leverich, G. T., & Sklar, L. S. (2009). Experimental evidence for
the conditions necessary to sustain meandering in coarse-bedded rivers. Proceedings of the
National Academy of Sciences, 106(40), 16936–16941.
https://doi.org/10.1073/pnas.0909417106
Cao, Z., Pender, G., & Meng, J. (2006). Explicit Formulation of the Shields Diagram for Incipient
Motion of Sediment. Journal of Hydraulic Engineering, 132(10), 1097–1099.
https://doi.org/10.1061/(ASCE)0733-9429(2006)132:10(1097)
Chamberlain, J. A., & Graus, R. R. (1975). Water Flow and Hydromechanical Adaptations of
Branched Reef Corals. 25(1), 112–125.
Chang, H. (1992). FLUVIAL PROCESSES IN RIVER ENGINEERING.
Chanson, H. (2004). The hydraulics of open channel flow: An introduction basic principles, sediment
motion, hydraulic modelling, design of hydraulic structures (2nd ed). Elsevier.
Chen, S.-N., Sanford, L. P., Koch, E. W., Shi, F., & North, E. W. (2007). A nearshore model to
investigate the effects of seagrass bed geometry on wave attenuation and suspended sediment
transport. Estuaries and Coasts, 30(2), 296–310. https://doi.org/10.1007/BF02700172
Chow, V. T. (2009). Open-channel hydraulics. Blackburn Press.
Clarke, S. J. (2002). Vegetation growth in rivers: Influences upon sediment and nutrient dynamics.
Progress in Physical Geography: Earth and Environment, 26(2), 159–172.
https://doi.org/10.1191/0309133302pp324ra
Clauser, F. H. (1956). The Turbulent Boundary Layer. In Advances in Applied Mechanics (Vol. 4, pp.
1–51). Elsevier. https://doi.org/10.1016/S0065-2156(08)70370-3

44

Cornacchia, L., Licci, S., Nepf, H., Folkard, A., Wal, D., Koppel, J., Puijalon, S., & Bouma, T. J.
(2018). Turbulence‐mediated facilitation of resource uptake in patchy stream macrophytes.
Limnology and Oceanography, 64(2), 714–727. https://doi.org/10.1002/lno.11070
Costanza, R., d’Arge, R., de Groot, R., Farber, S., Grasso, M., Hannon, B., Limburg, K., Naeem, S.,
O’Neill, R. V., Paruelo, J., Raskin, R. G., Sutton, P., & van den Belt, M. (1997). The value of
the world’s ecosystem services and natural capital. Nature, 387(6630), 253–260.
https://doi.org/10.1038/387253a0
Dey, S., & Raikar, R. V. (2007). Clear-Water Scour at Piers in Sand Beds with an Armor Layer of
Gravels. Journal of Hydraulic Engineering, 133(6), 703–711.
https://doi.org/10.1061/(ASCE)0733-9429(2007)133:6(703)
Dunn, C., Lopez, F., & Garcia, M. (1996). Mean flow and turbulence in a laboratory channel with
simulated vegetation. Hydraulic Eng.
Dynesius, M., & Nilsson, C. (1994). Fragmentation and Flow Regulation of River Systems in the
Northern Third of the World. Science, 266(5186), 753–762.
https://doi.org/10.1126/science.266.5186.753
Engström, J., Jansson, R., Nilsson, C., & Weber, C. (2011). Effects of river ice on riparian vegetation:
Ice and riparian vegetation. Freshwater Biology, 56(6), 1095–1105.
https://doi.org/10.1111/j.1365-2427.2010.02553.x
Etminan, V., Lowe, R. J., & Ghisalberti, M. (2017). A new model for predicting the drag exerted by
vegetation canopies: NEW MODEL FOR VEGETATION DRAG. Water Resources
Research, 53(4), 3179–3196. https://doi.org/10.1002/2016WR020090
Ettema, R. (2002). Review of Alluvial-channel Responses to River Ice. Journal of Cold Regions
Engineering, 16(4), 191–217. https://doi.org/10.1061/(ASCE)0887-381X(2002)16:4(191)
Ettema, R., & Daly, S. F. (2004). Sediment Transport Under Ice (Technical Report ERDC/CRREL
TR-04-20). U.S. Army Corps of Engineers Washington, DC 20314-1000.
Finnigan, J. (2000). Turbulence in Plant Canopies. Annual Review of Fluid Mechanics, 32(1), 519–
571. https://doi.org/10.1146/annurev.fluid.32.1.519
Fonseca, M. S., & Fisher, J. (1986). A comparison of canopy friction and sediment movement
between four species of seagrass with reference to their ecology and restoration. Marine
Ecology Progress Series, 29, 15–22. https://doi.org/10.3354/meps029015
Fonseca, M. S., & Kenworthy, W. J. (1987). Effects of current on photosynthesis and distribution of
seagrasses. Aquatic Botany, 27(1), 59–78. https://doi.org/10.1016/0304-3770(87)90086-6
Fourqurean, J. W., Duarte, C. M., Kennedy, H., Marbà, N., Holmer, M., Mateo, M. A., Apostolaki, E.
T., Kendrick, G. A., Krause-Jensen, D., McGlathery, K. J., & Serrano, O. (2012). Seagrass
ecosystems as a globally significant carbon stock. Nature Geoscience, 5(7), 505–509.
https://doi.org/10.1038/ngeo1477
Ghisalberti, M., & Nepf, H. (2002). Mixing layers and coherent structures in vegetated aquatic flows.
Journal of Geophysical Research, 107(C2), 3011. https://doi.org/10.1029/2001JC000871
45

Ghisalberti, M., & Nepf, H. (2006). The Structure of the Shear Layer in Flows over Rigid and
Flexible Canopies. Environmental Fluid Mechanics, 6(3), 277–301.
https://doi.org/10.1007/s10652-006-0002-4
Ghose-Hajra, M., McCorquodale, A., Mattson, G., Jerolleman, D., & Filostrat, J. (2015). Effects of
salinity and particle concentration on sediment hydrodynamics and critical bed-shear-stress
for erosion of fine grained sediments used in wetland restoration projects. Proceedings of the
International Association of Hydrological Sciences, 367, 435–441.
https://doi.org/10.5194/piahs-367-435-2015
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)07339429(2002)128:1(117)
Gran, K., & Paola, C. (2001). Riparian vegetation controls on braided stream dynamics. Water
Resources Research, 37(12), 3275–3283. https://doi.org/10.1029/2000WR000203
Granata, T., Serra, T., Colomer, J., Casamitjana, X., Duarte, C., & Gacia, E. (2001). Flow and particle
distributions in a nearshore seagrass meadow before and after a storm. Marine Ecology
Progress Series, 218, 95–106. https://doi.org/10.3354/meps218095
Greiner, J. T., McGlathery, K. J., Gunnell, J., & McKee, B. A. (2013). Seagrass Restoration Enhances
“Blue Carbon” Sequestration in Coastal Waters. PLoS ONE, 8(8), e72469.
https://doi.org/10.1371/journal.pone.0072469
Hansen, J., & Reidenbach, M. (2012). Wave and tidally driven flows in eelgrass beds and their effect
on sediment suspension. Marine Ecology Progress Series, 448, 271–287.
https://doi.org/10.3354/meps09225
Hassanzadeh, Y. (2012). Hydraulics of Sediment Transport. In J.-H. Zheng (Ed.), Hydrodynamics—
Theory and Model. InTech. https://doi.org/10.5772/25982
Hauxwell, J., Osenberg, C. W., & Frazer, T. K. (2004). Conflicting management goals: manatees and
invasive competitors inhibit restoration of a native macrophyte. Ecological Applications,
14(2), 571–586. https://doi.org/10.1890/02-5250
Helmuth, B. S. T., Sebens, K. P., & Daniel, T. L. (1997). Morphological variation in coral
aggregations: Branch spacing and mass flux to coral tissues. 209(1–2), 233–259.
Henderson, F. M. (1995). Open channel flow (Nachdr.). Prentice Hall.
Hicks, F. E. (2016). An introduction to river ice engineering for civil engineers and geoscientists.
publisher not identified.
Houser, C., Trimble, S., & Morales, B. (2015). Influence of Blade Flexibility on the Drag Coefficient
of Aquatic Vegetation. Estuaries and Coasts, 38(2), 569–577.
https://doi.org/10.1007/s12237-014-9840-3
Huai, W., Li, S., Katul, G. G., Liu, M., & Yang, Z. (2021). Flow dynamics and sediment transport in
vegetated rivers: A review. Journal of Hydrodynamics, 33(3), 400–420.
https://doi.org/10.1007/s42241-021-0043-7
46

Huang, I., Rominger, J., & Nepf, H. (2011). The motion of kelp blades and the surface renewal
model. Limnology and Oceanography, 56(4), 1453–1462.
https://doi.org/10.4319/lo.2011.56.4.1453
Irlandi, E. A., & Peterson, C. H. (1991). Modification of animal habitat by large plants: Mechanisms
by which seagrasses influence clam growth. Oecologia, 87(3), 307–318.
https://doi.org/10.1007/BF00634584
Jansson, R., Nilsson, C., & Renöfält, B. (2000). FRAGMENTATION OF RIPARIAN FLORAS IN
RIVERS WITH MULTIPLE DAMS. Ecology, 81(4), 899–903. https://doi.org/10.1890/00129658(2000)081[0899:FORFIR]2.0.CO;2
Jenkins, W. A., Murray, B. C., Kramer, R. A., & Faulkner, S. P. (2010). Valuing ecosystem services
from wetlands restoration in the Mississippi Alluvial Valley. Ecological Economics, 69(5),
1051–1061. https://doi.org/10.1016/j.ecolecon.2009.11.022
Kääb, A., Altena, B., & Mascaro, J. (2019). River-ice and water velocities using the Planet optical
cubesat constellation. Hydrology and Earth System Sciences, 23(10), 4233–4247.
https://doi.org/10.5194/hess-23-4233-2019
Katz, S. L., Izmest’eva, L. R., Hampton, S. E., Ozersky, T., Shchapov, K., Moore, M. V.,
Shimaraeva, S. V., & Silow, E. A. (2015). The “ M elosira years” of Lake B aikal: Winter
environmental conditions at ice onset predict under‐ice algal blooms in spring. Limnology
and Oceanography, 60(6), 1950–1964. https://doi.org/10.1002/lno.10143
Kemp, J. L., Harper, D. M., & Crosa, G. A. (2000). The habitat-scale ecohydraulics of rivers.
Ecological Engineering, 16(1), 17–29. https://doi.org/10.1016/S0925-8574(00)00073-2
Kobayashi, N., Raichle, A. W., & Asano, T. (1993). Wave Attenuation by Vegetation. Journal of
Waterway, Port, Coastal, and Ocean Engineering, 119(1), 30–48.
https://doi.org/10.1061/(ASCE)0733-950X(1993)119:1(30)
Koch, E. W. (1994). Hydrodynamics, diffusion-boundary layers and photosynthesis of the seagrasses
Thalassia testudinum and Cymodocea nodosa. Marine Biology, 118(4), 767–776.
https://doi.org/10.1007/BF00347527
Koch, E. W. (2001). Beyond Light: Physical, Geological, and Geochemical Parameters as Possible
Submersed Aquatic Vegetation Habitat Requirements. Estuaries, 24(1), 1.
https://doi.org/10.2307/1352808
Krishnan, K. S. G., Bertram, O., & Seibel, O. (2017). Review of hybrid laminar flow control systems.
Progress in Aerospace Sciences, 93, 24–52. https://doi.org/10.1016/j.paerosci.2017.05.005
Larsen, L. G., & Harvey, J. W. (2011). Modeling of hydroecological feedbacks predicts distinct
classes of landscape pattern, process, and restoration potential in shallow aquatic ecosystems.
Geomorphology, 126(3–4), 279–296. https://doi.org/10.1016/j.geomorph.2010.03.015
Lawler, D. M. (2008). Advances in the continuous monitoring of erosion and deposition dynamics:
Developments and applications of the new PEEP-3T system. Geomorphology, 93(1–2), 17–
39. https://doi.org/10.1016/j.geomorph.2006.12.016

47

Lawson, E.F. Chacho, B.E. Brockett, J.L. Wuebben, C.M. Collins, S.A. Arcone, & A.J. Delaney.
(1986). Morphology, hydraulics and sediment transport of an ice-covered river (CRREL
Report 86-11). Office of the Chief of Engineers.
Le Bouteiller, C., & Venditti, J. G. (2014). Vegetation-driven morphodynamic adjustments of a sand
bed. Geophysical Research Letters, 41(11), 3876–3883.
https://doi.org/10.1002/2014GL060155
Leonard, L. A., & Croft, A. L. (2006). The effect of standing biomass on flow velocity and turbulence
in Spartina alterniflora canopies, Estuarine. 69(3–4), 325–336.
https://doi.org/10.1016/j.ecss.2006.05.004
Li, S. S., & Millar, R. G. (2011). A two-dimensional morphodynamic model of gravel-bed river with
floodplain vegetation. Earth Surface Processes and Landforms, 36(2), 190–202.
https://doi.org/10.1002/esp.2033
Lind, L., Nilsson, C., Polvi, L. E., & Weber, C. (2014). The role of ice dynamics in shaping
vegetation in flowing waters: Ice dynamics and vegetation in flowing waters. Biological
Reviews, 89(4), 791–804. https://doi.org/10.1111/brv.12077
López, F., & García, M. (1998). open-channel flow through simulated vegetation: Suspended
sediment transport modeling. Water Resources Research, 34(9), 2341–2352.
https://doi.org/10.1029/98WR01922
Lowe, R. J., Koseff, J. R., & Monismith, S. G. (2005). Oscillatory flow through submerged canopies:
1. Velocity structure. Journal of Geophysical Research, 110(C10), C10016.
https://doi.org/10.1029/2004JC002788
Luettich, R. A., Harleman, D. R. F., & SomlyÓdy, Lá. (1990). Dynamic behavior of suspended
sediment concentrations in a shallow lake perturbed by episodic wind events. Limnology and
Oceanography, 35(5), 1050–1067. https://doi.org/10.4319/lo.1990.35.5.1050
Luhar, M., & Nepf, H. (2011). Flow-induced reconfiguration of buoyant and flexible aquatic
vegetation. Limnology and Oceanography, 56(6), 2003–2017.
https://doi.org/10.4319/lo.2011.56.6.2003
Madsen, J. D., Chambers, P. A., James, W. F., Koch, E. W., & Westlake, D. F. (2001). The
interaction between water movement, sediment dynamics and submersed macrophytes.
Hydrobiologia, 444(1/3), 71–84. https://doi.org/10.1023/A:1017520800568
Madsen, O. Secher. (1991). Mechanics of Cohesionless Sediment Transport in Coastal Waters. 15–
27.
Mars, R., Mathew, K., & Ho, G. (1999). The role of the submergent macrophyte Triglochin huegelii
in domestic greywater treatment. Ecological Engineering, 12(1–2), 57–66.
https://doi.org/10.1016/S0925-8574(98)00054-8
Mass, T., Genin, A., Shavit, U., Grinstein, M., & Tchernov, D. (2010). Flow enhances photosynthesis
in marine benthic autotrophs by increasing the efflux of oxygen from the organism to the
water. Proceedings of the National Academy of Sciences, 107(6), 2527–2531.
https://doi.org/10.1073/pnas.0912348107
48

Mcleod, E., Chmura, G. L., Bouillon, S., Salm, R., Björk, M., Duarte, C. M., Lovelock, C. E.,
Schlesinger, W. H., & Silliman, B. R. (2011). A blueprint for blue carbon: Toward an
improved understanding of the role of vegetated coastal habitats in sequestering CO 2.
Frontiers in Ecology and the Environment, 9(10), 552–560. https://doi.org/10.1890/110004
Micheli, E. R., & Kirchner, J. W. (2002). Effects of wet meadow riparian vegetation on streambank
erosion. 2. Measurements of vegetated bank strength and consequences for failure mechanics.
Earth Surface Processes and Landforms, 27(7), 687–697. https://doi.org/10.1002/esp.340
Miller, M. C., McCAVE, I. N., & Komar, P. D. (1977). Threshold of sediment motion under
unidirectional currents. Sedimentology, 24(4), 507–527. https://doi.org/10.1111/j.13653091.1977.tb00136.x
Moore, K. A. (2004). Influence of Seagrasses on Water Quality in Shallow Regions of the Lower
Chesapeake Bay. Journal of Coastal Research, 10045, 162–178.
https://doi.org/10.2112/SI45-162.1
Morris, J. T., Sundareshwar, P. V., Nietch, C. T., Kjerfve, B., & Cahoon, D. R. (2002). RESPONSES
OF COASTAL WETLANDS TO RISING SEA LEVEL. Ecology, 83(10), 2869–2877.
https://doi.org/10.1890/0012-9658(2002)083[2869:ROCWTR]2.0.CO;2
Muste, M., Braileanu, F., & Ettema, R. (2000). Flow and sediment transport measurements in a
simulated ice-covered channel. Water Resources Research, 36(9), 2711–2720.
https://doi.org/10.1029/2000WR900168
Nabaei, S. F., Afzalimehr, H., Sui, J., Kumar, B., & Nabaei, S. H. (2021). Investigation of the Effect
of Vegetation on Flow Structures and Turbulence Anisotropy around Semi-Elliptical
Abutment. Water, 13(21), 3108. https://doi.org/10.3390/w13213108
Namaee, M., & Sui, J. (2019). Impact of armour layer on the depth of scour hole around side-by-side
bridge piers under ice-covered flow condition. Journal of Hydrology and Hydromechanics,
67(3), 240–251. https://doi.org/10.2478/johh-2019-0010
Narayan, S., Beck, M. W., Wilson, P., Thomas, C. J., Guerrero, A., Shepard, C. C., Reguero, B. G.,
Franco, G., Ingram, J. C., & Trespalacios, D. (2017). The Value of Coastal Wetlands for
Flood Damage Reduction in the Northeastern USA. Scientific Reports, 7(1), 9463.
https://doi.org/10.1038/s41598-017-09269-z
Nedjimi, B., Beladel, B., & Guit, B. (2012). Biodiversity of Halophytic Vegetation in Chott
&lt;i&gt;Zehrez&lt;/i&gt; Lake of Djelfa (Algeria). American Journal of Plant Sciences,
03(11), 1527–1534. https://doi.org/10.4236/ajps.2012.311184
Nepf, H. (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. (2012a). Flow and transport in regions with aquatic vegetation. Annu Rev Fluid Mech, 44(1),
123–142. https://doi.org/10.1146/annurev-fluid-120710-101048
Nepf, H. (2012b). Hydrodynamics of vegetated channels. Journal of Hydraulic Research, 50(3), 262–
279. https://doi.org/10.1080/00221686.2012.696559

49

Nepf, H., & Ghisalberti, M. (2008). Flow and transport in channels with submerged vegetation. Acta
Geophysica, 56(3). https://doi.org/10.2478/s11600-11008-10017-y
Nepf, H., & Vivoni, E. R. (2000). Flow structure in depth-limited, vegetated flow. Journal of
Geophysical Research: Oceans, 105(C12), 28547–28557.
https://doi.org/10.1029/2000JC900145
Neumeier, U. (2007). Velocity and turbulence variations at the edge of saltmarshes. Continental Shelf
Research, 27(8), 1046–1059. https://doi.org/10.1016/j.csr.2005.07.009
Neumeier, U., & Amos, C. L. (2006). The influence of vegetation on turbulence and flow velocities in
European salt-marshes. Sedimentology, 53(2), 259–277. https://doi.org/10.1111/j.13653091.2006.00772.x
Newson, M. (1992). Land, water and development. River basin systems and their sustainable
management. ROUTLEDGE,.
Nezu, I., & Sanjou, M. (2008). Turburence structure and coherent motion in vegetated canopy openchannel flows. Journal of Hydro-Environment Research, 2(2), 62–90.
https://doi.org/10.1016/j.jher.2008.05.003
Nilsson, C., Lepori, F., Malmqvist, B., Törnlund, E., Hjerdt, N., Helfield, J. M., Palm, D., Östergren,
J., Jansson, R., Brännäs, E., & Lundqvist, H. (2005). Forecasting Environmental Responses to
Restoration of Rivers Used as Log Floatways: An Interdisciplinary Challenge. Ecosystems,
8(7), 779–800. https://doi.org/10.1007/s10021-005-0030-9
Nyantekyi-Kwakye, B., Pahlavan, H., Clark, S. P., Tachie, M. F., & Dow, K. (2018). Roughness
effect on turbulent flow structure beneath a simulated ice jam. Journal of Hydraulic
Research, 57(2), 238–249. https://doi.org/10.1080/00221686.2018.1473298
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
Perignon, M. C., Tucker, G. E., Griffin, E. R., & Friedman, J. M. (2013). Effects of riparian
vegetation on topographic change during a large flood event, Rio Puerco, New Mexico, USA:
VEGETATION EFFECTS ON TOPOGRAPHIC CHANGE. Journal of Geophysical
Research: Earth Surface, 118(3), 1193–1209. https://doi.org/10.1002/jgrf.20073
Petryk S & Bosmajian G. (1975). Analysis of flow through vegetation. J Hydraul Div, 101(7), 871–
884.
Poggi, D., Porporato, A., Ridolfi, L., Albertson, J. D., & Katul, G. G. (2004). The Effect of
Vegetation Density on Canopy Sub-Layer Turbulence. Boundary-Layer Meteorology, 111(3),
565–587. https://doi.org/10.1023/B:BOUN.0000016576.05621.73
Prowse, T. D. (1994). Environmental significance of ice to streamflow in cold regions. Freshwater
Biology, 32(2), 241–259. https://doi.org/10.1111/j.1365-2427.1994.tb01124.x
Prowse, T. D. (2001). River-Ice Ecology. II: Biological Aspects. Journal of Cold Regions
Engineering, 15(1), 17–33. https://doi.org/10.1061/(ASCE)0887-381X(2001)15:1(17)
50

Pujol, D., Colomer, J., Serra, T., & Casamitjana, X. (2010). Effect of submerged aquatic vegetation
on turbulence induced by an oscillating grid. Continental Shelf Research, 30(9), 1019–1029.
https://doi.org/10.1016/j.csr.2010.02.014
Ranzi, R., Bochicchio, M., & Bacchi, B. (2002). Effects on floods of recent afforestation and
urbanisation in the Mella River (Italian Alps). Hydrology and Earth System Sciences, 6(2),
239–254. https://doi.org/10.5194/hess-6-239-2002
Recking, A. (2009). Theoretical development on the effects of changing flow hydraulics on incipient
bed load motion: INCIPIENT MOTION CONDITIONS. Water Resources Research, 45(4).
https://doi.org/10.1029/2008WR006826
Renman, G. (1989). Distribution of littoral macrophytes in a North Swedish riverside lagoon in
relation to bottom freezing. Aquatic Botany, 33(3–4), 243–256. https://doi.org/10.1016/03043770(89)90040-5
Richardson, D. M., Holmes, P. M., Esler, K. J., Galatowitsch, S. M., Stromberg, J. C., Kirkman, S. P.,
Pyšek, P., & Hobbs, R. J. (2007). Riparian vegetation: Degradation, alien plant invasions, and
restoration prospects: Riparian vegetation: degraded, invaded, transformed. Diversity and
Distributions, 13(1), 126–139. https://doi.org/10.1111/j.1366-9516.2006.00314.x
Rominger, J. T., & Nepf, H. (2014). Effects of blade flexural rigidity on drag force and mass transfer
rates in model blades. Limnology and Oceanography, 59(6), 2028–2041.
https://doi.org/10.4319/lo.2014.59.6.2028
Rood, S. B., Goater, L. A., Mahoney, J. M., Pearce, C. M., & Smith, D. G. (2007). Floods, fire, and
ice: Disturbance ecology of riparian cottonwoodsThe review is one of a selection of papers
published in the Special Issue on Poplar Research in Canada. Canadian Journal of Botany,
85(11), 1019–1032. https://doi.org/10.1139/B07-073
Sánchez-González, J. F., Sánchez-Rojas, V., & Memos, C. D. (2011). Wave attenuation due to
Posidonia oceanica meadows. Journal of Hydraulic Research, 49(4), 503–514.
https://doi.org/10.1080/00221686.2011.552464
Sand-jensen, K. (1998). Influence of submerged macrophytes on sediment composition and near-bed
flow in lowland streams: Influence of submerged macrophytes in lowland streams.
Freshwater Biology, 39(4), 663–679. https://doi.org/10.1046/j.1365-2427.1998.00316.x
Schlichting, H., & Gersten, K. (2000). Boundary-Layer Theory. Springer Berlin Heidelberg.
https://doi.org/10.1007/978-3-642-85829-1
Sharma, S., Meyer, M. F., Culpepper, J., Yang, X., Hampton, S., Berger, S. A., Brousil, M. R.,
Fradkin, S. C., Higgins, S. N., Jankowski, K. J., Kirillin, G., Smits, A. P., Whitaker, E. C.,
Yousef, F., & Zhang, S. (2020). Integrating Perspectives to Understand Lake Ice Dynamics in
a Changing World. Journal of Geophysical Research: Biogeosciences, 125(8).
https://doi.org/10.1029/2020JG005799
Shi, Z., Pethick, J. S., Burd, F., & Murphy, B. (1996). Velocity profiles in a salt marsh canopy. GeoMar. Lett, 16(4), 319–323. https://doi.org/10.1007/BF01245563

51

Simon, A., & Collison, A. J. C. (2002). Quantifying the mechanical and hydrologic effects of riparian
vegetation on streambank stability. Earth Surface Processes and Landforms, 27(5), 527–546.
https://doi.org/10.1002/esp.325
Siniscalchi, F., Nikora, V. I., & Aberle, J. (2012). Plant patch hydrodynamics in streams: Mean flow,
turbulence, and drag forces: PLANT PATCH HYDRODYNAMICS. Water Resources
Research, 48(1). https://doi.org/10.1029/2011WR011050
Sontek, A.D.V. (1997). Operation Manual, Firmware Version 4.0, San Diego, CA, USA,.
SonTek-IQ Series. (2017). 135.
Sui, J., Hicks, F. E., & Menounos, B. (2006). Observations of riverbed scour under a developing
hanging ice dam. Canadian Journal of Civil Engineering, 33(2), 214–218.
https://doi.org/10.1139/l05-094
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)0733-9429(2002)128:8(781)
Sui, J., Wang, D., & Karney, B. W. (2000). Suspended sediment concentration and deformation of
riverbed in a frazil jammed reach. Canadian Journal of Civil Engineering, 27(6), 1120–1129.
https://doi.org/10.1139/l00-038
Sui, J., Wang, J., Balachandar, R., Sun, Z., & Wang, D. (2008). Accumulation of frazil ice along a
river bend. Canadian Journal of Civil Engineering, 35(2), 158–169.
https://doi.org/10.1139/L07-093
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/S1001-6279(10)60026-1
Takács, K., Kern, Z., & Nagy, B. (2013). Impacts of anthropogenic effects on river ice regime:
Examples from Eastern Central Europe. Quaternary International, 293, 275–282.
https://doi.org/10.1016/j.quaint.2012.12.010
Tal, M., & Paola, C. (2007). Dynamic single-thread channels maintained by the interaction of flow
and vegetation. Geology, 35(4), 347. https://doi.org/10.1130/G23260A.1
Tang, J., Ye, S., Chen, X., Yang, H., Sun, X., Wang, F., Wen, Q., & Chen, S. (2018). Coastal blue
carbon: Concept, study method, and the application to ecological restoration. Science China
Earth Sciences, 61(6), 637–646. https://doi.org/10.1007/s11430-017-9181-x
Tang, T. C. C., & Davar, K. S. (1985). Resistance to flow in partially-covered channels.

52

Thellman, A., Jankowski, K. J., Hayden, B., Yang, X., Dolan, W., Smits, A. P., & O’Sullivan, A. M.
(2021). The Ecology of River Ice. Journal of Geophysical Research: Biogeosciences, 126(9).
https://doi.org/10.1029/2021JG006275
Tinoco, R. O., & Coco, G. (2016). A laboratory study on sediment resuspension within arrays of rigid
cylinders. Advances in Water Resources, 92, 1–9.
https://doi.org/10.1016/j.advwatres.2016.04.003
Türker, U., Yagci, O., & Kabdaşlı, M. S. (2006). Analysis of coastal damage of a beach profile under
the protection of emergent vegetation. Ocean Engineering, 33(5–6), 810–828.
https://doi.org/10.1016/j.oceaneng.2005.04.019
Twiss, M. R., McKay, R. M. L., Bourbonniere, R. A., Bullerjahn, G. S., Carrick, H. J., Smith, R. E.
H., Winter, J. G., D’souza, N. A., Furey, P. C., Lashaway, A. R., Saxton, M. A., & Wilhelm,
S. W. (2012). Diatoms abound in ice-covered Lake Erie: An investigation of offshore winter
limnology in Lake Erie over the period 2007 to 2010. Journal of Great Lakes Research,
38(1), 18–30. https://doi.org/10.1016/j.jglr.2011.12.008
Uzuner, M. S. (1975). The composite roughness of ice covered streams. Journal of Hydraulic
Research, 13(1), 79–102. https://doi.org/10.1080/00221687509499721
Venditti, J. G., Church, M., & Bennett, S. J. (2006). On interfacial instability as a cause of transverse
subcritical bed forms: BED FORM INITIATION BY INTERFACIAL INSTABILITY. Water
Resources Research, 42(7). https://doi.org/10.1029/2005WR004346
Vogel, S. (1984). Drag and Flexibility in Sessile Organisms. American Zoologist, 24(1), 37–44.
https://doi.org/10.1093/icb/24.1.37
Wahl, T. L. (2003). Discussion of “Despiking Acoustic Doppler Velocimeter Data” by Derek G.
Goring and Vladimir I. Nikora. Journal of Hydraulic Engineering, 129(6), 484–487.
https://doi.org/10.1061/(ASCE)0733-9429(2003)129:6(484)
Walling, D. E. (2006). Human impact on land–ocean sediment transfer by the world’s rivers.
Geomorphology, 79(3–4), 192–216. https://doi.org/10.1016/j.geomorph.2006.06.019
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/S1001-6058(08)60036-0
Ward, J. V., Tockner, K., Uehlinger, U., & Malard, F. (2001). Understanding natural patterns and
processes in river corridors as the basis for effective river restoration. Regulated Rivers:
Research & Management, 17(4–5), 311–323. https://doi.org/10.1002/rrr.646
Waycott, M., Longstaff, B., & Mellors, J. (2005). Seagrass population dynamics and water quality in
the Great Barrier Reef region: A review and future research directions. 51((1-4)), 343–350.
https://doi.org/10.1016/j.marpolbul.2005.01.017. PMID: 15757733.
Wei Huang, Yano, S., Lin Lin, & Jianmin Zhang. (2011). Using functional indicators to assess the
river health under partial flow restoration. 2011 International Symposium on Water Resource
and Environmental Protection, 501–504. https://doi.org/10.1109/ISWREP.2011.5893053

53

Weitzman, J., Aveni-Deforge, K., Koseff, J., & Thomas, F. (2013). Uptake of dissolved inorganic
nitrogen by shallow seagrass communities exposed to wave-driven unsteady flow. Marine
Ecology Progress Series, 475, 65–83. https://doi.org/10.3354/meps09965
White, K. D., Tuthill, A. M., & Furman, L. (2007). STUDIES OF ICE JAM FLOODING IN THE
UNITED STATES. In O. F. Vasiliev, P. H. A. J. M. Van Gelder, E. J. Plate, & M. V. Bolgov
(Eds.), Extreme Hydrological Events: New Concepts for Security (Vol. 78, pp. 255–268).
Springer Netherlands. https://doi.org/10.1007/978-1-4020-5741-0_16
Widdows, J., Pope, N., Brinsley, M., Asmus, H., & Asmus, R. (2008). Effects of seagrass beds
(Zostera noltii and Z. marina) on near-bed hydrodynamics and sediment resuspension.
Marine Ecology Progress Series, 358, 125–136. https://doi.org/10.3354/meps07338
Wilcock, R. J., Champion, P. D., Nagels, J. W., & Croker, G. F. (1999). The influence of aquatic
macrophytes on the hydraulic and physico-chemical properties of a New Zealand lowland
stream. Hydrobiologia, 416, 203–214. https://doi.org/10.1023/A:1003837231848
Woo, M., Thorne, R., Szeto, K., & Yang, D. (2008). Streamflow hydrology in the boreal region under
the influences of climate and human interference. Philosophical Transactions of the Royal
Society B: Biological Sciences, 363(1501), 2249–2258.
https://doi.org/10.1098/rstb.2007.2197
Worcester, S. (1995). Effects of eelgrass beds on advection and turbulent mixing in low current and
low shoot density environments. Marine Ecology Progress Series, 126, 223–232.
https://doi.org/10.3354/meps126223
Wu, P., Hirshfield, F., Sui, J., Wang, J., & Chen, P. (2014). Impacts of ice cover on local scour
around semi-circular bridge abutment. Journal of Hydrodynamics, 26(1), 10–18.
https://doi.org/10.1016/S1001-6058(14)60002-0
Yager, E. M., & Schmeeckle, M. W. (2013). The influence of vegetation on turbulence and bed load
transport: VEGETATION, TURBULENCE, BED LOAD FLUX. Journal of Geophysical
Research: Earth Surface, 118(3), 1585–1601. https://doi.org/10.1002/jgrf.20085
Yalin, M. S. (1972). Mechanics of sediment transport (1. ed). Pergamon Press.
Yang, C. T. (2003). Sediment transport: Theory and practice. Krieger Pub., Malabar, Fla.,.
Yang, X., Pavelsky, T. M., & Allen, G. H. (2020). The past and future of global river ice. Nature,
577(7788), 69–73. https://doi.org/10.1038/s41586-019-1848-1
Yi, Y., Tang, C., Yi, T., Yang, Z., & Zhang, S. (2017). Health risk assessment of heavy metals in fish
and accumulation patterns in food web in the upper Yangtze River, China. Ecotoxicology and
Environmental Safety, 145, 295–302. https://doi.org/10.1016/j.ecoenv.2017.07.022
Zhang, M., & Yu, G. (2017). Critical conditions of incipient motion of cohesive sediments:
EROSION THRESHOLD OF COHESIVE SEDIMENTS. Water Resources Research, 53(9),
7798–7815. https://doi.org/10.1002/2017WR021066

54

3. Effects of submerged vegetation arrangement patterns and density on flow structure
3.1 Introduction
In natural rivers and streams, various arrangement patterns of vegetation can be seen
very often in channel bed, along river banks or on flood plains. Different characteristics of
vegetation elements such as vegetation density, shape, flexibility affect the bending degree of
flexible vegetation and have different impacts on flow structure (Fathi-Moghadam, M et al.,
2011; Kouwen, 1992).
Vegetation creates ecological habitat and plays an active role in maintaining and
protecting biological diversity (Nedjimi et al., 2012) by providing food and shelter for fish and
many other aquatic creatures (Short et al., 2016; Waycott et al., 2005). There is an interaction
between vegetation and bed deformation. On the one hand, vegetation influences flow
structure, sediment erosion and deposition (López F & García M, 1997; Neumeier & Ciavola,
2004; Shahmohammadi et al., 2018). On the other hand, as a result of sediment erosion and
deposition, organic materials attached to sediment particles spread throughout river bed and
affect vegetation growth and spread (Vandenbruwaene et al., 2011). Due to decrease in flow
velocity caused by vegetation in channel bed, erosion rates decrease (Trimble, 1997). Chen et
al. (2011) showed that both the length and depth of scour holes decrease with the increases in
vegetation density (S.-C. Chen et al., 2011). Net deposition increased with the distance from
the leading edge of vegetation, associated with a decrease in vertical velocity and TKE (J.
Zhang et al., 2020).
Vegetation on riverbanks is a crucial factor in reducing flood damage and coastal erosion
by increasing bank stability and damping waves (Othman, 1994; Pollen & Simon, 2005;
Arkema et al., 2017; Barbier et al., 2011; Afzalimehr & Dey, 2009). Yue et. al (2020) reported

55

that vegetation roots and sand-root composites provide effective reinforcement to
unconsolidated banks, control bank erosion, and thus reinforce the stability of banks (Yu et al.,
2020).
In the past decades, to better understand the hydrodynamics in the presence of vegetation
in rivers, many research works have been conducted. One of the main concerns is the high
turbidity of flowing water in rivers. Water turbidity can negatively affect aquatic creatures.
Vegetation is considered as a great measure to reduce resuspension and damping of waves and
induce deposition, since additional drag resulted from vegetation reduces the mean flow
velocity and bed shear stress within vegetated regions compared to that of the bare channels
(Hansen & Reidenbach, 2012; J Sanchez-Gonzalez et al., 2011; Schleiss et al., 2016). Ros et
al. (2014) found that resuspended sediment concentrations decreased as the flexible canopy
density increased (Ros A et al., 2014). On the other hand, Serra et. al. (2018) and Zhang et. al.
(2018) pointed out that vegetation can promote the near-bed turbulence, which will cause
enhanced resuspension (Serra et al., 2018; Y. Zhang et al., 2018). Tinoco and Coco (2018)
demonstrated a positive correlation between turbulent kinetic energy levels and the vegetation
array density since the Turbulence Kinetic Energy (TKE) is the primary driver of
resuspension(Tinoco & Coco, 2018). Although it is commonly thought that the presence of
vegetation in rivers can lead to decrease resuspension and deposit sediment, the scour zone
around vegetation shows that the presence of vegetation can erode the bed (Bouma et al., 2007;
Temmerman et al., 2007). These various phenomena are because of different vegetation
arrangement and densities. As claimed by Nepf (2012), with a low vegetation arrangement
density, the near bed turbulence can be higher than that over the neighbor bare bed (Nepf,
2012).

56

The vegetation distribution can be classified as either dense or sparse by using
which

ℎ, in

is vegetation drag coefficient, a is vegetation density

, and h is the vegetation

bending height. A vegetation patch can be considered as dense if

ℎ > 0.1 (Belcher et al.,

2003). In dense vegetation, the turbulence near the channel bed reduces, contributing to
sediment retention. For the sparse vegetation,

ℎ < 0.1, the turbulence near the bed with

the presence of sparse vegetation will increase as stem density increases.
Because of vegetation's positive impacts on water quality, habitat, and channel stability,
researchers now advocate replanting and restoring projects in rivers. Especially in agricultural
waterways, floodways and emergency spillways. The expansion of vegetation in fluvial
systems may worsen the flood impact since highly dense vegetation reduces the channel's
capacity and width. Therefore, an accurate and critical assessment of the vegetation density
and distribution pattern through reduction of bulk velocity is crucial in sustainable restoration
projects. Results of this study will provide vital information for river management, channel
restoration, and rehabilitation of fluvial environments through understanding the effect of
various vegetation densities, arrangement patterns, and morphology.

3.2 Materials and Methods
3.2.1 Flume, ADV and SonTek IQ used for this study
Experiments have been carried out in a large-scale outdoor flume. This flume is 38-m
long, 2.0-m wide, and 1.3-m deep, as showed in Figure 2.1. The longitudinal slope of the flume
bed was 0.2%. Two water depths of 20 cm and 30 cm have been used for this experimental
study. These water depths were chosen based on a real situation in nature since the submerged
vegetation typically grows in shallow regions of rivers. The desired constant flow rate, which
is 100 cm3/s in this study, was obtained by adjusting these three valves.

57

The aspect ratio W/H is defined as the ratio of the flume width to water depth. For both
water depths of 20 cm and 30 cm used in this experimental study, the flume is classified as a
wide flume since the aspect ratio is greater than 5 to 10. This means that in this flume, the
effects of the side walls of the channel and the secondary currents can be ignored in the center
zone of the flume (Ven Te Chow, n.d.).
In this experimental study, a down-looking Acoustic Doppler Velocimeter (ADV) 10MHz developed by Nortek, was used to measure the instantaneous three-dimensional velocity
components with a sampling rate of 25 Hz and a sampling volume of 0.25 cc (Figure 3.1 a).
The duration of each measurement was 2 min, acquiring 3000 instantaneous velocity data at
each measurement point.
The equilibrium state of the scour process in vegetated channels will achieve after 48
hours (Nabaei et al., 2021). To make sure that the exact flow rate has been obtained over the
duration of 48 hours, a SonTek-IQ Plus was used (Figure 3.1 b). This precise and robust
apparatuse was also used to measure the average velocity and water depth with advanced postprocessing functions (Sontek-Iq-Principles-of-Operation.Pdf, n.d.).

Figure 3.1: Apparatus used in the study (a) ADV (b) Sontek IQ

58

3.2.2 Sediment used in experiments
The sandbox is filled with non-uniform sediment with a median particle size (
0.50 mm. The standard deviation ( =

⁄

) of

) used to analyze the uniformity of the

distributions where

and

are 84% and 16% finer particle diameters, respectively. The

smaller the value of

, the well-sorted the sediment is (Blott & Pye, 2001). The standard

deviation for the sand with median grain size of 0.50 mm in this study is 1.97. Based on that,
the sand size used in this experiment is non-uniform. The grain size distribution was obtained
using a mechanical shaker and seven different-sized sieves. Figure 3.2 shows the grain size
distributions of the bed material.
The following equation proposed by Hager (1999) is used for determining the roughness
coefficient of the channel bed (Hager, 2010):
= 0.039
Where

( / )

3.1

is the roughness coefficient of the channel bed and

sediment particle. Therefore, the roughness coefficient of sand bed,
for

= 0.0005 m.

Figure 3.2: Grain size distribution of bed materials

59

is median grain size of
, is estimated as 0.011

3.2.3 Vegetation settings
The model flexible vegetation elements used in this study are made of plastic material.
Every vegetation element was attached to a grid mesh panel with the spacing distances of 15
cm and 25 cm in a square configuration and 10.61 cm and 17.68 cm in a staggered
configuration respectively.
Figure 3.3 shows the positions for measurement using an ADV (ADV positions) in
channel bed with two different vegetation arrangement patterns, namely, the square and
staggered configurations.

Figure 3.3: Schematic top view of a vegetative zone in the flume. Black pronged shape shows the positions of
individual vegetation elements. Black circles are ADV measurement locations in the wake of each vegetation
element. Red circles show the ADV location between two vegetation elements, and green circles show the ADV
location in the center of four vegetation elements which have been placed in a square pattern. The spacing
distance between adjacent vegetation elements is shown in the figure.

After a certain distance from the upstream edge of the submerged vegetation patch, the
flow will be fully developed. Upstream of submerged vegetation, flow follows boundary layer
conditions. Once the flow approaches submerged vegetation, this condition turns into a mixing
layer. In the mixing layer flow, the shear layer known as Kelvin Helmholtz vortices will be
developed and reach an equilibrium in size depending on the vegetation density and
submergence ratio (Huai et al., 2019). The flow within the submerged vegetation is fully
developed when the equilibrium is achieved. In this study, all velocity profiles are collected

60

using the ADV in the fully developed flow inside of the vegetation patch, which is different
from the fully developed flow in channels without the presence of vegetation.
The canopy zone can be divided into two sub-zones: the longitudinal exchange zone ( <
ℎ ) and vertical exchange zone ( > ℎ ) (note that z is vertical distance from the bed and ℎ
is penetration depth). The penetration depth ( = ℎ ) is defined as the point into the canopy
that shear stress decays to its 10% of the maximum value. As canopy density increases (C Dah
> 0.2), the penetration depth decreases (Aberle & Järvelä, 2015). Note that CD is the drag
coefficient of vegetation, a is vegetation density a (

), and ℎ is the bending height of

vegetation. The canopy becomes less ventilated since eddies no longer enter the bed (Nikora,
2010). The designated momentum in the longitudinal exchange zone is a balance of pressure
gradient or bed slope and vegetative drag. Turbulence in this region is generated at stem wakes
and represents the stem morphology. However, in the vertical exchange zone, flow is affected
by momentum balance, contributes to scalar exchange, and turbulence is generated by the KH
instabilities (Nepf & Vivoni, 2000). In other words, the difference in drag magnitude between
the non-vegetated and vegetated zones leads to the Kelvin–Helmholtz (KH) vortices occurring
at the interface between vegetated zones and water. The KH vortices can promote the mass
and momentum transport within and over canopies (Nepf & Vivoni, 2000; M. R. Raupach et
al., 1996a). For instance, turbulent mass exchange across the canopy-water interface can
regulate the nutrients and contaminants.
In one vegetation settings, all vegetation elements were placed in a fully non-bending
setting to represent the stiff and rigid vegetation patch (Figure 3.4 a). In this way, the vegetation
exhibits no deformation during the experiments, representing the real situation of reeds and
sedges in natural rivers. In another setting, all vegetation elements were deflected, representing

61

the flexible vegetation in streams (Figure 3.4 b). The height of non-bending and deflected
vegetation elements in 20-cm water depth was 12.6 cm and 8 cm, respectively and 19 cm and
12 cm in the 30-cm water depth. As you saw in Figure 2.1, the length of each sandbox is around
5.5 m. The 3-m long vegetation region was located in the middle of the sandbox. The
vegetation has a certain degree of flexibility and can swing under flow, but it does not deform.
The morphological properties of the vegetation such as the vegetation deflected height are
related to some other hydraulic properties of flow such as flow depth and velocity.

Figure 3.4: ADV position between two vegetation elements in (a) non-bending vegetation setting (b) deflected
vegetation setting

The vegetation Reynolds number associated is defined as:
=
where,

3.2

is the mean flow velocity, and d is the stem diameter.
=

3.3

where, g is the gravitational acceleration and H is the water depth. Both calculated Reynolds
numbers and Froude numbers indicated that the flow was fully turbulent and subcritical for all
cases; therefore, no dependence on Fr number was expected.
62

In this study, 32 experimental runs have been conducted including two different
submergence ratio, four different vegetation density with two different layout including square
and staggered configurations for two flow depths of 20 cm and 30 cm. Some of measured
hydraulic data for the flow depth of 20 cm are presented in Table 3.1.

Table 3.1: Some data for the flow depth of 20 cm

Configuration Density
Flexibility U
(cm/s)
(stem/ )

16
square
36

32
staggered
72

λ

∗

h/H

(cm/s)

deflected

15.15

2423.52 0.0487 3.08

2

nonbending

17.31

2770.35 0.0359 2.94

1.3

deflected

14.87

2378.56 0.0874 3.42

2

nonbending

17.58

2813.30 0.1186 3.49

1.3

deflected

14.73

2356.67 0.0961 2.56

2

nonbending

18.11

2897.52 0.0709 3.16

1.3

deflected

12.46

1993.90 0.168

2.68

2

nonbending

16.93

2708.75 0.228

3.49

1.3

3.3 Results and discussions
3.3.1 Velocity
In a channel with the presence of vegetation, there is an inner layer called the emergent
zone that is controlled by stem-scale turbulence. Above that layer, there is a layer with Kelvin–
Helmholtz (KH) vorticities that dominate mass and momentum exchange. The logarithmic
layer refers to the upper layer of turbulent flow where the velocity profile follows a log shape
(Dyer, 1989). Kazem et al. reported these three layers were present in all cases of their
63

experiments (Kazem et al., 2021a). The logarithmic profile may be described by the Karman Prandtl equation:
=

∗(

∗

3.4

)/

where, u* is the shear velocity, z0 is the roughness height and κ is the von Karman constant,
which is 0·41. The value of δ* was determined to be 0.02 m through Eq. 1.8 for non-bending
vegetation and 0.03 for deflected vegetation. In this study, z0 is assumed to be equal to D50.
Results of the velocity showed there are significant differences by changing the density,
morphology and layout of vegetation. Also, velocity is affected by both the measurement
position and water depth using a ADV.
Figure 3.5 shows velocity profiles in the presence of deflected and non-bended
vegetation patch in the channel bed. One can see from this figure, these velocity profiles
deviate from the logarithmic law distribution (the Karman - Prandtl Equation) and are confined
to the upper part of the flow in the presence of vegetation patch. Also, there exist very good
correlation-ship between u/u* and (z- δ*)/z0. Note: a logarithmic profile in the flow's inner layer
cannot developed due to the presence of vegetation (Shi et al., 1996).

64

Figure 3.5: One sample of fitting Logarithmic Law distribution on the upper layer of velocity profile in a
deflected and non-bending vegetation (staggered arrangement, flow depth: 30 cm)

3.3.1.1 Effects of vegetation density on streamwise velocity
The velocity profiles for the different vegetation densities in the fully developed region
are compared, as shown in Figure 3.6. One can observe from Figure 3.6 that with the increase
in the vegetation density (a=0.624

), the flow velocity within the canopy decreases, and

correspondingly the flow velocity above the canopy increases.
In the rear of vegetation, wake zone, vegetation creates resistance to flow, causes flow
separation and decrease in flow velocity near the bed. This phenomenon is the main reason for
sediment retention especially behind deflected vegetation patch with high density. Although
this statement is generally true, scour holes around vegetation stems have been observed in
many studies and are dependent on vegetation density. Vegetation deflection can be viewed as
a passive “drag-reduction” strategy exhibited by vegetation. As shown in Figure 3.6 a, the
inflection points at the top of the deflected vegetation in the wake zone behind the vegetation
are sensible (see arrows in Figure 3.6 a). This finding is in good agreement with that of other
researchers that velocity profiles in flows with submerged vegetation contain an inflection

65

point near the top of the vegetation (Aberle & Järvelä, 2015; Afzalimehr et al., 2017). There is
an increase in velocity on top of the canopy of the deflected vegetation at z/H=0.4 compared
to the inner layer of vegetation. The difference between the drag magnitude in the nonvegetated zone and that in the vegetated zone causes the Kelvin–Helmholtz (KH) vortices at
the interface between vegetation and non-vegetation layer. The KH vortices promote mass and
momentum transport both within and over canopies (M. R. Raupach et al., 1996b; Nepf &
Vivoni, 2000). The KH instabilities significantly affect the large-scale turbulence structures
and the momentum transfer between the non-vegetated and vegetated regimes. The effects of
KH instabilities show their effect as an inflection point in velocity profiles (Aberle & Järvelä,
2015; Afzalimehr et al., 2017). Decreasing deflected vegetation spacing (i.e., increasing
canopy density) largely retards streamwise velocity at (z/H≅0.3), slightly below the inflection
point (see Figure 3.6 a). The inflectional region tends to disappear when the canopy becomes
sparser resulting in an increase of the shear length scale associated to the velocity field. Nonbending vegetation lacks this.
On the other hand, in the presence of the non-bending vegetation in channel bed, for the
sparsest vegetation (a=0.256

), the highest velocity occurs near the bed and lowest velocity

near water surface. The peak velocity occurs at the depth of z/H=0.1 that is the sheath section
where the frontal width is minimal. Because the sheath section is more porous than the middle
vegetated layer, it can handle larger flows (Chen et al., 2011). A high negative velocity gradient
happened from z/H=0.1 to z/H=0.15. Then a decreasing trend of velocity to the water surface
is noticeable.
According to Figure 3.6, it is suggested that the dense deflected vegetation (λ≥0.1) results
in the decrease in sediment transport in streams by reducing the velocity near the bed more

66

than non-bending vegetation and sparse densities. Therefore, it is suggested that dense
vegetation provides better protection for beds subject to erosion and scour.

Figure 3.6: Velocity profiles with high vegetation density (a=0.624 m ) and lower vegetation density (a=0.256
m ) (a) deflected vegetation (b) non-bending vegetation (Water depth: 20 cm and square arrangement of
vegetation in the wake behind vegetation (black circles in Figure 3.3)

3.3.1.2 Effects of water depth of streamwise velocity
In the presence of non-bending vegetation in the channel bed with the flow depth of 20
cm, a high velocity gradient has been observed from the channel bed z/H=0 to the depth of
z/H=0.1 where a peak velocity reached. After this depth, a decreasing trend of velocity toward
the water surface (when 0.1<z/H<1.0) is noticeable (Figure 3.7). However, for the deeper flow
of 30 cm, the peak velocity occurs at a larger distance from the channel bed but closer to the
water surface. It has been also noticed that, from the depth of z/H= 0.1 to the water surface,
the value of flow velocity doesn’t change. The dip phenomenon (the position at which the
maximum velocity appears below the water surface) was observed for the case of the nonbending vegetation.
In the wake zone of deflected vegetation, the velocity in the inner layer of 20-cm-depth
flow is less than that in the 30-cm-depth flow and the velocity in the upper layer in the 20-cmdepth flow is more than that in the 30-cm-depth flow. It can be concluded that, by keeping the
67

same submergence ratio, the shallower the flow depth, the lower the flow velocity in the inner
layer in the wake zone of deflected vegetation, and the higher the velocity in the outer layer.
Thus, both the flow depth and morphology of vegetation have a substantial effect on the
velocity profile. For the non-bending vegetation case, a peak velocity value appears near the
bed in shallow water, implying that the non-bending vegetation acts like an emergent
vegetation. Therefore, fine sediment particles cannot be easily retained behind vegetation patch
due to high flow velocities. In contrast, in the presence of deflected vegetation in a channel
bed, the velocity near bed is smaller than that of non-bending vegetation mainly due to the
sheltering effect behind vegetation (see section 3.2. Turbulence Kinetic Energy for more
information). In a deeper flow (30 cm), the peak velocity is shifted toward water surface
compared to that in a shallower flow (20 cm) with high velocity near the channel bed. As a
consequence, sediment deposition is more probable in a deeper flow comparing to that in a
shallower flow.

Figure 3.7: Comparison of velocity profiles in the wake zone behind vegetation elements arranged in a square
configuration, (a) water depth = 20 cm (b) water depth = 30 cm

68

3.3.1.3 Effects of square arrangement on velocity profile
Figure 3.8 shows the dimensionless time-averaged streamwise velocity distribution
between two vegetation elements (red circles in Figure 3.3) and in the center of four vegetation
elements (green circles in Figure 3.3) with a density of a=0.624

in the flow with the depth

of 20 cm compared to that in the flow with the depth of 30 cm.
In the presence of dense non-bending vegetation with a square arrangement pattern in
the channel bed, for the flow with a depth of 20 cm, the difference between mean streamwise
velocities in the middle of two vegetation elements and those in the wake of vegetation
elements is 27.39%; and between mean streamwise velocities in the center of four vegetation
elements and those in the wake of vegetation elements is 30.64%. In the presence of dense
deflected vegetation in the channel bed, these values are 26.79% and 28.08%, respectively. For
the flow with a depth of 30 cm, the same trend was calculated. According to these results, in
the presence of dense vegetation of λ≥0.1, the velocity in the middle of two vegetation elements
is lower than that in the center of four vegetation elements. Accordingly, in vegetation with a
high density, the width of the wake behind vegetation is narrow, leading to the increase in the
flow velocity in the center of the vegetation elements. In other words, the vegetation with a
high density reduces the flow cross-sectional area locally, and thus results in a narrow wake
behind vegetation which diminish faster within a shorter distance compared to that for the case
of sparse vegetation. In contrast, in the presence of sparse non-bending vegetation with low
density (i. e. λ<0.1) in the flow with a depth of 20 cm, the difference between the mean
streamwise velocities in the middle of two vegetation elements and those in the wake of
vegetation elements is 20.56%; and the difference between the mean streamwise velocities in
the center of four vegetation elements and those in the wake of vegetation elements is 12.05%.
For the case of deflected vegetation, these differences are 34.48% and 33.75%, respectively.
69

The same trend was observed in the flow with a depth of 30 cm. This finding shows that, in
the presence of sparse vegetation in the bed, the mean streamwise velocity in the middle of
two vegetation elements is higher than that in the center of four vegetation elements. This effect
indicates the presence of a wide wake behind each vegetation element that attenuate the
velocity at the center of four vegetation elements.

Figure 3.8: Dimensionless time-averaged streamwise velocity distribution in the presence of square vegetation
configuration with a vegetation density of a=0.624 m . ADV locations: between two vegetation elements (red
circles in Figure 3.3) and in the center of four vegetation elements (green circles in Figure 3.3) (a) water depth =
20 cm (b) water depth=30 cm.

3.3.1.4 Effects of staggered arrangement on velocity profile
Figure 3.9 shows the velocity profiles in the presence of both deflected and non-bending
vegetation arranged in a staggered layout in flows with different depths of 20 cm and 30 cm,
respectively. The characteristics of velocity profiles of flow in the presence of vegetation with
staggered arrangement follow the same trend as those of velocity profiles in the wake of
vegetation arranged in a square configuration, as discussed above. However, velocity profiles
are more inflectional in vegetation with staggered arrangement compared to square
arrangement. As one can see from Figure 3.9, the velocity profile for the case of the staggered
vegetation arrangement in the wake of deflected vegetation has a “S” shape. In the middle part

70

close to the leaf zone of vegetation, the flow velocity reaches its maximum. In this zone, the
drag force causes an appreciable retardation of the mean velocity; in the flow with a depth of
30 cm, this zone is located at 0.1<z/H<0.15, and in the flow with a depth of 20 cm, this zone
is located at 0.15<z/H<0.25. As the velocity increases with the distance above the vegetation
zone, the drag resulted from vegetative gradually diminishes, and the shear stresses decline till
zero at the free water surface.

Figure 3.9: Velocity profiles in the wake zone behind non-bending vegetation elements deflected vegetation
elements which arranged in the staggered configuration in flow with the depths of 20 cm and 30 cm

3.3.1.5 Velocity contours in square arrangement
In Figure 3.10, two-dimensional and three-dimensional velocity contours are presented
near the bed (at a depth of z/H=0.1) and at the top of deflected vegetation (at a depth of
z/H=0.4). The depression spot in the contours in Figure 3.10 a illustrates the wake zone of
vegetation in the separation flow zone where sediment deposition was observed. Near the bed,
velocity is higher between rows of vegetation elements. These graphs demonstrate that velocity
in the center of the square formed by four vegetation elements is lower than that in the middle
two vegetation elements. This Figure confirms the results of section (3.3.1.4). Some spikes in

71

Figure 3.10 indicate high velocities at the interface between the deflected vegetation and nonvegetation layer as inflection points in velocity profiles compared to its neighboring zone.

Figure 3.10: Contours and 3D velocity graphs in vegetation with density of λ=0.09 at (a) near the bed at the
depth of z/H=0.1 (b) top of deflected vegetation at the depth of z/H=0.4

72

3.3.2 Turbulence Kinetic Energy (TKE)
The generation of vortices in the stem wake zone behind vegetation drains energy from
the mean flow and feeds it into turbulent kinetic energy (TKE). In this case, turbulent energy
is produced at the same rate as the work done by the flow against vegetation drag (M. Raupach
& Shaw, 1982). Most sediment transport models are based on bed shear stress in a bare channel
since turbulence is related to bed stress. However, in vegetated channels, the turbulence level
is related to the vegetative drag and has little or no link to the bed shear stress (Nepf, 1999).
The local turbulent kinetic energy was defined as:
= 1⁄2
where, ′, ′, and

(

+

+

3.5

)

′ represent the root-mean-square velocity fluctuations (RMS), indicating

the mean energy per unit mass related to turbulent eddies in streamwise, lateral and vertical
directions, respectively; and

⎧
⎨
⎩

( )=

is the water density.

=

( )= ′=
(

)=

3.6

′

′=

′

Compared to that TKE measured between two vegetation elements and those in the
center of squares formed by four vegetation elements (vegetation-free streamline), as showed
in Figure 3.11, the TKE was significantly enhanced by vegetation. In this study, this trend will
be discussed in greater detail.
The TKE in Figure 3.11 in the wake of the vegetation depicts that the maximum
( ),

( ), and

(

) occur either at the sheath section of the vegetation (at the

depth of z/H=0.1) or above the top of the vegetation (at the depth of z/H≥0.4).
In the sheath section, the frontal projected area is small, and flow can mostly pass through
the sheath section. Furthermore, stem scale turbulence was boosted at sheath section.
73

Turbulence generated by individual stem wakes was attributed to the enhancement of TKE
behind vegetation at the depth of about z/H=0.1. The near-bed turbulence kinetic energy is
enhanced by both bed-generated and vegetation-generated turbulence in the presence of
submerged vegetation. In the region slightly far from the channel bed to the vegetation top, the
presence of the Von Karman Street vortexes results in the enhancement of TKE comparing to
that in unvegetated channels. Due to the increased turbulent kinetic energy (TKE) associated
with the von Karman vortex street, which inhibits sediment deposition, the location of the
vortex formation indicates an important transition between zones where net deposition
increases and zones where net deposition diminishes compared to those without presence of
vegetation in the bed (Z. Chen et al., 2012).
On the other hand, there are no obstructions to the flow at the top of the vegetation. Thus,
the TKE terms reach their maximum values. This result confirms that of Afzalimehr et al
(2011) (Afzalimehr et al., 2011). During the transition from the vegetated zone to the
unvegetated zone, the kinetic energy has the opportunity to enhance itself.
While in the profiles at the points either between two vegetation elements or in the center
of square formed by four vegetation elements, the TKE near the bed was greater than the TKE
behind vegetation elements. As showed in Figure 3.11, TKE near the bed (z/H=0) in the wake
of vegetation elements starts at zero; however, a TKE between two vegetation elements and in
the center of square formed by four vegetation elements (vegetation-free streamlines) does not
equal zero (TKE>0). This is a well-known effect of the submerged vegetation on turbulence
and called as sheltering or dampening effect. A sheltering effect occurs when two bodies are
positioned so that one is located in the wake of the upstream body (M. R. Raupach, 1992). The
downstream body experiences a lower approaching velocity than that for the upstream body,

74

resulting in a lower drag force. Depending on how vegetation elements are arranged, the
sheltering effect can be relevant to vegetation-covered flows (Etminan et al., 2017).
As showed in Figure 3.11, the TKE profiles for vegetation densities of a=0.624 m-1 and
a=0.256 m-1, indicate a greater effect of this phenomenon in a denser vegetation due to a shorter
distance between vegetation elements (or smaller spacing distance between vegetation
elements). Therefore, the sheltering effect is more evident in a denser vegetation comparing to
that in a sparse vegetation. This effect can enhance sediment deposition and protect the bed
from erosion (Leonard & Croft, 2006; Neumeier & Amos, 2006). Nosrati et al. 2022 found
that the bending deformation of vegetation results in a significant reduction in the spacing
distance between vegetation elements, causing an intensified sheltering effect and a lower form
drag force (Nosrati et al., 2022). The TKE decreases significantly near the bed (0<z/H<0.05)
in the wake zone of a denser vegetation. Also, with the decrease in the flow depth from 30 cm
to 20 cm, the TKE near the bed decreases. Shahmohammadi et al. (2018) found that the TKE
in bare channels is greater compared to the upstream approaching flow from a vegetated
channel (Shahmohammadi et al., 2018). Results of the present study are in good agreement
with that of Shahmohammadi et al (2018), namely, as the vegetation density decreases, the
TKE near the bed (z/H=0) increases (Shahmohammadi et al., 2018).

75

Figure 3.11: Comparison of Turbulence Kinetic Energy (TKE) between deflected vegetation morphology and
non-bending vegetation morphology at different positions (a) higher vegetation density (a=0.624 m -1) (b) lower
vegetation density (a=0.256 m-1)

One can see from Figure 3.12, in the wake zone behind each vegetation element, the
TKE value at top of the deflected vegetation has a high value, confirming the presence of KH
vortices at that flow depth. This result is in agreement with that of Kazem et al. (2021) (Kazem
et al., 2021b). Also, near the channel bed, the high value of TKE took place in the pathway
between vegetation elements. This high value of TKE should be the main cause of sediment
transport in vegetated channels. It has been noticed from Figure 3.12 b that the TKE has low
value in front of each vegetation element near the bed that was discussed above as a sheltering
effect.

76

Figure 3.12: Contour of Turbulence Kinetic Energy (TKE) for deflected vegetation case having a square
configuration (λ=0.04, water depth = 30 cm). (a) around the top of vegetation z/H=0.4 (b) near the bed z/H=0

3.3.3 Shear Stress
In this study, the primary turbulent Reynolds Shear Stress (RSS) at a distance from the
bed of z was determined from:
( )=− <
where,
variables,

>

3.7

is the mass density of fluid, angle brackets denote the spatial average of flow
and

are instantaneous velocity fluctuations in the longitudinal and vertical

directions, respectively. The RSS values were normalized by the square of shear velocity ( ∗ ).
Results show that the presence of vegetation in a channel bed causes deviation of the
RSS distribution from the linear one. It is also noticed that the RSS distribution is influenced
by the aspect ratio (W/H) (Afzalimehr et al., 2011).
In Figure 3.13, in the presence of vegetation elements with a square arrangement ( =
0.624

), the RSS has been displayed at following locations: in the middle of two

vegetation elements (red circles in Figure 3.3), at the center of the square formed by four
vegetation elements (green circles in Figure 3.3), in the wake zone of vegetation elements
(black circles in Figure 3.3) and in the wake zone of vegetation elements with staggered
configuration ( = 1.2

). At the same location as showed in Figure 3.13, the RSS presents
77

in Figure 3.14 for vegetation densities of ( = 0.256
0.506

) for a square configuration and ( =

) for a staggered configuration of vegetation elements.

Results showed that the RSS is highly affected by vegetation density, morphology and
the place for data collection as displayed in Figure 3.13 and Figure 3.14. For the case of nonbending vegetation with a square configuration and density of ( = 0.624

), the RSS

doesn’t change much throughout the flow depth between two vegetation elements, and at the
center of the square formed by four vegetation elements with a slightly fluctuation pattern
(Figure 3.13 b and Figure 3.14 b). Inside the inner layer of the vegetation, however, more
fluctuation in shear stress has been noticed with the negative values of RSS near the water
surface. The negative values of RSS near the water surface for the non-bending vegetation case
are attributed to turbulent fluxes associated with vegetation morphology and negative
streamwise velocity gradients (see Figure 3.8 a).
For the deflected vegetation case (Figure 3.13 a), similar to the non-bending vegetation
case (Figure 3.13 b), constant RSS through the water depth was observed between two
vegetation elements and at the center of the square formed by four vegetation elements.
However, the RSS values for the deflected vegetation case are higher than those for the nonbending vegetation case. For the case of deflected vegetation with a square configuration, at
the center of the square formed by four vegetation elements and between two vegetation
elements (see Figure 3.13 a), the RSS has a maximum value at a depth of z/H=0.15. However,
in the wake zone behind the deflected vegetation, the maximum value of RSS occurred at an
elevation slightly higher above the top of the vegetation, indicating the presence of the KH
instability at the top of the deflected vegetation and slightly above top of the vegetation
(z/H≥0.4). As one can see from Figure 3.13 a, above the top of vegetation, the increasing trend

78

of RSS is continuous. The Shift of the maximum RSS above the top of the vegetation is caused
by presence of branches that alter the peak of RSS to a higher location above the top of the
vegetation. Near the channel bed, the RSS is close to zero and starts to increase around z/H=0.1
that is associated with stem scale turbulence at this zone. Then, the RSS reaches the peak value
at the depth above of vegetation bending height, namely around z/H=0.4. When the vegetation
is deflected, the drag discontinuity at the edge of the vegetation produces a shear layer at this
interface. The Kelvin-Helmholtz instability forms large coherent vortices within the shear
layer, and these structures dominate vertical transport between vegetation and the water
column above.
When the vegetation elements are staggered layout, the RSS (Figure 3.13 c, d, Figure
3.14 c, d) are similar to those in the wake zone of squared layout elements with intensified RSS
values. Thus, the streamwise velocity, TKE, and RSS for the staggered layout vegetation are
intensified compared to those for a square configuration.
The canopy morphology and resistance affect the depth to which KH vortices penetrate
the canopy. In the present study, the range of λ is 0.04 < ah=λ ≈<0.23; consequently, the mixing
layer eddies penetrate toward the bed and are responsible for turbulence patterns across the
vegetation (Nepf & Ghisalberti, 2008). As a result, no penetration depth needs to be calculated
in the present study because the eddies reach the bed.

79

Figure 3.13: Normalized Reynolds Shear Stress (flow depth = 20 cm) (a) Square configuration of deflected
vegetation in the wake zone of vegetation, between two vegetation elements and in the center of four vegetation
elements with λ=0.09 (b) Square configuration of non-bending vegetation in the wake zone of vegetation,
between two vegetation elements and in the center of four vegetation elements with λ=0.12 (c) Staggered
configuration of deflected vegetation in wake of three random vegetation elements with λ=0.17 (d) Staggered
configuration of non-bending vegetation in wake of three random vegetation elements with λ=0.23

80

Figure 3.14: Normalized Reynolds Shear Stress in (water depth = 20 cm) (a) Square configuration of deflected
vegetation in the wake of vegetation, between two vegetation elements and in the center of four vegetation
elements with λ=0.04 (b) Square configuration of non-bending vegetation in the wake of vegetation, between
two vegetation elements and in the center of four vegetation elements with λ=0.05 (c) Staggered configuration
of deflected vegetation in wake of three random vegetation elements with λ=0.07 (d) Staggered configuration of
non-bending vegetation in wake of three random vegetation elements with λ=0.1

To assess the effect of the vegetation density on the RSS, comparing Figure 3.13 to
Figure 3.14, almost the same distribution pattern for the RSS was observed for all four graphs.
It is found that the RSS value increases with the decrease in the spacing distance between
vegetation elements. In other words, as the density of vegetation increases, both the negative
81

and positive values of RSS throughout the water depth increases. This result is in agreement
with that of Barahimi et al. 2018 (Brahimi & Afzalimehr, 2019) who concluded there existed
greater maximum and smaller minimum values of Reynolds shear stress in a dense vegetation
comparing to that in a sparse vegetation. However, for dense vegetation (λ>0.1), as the
vegetation density increases, the influence of the bed shear stress decreases. Based on that, the
submerged vegetation can be viewed as an extra layer of riverbed, implying that the dense
vegetation has shielded riverbed roughness from its effects. As a result, the influence of the
bed can be negligible near the bed, and the vegetation density affects the flow structure as a
new layer of rigidity (Neumeier & Ciavola, 2004). As the trend clearly showed in Figure 3.13
d (the densest vegetation) that the RSS near the bed is negative compared to other profiles
which have zero or positive RSS near the bed.

3.4 Conclusions
Based on experiments in a large-scale flume, this study aims to better understand the
impact of morphology, density, and arrangement of submerged vegetation on flow velocity,
Turbulence Kinetic Energy (TKE), and Reynolds shear stress. Most of data were collected in
the wake zones behind vegetation elements, between two vegetation elements and at the center
of square formed by four vegetation elements. Results showed that flow depth, density and
morphology of vegetation in the bed had a substantial effect on velocity profiles. Following
conclusions were drawn from this study.
In the presence of vegetation in the bed with a high density (λ=0.09 and λ=0.17), the
velocity between two vegetation elements is lower than at the center of square formed by four
vegetation elements. In other word, in the presence of vegetation with a high density, the width
of the wake zone behind vegetation element is narrow, therefore, it leads to the increase in
82

velocity at the center of the square formed by four vegetation elements. In other word, the
vegetation with a high density reduces the flow cross-sectional area locally, and thus results in
a narrow wake behind vegetation which diminish faster within a shorter distance compared to
that for the case of sparse vegetation. On the other hand, for the case of sparse vegetation
(λ=0.04 and λ=0.07), the mean streamwise velocity between two vegetation elements is higher
than that at the center of square formed by four vegetation elements. This effect indicates the
presence of a wide wake behind each vegetation element that attenuate the velocity at the center
of four vegetation elements. With the decrease in the spacing distance between the deflected
vegetation elements (i.e., increasing canopy density), the streamwise velocity will be largely
retarded at the flow depth of z/H≅0.3 which is slightly below the inflection point. The
inflectional region tends to disappear when the vegetation canopy becomes sparser since the
shear length scale associated to the velocity field will be increased. This kind of inflection
point has not been observed in the non-bending vegetation. Besides, velocity profiles are more
inflectional for the case of staggered arrangement of vegetation elements compared to that for
the case of square arrangement of vegetation elements.
The dense deflected vegetation (λ≥0.1) results in the decrease in sediment transport in
streams by reducing the velocity near the bed more than non-bending vegetation and sparse
densities. Therefore, it is suggested that dense vegetation provides better protection for beds
subject to erosion and scour.
The TKE behind vegetation starts at zero at the bed (z/H=0); however, the TKE between
two vegetation elements and at the center of the square formed by four vegetation elements
has a value greater than zero (TKE>0). This is a well-known effect of submerged vegetation
on turbulence and called as sheltering or dampening effect. A greater sheltering effect was

83

observed in denser vegetation due to a shorter distance between vegetation elements. The TKE
in the wake of the vegetation depicts that the maximum

( ),

( ), and

(

)

occur either at the sheath section of the vegetation (at the depth of z/H=0.1) or above the top
of the vegetation (at the depth of z/H≥0.4). In the sheath section, the frontal projected area is
small, and flow can mostly pass through the sheath section. Furthermore, stem scale turbulence
was boosted at sheath section. In the region slightly far away from the channel bed to the
vegetation top, the presence of the Von Karman Street vortexes results in the enhancement of
TKE comparing to that in unvegetated channels.
In the wake zone behind the deflected vegetation, the maximum value of RSS occurred
at an elevation slightly higher above the top of the vegetation, indicating the presence of the
KH instability at the top of the deflected vegetation and slightly above top of the vegetation
(z/H≥0.4). Above the top of vegetation, the increasing trend of RSS is continuous. The Shift
of the maximum RSS above the top of the vegetation is caused by presence of branches that
alter the peak of RSS to a higher location above the top of the vegetation. Within the range of
vegetation density in this study (0.04 < λ ≈<0.23), as the vegetation density increases, the
negative and positive values of RSS throughout the flow depth increase. However, for dense
vegetation (λ>0.1), as the vegetation density increases, the influence of the bed shear stress
decreases. Based on that, the submerged vegetation can be viewed as an extra layer of riverbed,
implying that the dense vegetation has shielded riverbed roughness from its effects. When the
vegetation elements are staggered layout, the RSS are similar to those in the wake zone of
squared layout elements with intensified RSS values.
In the presence of non-bending vegetation in the channel bed with the flow depth of 20 cm, a
high velocity gradient appears from the depth of z/H=0 to z/H=0.1 reaching a peak velocity at

84

the depth of z/H=0.1 and a decreasing trend of velocity toward the water surface is noticeable.
However, for the deeper flow of 30 cm, the peak velocity occurs at a higher location close to
the water surface. The constant value of velocity from the depth of z/H= 0.1 to the water surface
has been observed. The dip phenomenon was observed in the non-bending vegetation case.
3.5 Bibliography
Aberle, J., & Järvelä, J. (2015). Hydrodynamics of Vegetated Channels. In P. Rowiński & A.
Radecki-Pawlik (Eds.), Rivers – Physical, Fluvial and Environmental Processes (pp. 519–
541). Springer International Publishing. https://doi.org/10.1007/978-3-319-17719-9_21
Afzalimehr, H., Barahimi, M., & Sui, J. (2017). Non-uniform flow over cobble bed with submerged
vegetation strip. Proceedings of the Institution of Civil Engineers - Water Management,
172(2), 86–101. https://doi.org/10.1680/jwama.17.00039
Afzalimehr, H., & Dey, S. (2009). Influence of bank vegetation and gravel bed on velocity and
Reynolds stress distributions. 24(2), 236–246. https://doi.org/10.1016/S1001-6279(09)600305
Afzalimehr, H., Moghbel, R., Gallichand, J., & Sui, J. (2011). Investigation of turbulence
characteristics in channel with dense vegetation. International Journal of Sediment Research,
26(3), 269–282. https://doi.org/10.1016/S1001-6279(11)60093-0
Arkema, K. K., Griffin, R., Maldonado, S., Silver, J., Suckale, J., & Guerry, A. D. (2017). Linking
social, ecological, and physical science to advance natural and nature-based protection for
coastal communities: Advancing protection for coastal communities. Annals of the New York
Academy of Sciences, 1399(1), 5–26. https://doi.org/10.1111/nyas.13322
Barbier, E. B., Hacker, S. D., Kennedy, C., Koch, E. W., Stier, A. C., & Silliman, B. R. (2011). The
value of estuarine and coastal ecosystem services. Ecological Monographs, 81(2), 169–193.
https://doi.org/10.1890/10-1510.1
Belcher, S. E., Jerram, N., & Hunt, J. C. R. (2003). Adjustment of a turbulent boundary layer to a
canopy of roughness elements. Journal of Fluid Mechanics, 488, 369–398.
https://doi.org/10.1017/S0022112003005019
Blott, S. J., & Pye, K. (2001). GRADISTAT: A grain size distribution and statistics package for the
analysis of unconsolidated sediments. Earth Surface Processes and Landforms, 26(11),
1237–1248. https://doi.org/10.1002/esp.261
Bouma, T. J., van Duren, L. A., Temmerman, S., Claverie, T., Blanco-Garcia, A., Ysebaert, T., &
Herman, P. M. J. (2007). Spatial flow and sedimentation patterns within patches of epibenthic
structures: Combining field, flume and modelling experiments. Continental Shelf Research,
27(8), 1020–1045. https://doi.org/10.1016/j.csr.2005.12.019
Brahimi, M., & Afzalimehr, H. (2019). Effect of submerged vegetation density on flow under
favorable pressure gradient. 1(57). https://doi.org/10.1007/s42452-018-0052-5
85

Chen, S.-C., Kuo, Y.-M., & Li, Y.-H. (2011). Flow characteristics within different configurations of
submerged flexible vegetation. Journal of Hydrology, 398(1–2), 124–134.
https://doi.org/10.1016/j.jhydrol.2010.12.018
Chen, Z., Ortiz, A., Zong, L., & Nepf, H. (2012). The wake structure behind a porous obstruction and
its implications for deposition near a finite patch of emergent vegetation. Water Resources
Research, 48(9), 2012WR012224. https://doi.org/10.1029/2012WR012224
Dyer, K. R. (1989). Sediment processes in estuaries: Future research requirements. J. Geophys. Res.,
94, 14327–14339. https://doi.org/10.1029/JC094iC10p14327
Etminan, V., Lowe, R. J., & Ghisalberti, M. (2017). A new model for predicting the drag exerted by
vegetation canopies: NEW MODEL FOR VEGETATION DRAG. Water Resources
Research, 53(4), 3179–3196. https://doi.org/10.1002/2016WR020090
Fathi-Moghadam, M, Drikvandi, Kh, Lashkarara, B, & Hammadi, K. (2011). Determination of
friction factor for rivers with nonsubmerged vegetation in banks and floodplains. 6(22),
4714–4719.
Hager, W. H. (2010). Wastewater hydraulics: Theory and practice (2nd ed). Springer.
Hansen, J., & Reidenbach, M. (2012). Wave and tidally driven flows in eelgrass beds and their effect
on sediment suspension. Marine Ecology Progress Series, 448, 271–287.
https://doi.org/10.3354/meps09225
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
J Sanchez-Gonzalez, V Sanchez-Rojas, & C Memos. (2011). Wave attenuation due to Posidonia
Oceanica meadows. 49, 503–514. https://doi.org/doi:10.1080/00221686.2011.552464
Kazem, M., Afzalimehr, H., & Sui, J. (2021a). Characteristics of Turbulence in the Downstream
Region of a Vegetation Patch. Water, 13(23), 3468. https://doi.org/10.3390/w13233468
Kazem, M., Afzalimehr, H., & Sui, J. (2021b). Formation of Coherent Flow Structures beyond
Vegetation Patches in Channel. Water, 13(20), 2812. https://doi.org/10.3390/w13202812
Kouwen, N. (1992). Modern Approach to Design of Grassed Channels. Journal of Irrigation and
Drainage Engineering, 118(5), 733–743. https://doi.org/10.1061/(ASCE)07339437(1992)118:5(733)
Leonard, L. A., & Croft, A. L. (2006). The effect of standing biomass on flow velocity and turbulence
in Spartina alterniflora canopies, Estuarine. 69(3–4), 325–336.
https://doi.org/10.1016/j.ecss.2006.05.004
López F & García M. (1997). Open-Channel Flow Through Simulated Vegetation: Turbulence
Modeling and Sediment Transport.

86

Nabaei, S. F., Afzalimehr, H., Sui, J., Kumar, B., & Nabaei, S. H. (2021). Investigation of the Effect
of Vegetation on Flow Structures and Turbulence Anisotropy around Semi-Elliptical
Abutment. Water, 13(21), 3108. https://doi.org/10.3390/w13213108
Nedjimi, B., Beladel, B., & Guit, B. (2012). Biodiversity of Halophytic Vegetation in Chott
&lt;i&gt;Zehrez&lt;/i&gt; Lake of Djelfa (Algeria). American Journal of Plant Sciences,
03(11), 1527–1534. https://doi.org/10.4236/ajps.2012.311184
Nepf, H. (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. (2012). Hydrodynamics of vegetated channels. Journal of Hydraulic Research, 50(3), 262–
279. https://doi.org/10.1080/00221686.2012.696559
Nepf, H., & Ghisalberti, M. (2008). Flow and transport in channels with submerged vegetation. Acta
Geophysica, 56(3). https://doi.org/10.2478/s11600-11008-10017-y
Nepf, H., & Vivoni, E. R. (2000). Flow structure in depth-limited, vegetated flow. Journal of
Geophysical Research: Oceans, 105(C12), 28547–28557.
https://doi.org/10.1029/2000JC900145
Neumeier, U., & Amos, C. L. (2006). The influence of vegetation on turbulence and flow velocities in
European salt-marshes. Sedimentology, 53(2), 259–277. https://doi.org/10.1111/j.13653091.2006.00772.x
Neumeier, U., & Ciavola, P. (2004). Flow Resistance and Associated Sedimentary Processes in a
Spartina maritima Salt-Marsh. Journal of Coastal Research, 202, 435–447.
https://doi.org/10.2112/1551-5036(2004)020[0435:FRAASP]2.0.CO;2
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
Nosrati, K., Afzalimehr, H., & Sui, J. (2022). Drag Coefficient of Submerged Flexible Vegetation
Patches in Gravel Bed Rivers. Water, 14(5), 743. https://doi.org/10.3390/w14050743
Othman, M. A. (1994). Value of mangroves in coastal protection. Hydrobiologia, 285(1–3), 277–282.
https://doi.org/10.1007/BF00005674
Pollen, N., & Simon, A. (2005). Estimating the mechanical effects of riparian vegetation on stream
bank stability using a fiber bundle model: MODELING ROOT REINFORCEMENT OF
STREAM BANKS. Water Resources Research, 41(7).
https://doi.org/10.1029/2004WR003801
Raupach, M. R. (1992). Drag and drag partition on rough surfaces. Boundary-Layer Meteorology,
60(4), 375–395. https://doi.org/10.1007/BF00155203
Raupach, M. R., Finnigan, J. J., & Brunei, Y. (1996a). Coherent eddies and turbulence in vegetation
canopies: The mixing-layer analogy. Boundary-Layer Meteorology, 78(3–4), 351–382.
https://doi.org/10.1007/BF00120941

87

Raupach, M. R., Finnigan, J. J., & Brunei, Y. (1996b). Coherent eddies and turbulence in vegetation
canopies: The mixing-layer analogy. Boundary-Layer Meteorology, 78(3–4), 351–382.
https://doi.org/10.1007/BF00120941
Raupach, M., & Shaw, R. (1982). Averaging procedures for flow within vegetation canopies. Bound.
Lay. Met., 22(1), 79–90. https://doi.org/10.1007/BF00128057
Ros A, Colomer J, Serra T, Pujol D, Soler M, & Casamitjana X. (2014). Experimental observations
on sediment resuspension within submerged model canopies under oscillatory flow. 91, 220–
231. https://doi.org/10.1016/j.csr.2014.10.004
Schleiss, A. J., Franca, M. J., Juez, C., & De Cesare, G. (2016). Reservoir sedimentation. Journal of
Hydraulic Research, 54(6), 595–614. https://doi.org/10.1080/00221686.2016.1225320
Serra, T., Oldham, C., & Colomer, J. (2018). Local hydrodynamics at edges of marine canopies under
oscillatory flows [Data set]. The University of Western Australia.
https://doi.org/10.26182/5B6D4C6392813
Shahmohammadi, R., Afzalimehr, H., & Sui, J. (2018). Impacts of turbulent flow over a channel bed
with a vegetation patch on the incipient motion of sediment. Canadian Journal of Civil
Engineering, 45(9), 803–816. https://doi.org/10.1139/cjce-2017-0474
Shi, Z., Pethick, J. S., Burd, F., & Murphy, B. (1996). Velocity profiles in a salt marsh canopy. GeoMar. Lett, 16(4), 319–323. https://doi.org/10.1007/BF01245563
Short, F. T., Short, C. A., & Novak, A. B. (2016). Seagrasses. In C. M. Finlayson, G. R. Milton, R. C.
Prentice, & N. C. Davidson (Eds.), The Wetland Book (pp. 1–19). Springer Netherlands.
http://link.springer.com/10.1007/978-94-007-6173-5_262-1
Sontek-iq-principles-of-operation.pdf. (n.d.).
Temmerman, S., Bouma, T. J., Van de Koppel, J., Van der Wal, D., De Vries, M. B., & Herman, P.
M. J. (2007). Vegetation causes channel erosion in a tidal landscape. Geology, 35(7), 631.
https://doi.org/10.1130/G23502A.1
Tinoco, R. O., & Coco, G. (2018). Turbulence as the Main Driver of Resuspension in Oscillatory
Flow Through Vegetation. Journal of Geophysical Research: Earth Surface, 123(5), 891–
904. https://doi.org/10.1002/2017JF004504
Trimble, W. S. (1997). Stream channel erosion and change resulting from riparian forests. 25(5).
https://doi.org/10.1130/0091-7613(1997)025%3C0467:SCEACR%3E2.3.CO;2
Vandenbruwaene, W., Temmerman, S., Bouma, T. J., Klaassen, P. C., de Vries, M. B., Callaghan, D.
P., van Steeg, P., Dekker, F., van Duren, L. A., Martini, E., Balke, T., Biermans, G.,
Schoelynck, J., & Meire, P. (2011). Flow interaction with dynamic vegetation patches:
Implications for biogeomorphic evolution of a tidal landscape: FLOW INTERACTION
WITH DYNAMIC PATCHES. Journal of Geophysical Research: Earth Surface, 116(F1),
n/a-n/a. https://doi.org/10.1029/2010JF001788
Ven Te Chow. (n.d.). Open-channel Hydraulics. Blackburn Press, 2009.

88

Waycott, M., Longstaff, B., & Mellors, J. (2005). Seagrass population dynamics and water quality in
the Great Barrier Reef region: A review and future research directions. 51((1-4)), 343–350.
https://doi.org/10.1016/j.marpolbul.2005.01.017. PMID: 15757733.
Yu, G.-A., Li, Z., Yang, H., Lu, J., Huang, H. Q., & Yi, Y. (2020). Effects of riparian plant roots on
the unconsolidated bank stability of meandering channels in the Tarim River, China.
Geomorphology, 351, 106958. https://doi.org/10.1016/j.geomorph.2019.106958
Zhang, J., Lei, J., Huai, W., & Nepf, H. (2020). Turbulence and Particle Deposition Under Steady
Flow Along a Submerged Seagrass Meadow. Journal of Geophysical Research: Oceans,
125(5). https://doi.org/10.1029/2019JC015985
Zhang, Y., Tang, C., & Nepf, H. (2018). Turbulent Kinetic Energy in Submerged Model Canopies
Under Oscillatory Flow. Water Resources Research, 54(3), 1734–1750.
https://doi.org/10.1002/2017WR021732

89

4. Deformation of vegetated channel bed under ice-covered flow conditions
4.1 Introduction
The winter season is considered one of the critical challenges for stream ecosystems. In
cold climates, river ice plays a crucial role in fluvial hydraulics. Ice cover can affect the river
flow, sediment fate, quality of the water, stability of channel banks, and aquatic habitat (Brown
et al., 2011; Thellman et al., 2021). The presence of an ice cover on water surface may change
the position and width of thalwegs, erode and deposit bed materials, weaken riverbank stability
(Sui et al., 2000). As ice cover/floes move along a river, vegetation elements in channel bed
and banks can be also abraded. Under an ice jammed flow condition, water level will be
increased significantly (Sui et al., 2002, 2005, 2008). These impacts reduce riverbank
resistance to erosion and increase the local supply of sediment to the channel (Ettema, 2002;
Sui et al., 2006).
Up to date, research work in understanding ice cover in small rivers have not made as
much progress as in large rivers. In river ecosystems, the presence of an ice cover can be both
beneficial and disruptive. Ice cover can allow light penetration and maintain aquatic vegetation
and creature diversity under stable covered condition. In rivers with warm groundwater
connectivity, river ice can insulate aquatic habitats. In small rivers especially, ice jams reduce
flow and lead to deformation of riverbed that can provide temporary habitat for aquatic
creatures, where turbulent frazil ice does not accumulate (Thellman et al., 2021). However,
under disrupting conditions such as formation of ice cover, freeze-thaw cycles, and river
breakup, river ice can scour or rearrange habitats, impede light, and alter riverine flow paths
(Casson et al., 2019).

90

4.1.1 Ice and sediment concentration
In natural rivers, due to the formation of a sheet ice cover, flow velocity under the ice
cover is reduced, and thus, the erosion and transport of sediment decrease during an icecovered period and degradation occurs (Burrell & Beltaos, 2019; Lawson et al., 1986; Sui et
al., 2010). In addition, with the increase in the roughness of an cover such as ice jam, flow
depth under an ice cover increases and the bulk velocity correspondingly decreases (Smith, &
Ettema, 1995), and the deformation of the bed will be increased (Namaee and Sui, 2019a,
2019b, 2019c). The Decrease in flow velocity and bed shear stress leads to a significant
reduction in suspended sediment transport (Sui et al., 2000). As a result of reduced bed shear
stress, the ability of the flow to transport material as bed load is also decreased (Lau &
Krishnappan, 1985).
When an ice jam collapses, both water and ice stored in a channel will be released and
surged to downstream, amplifying erosion and sediment transport rates (Sui et al., 2000;
Vandermause & Ettema, 2017). Based on field data of sediment concentration collected along
a 70-km long Hequ Reach of the Yellow River, it is reported that, during the formation of ice
jams and break-up periods, the suspended load carried by the flow is coarser, as finer sediments
from land sources are reduced and finer sediments are entangled in ice, resulting in a
predominant source of sediment being the coarser material of the riverbed (Sui et al., 2000).
Consequently, sediment concentrations are more likely to increase during the dynamic
transient phase of ice breakup than that during stable ice-covered period. Since moving ice
floes scrape and gouges riverbanks, it results in releasing sediment during the thawing process
of riverbanks and removing floodplain vegetation by ice force. As a consequence, sediment
concentrations in rivers and streams will be increased (Beltaos & Burrell, 2021). The
occurrence and amount of bank erosion depends upon several hydraulic factors, such as flow
91

energy, wave action, and the presence of bankfast ice, together with several non-hydraulic
factors, such as bank morphology, frost action, vegetation cover, and the effects of human and
animal action (Chassiot et al., 2020).
There is a lack of reliable and accurate methods for estimating flow resistance in icecovered channels. There are a few reasons for literature being scarce in cold regions. The
adverse weather conditions, river cross-section changing, lack of suitable method and sampling
equipment for use in winter due to freezing of equipment in cold weather, a short timeline of
events and fieldwork logistics are some of the main reasons for the scarcity of literature in cold
regions (Ettema et al., 2000; Toniolo et al., 2013).

4.1.2 Presence of ice cover and vegetation in rivers
Most of the research works in fluvial hydraulics focus on their objectives without a
presence of an ice cover or ice jam, largely ignoring the impact of an ice cover on flow structure
and sediment transport in presence of vegetation in boreal streams and rivers. The interaction
of ice cover and riverine vegetation is hardly studied when compared to the effects of summer
events, such as droughts and floods (Rood et al., 2007; Scrimgeour et al., 1994).
Generally, ice action creates habitat heterogeneity, which favors riverine species
diversity (Lind et al., 2014). Some frost tolerant plants can survive for several months under
an ice cover. Their ability to survive under an ice cover gives them an advantage over annual
plants, as they will occupy the habitat once it melts (Renman, 1989). The erosive power of
moving ice floes in rivers favours vegetatively reproducing plants with budding parts
underground, plants with abundant seeds, or sturdy plants, for example those with widespread
root systems. Plants with combinations of these traits have a higher chance of overwintering
survival (Engström et al., 2011). Furthermore, an ice cover on water surface may also benefit

92

biota by providing insulation against extreme weather events (Andrews et al., 2019, 2020) and
acting as a stable substrate for colonization in turbulent or scouring conditions (Katz et al.,
2015; Twiss et al., 2012). However, during an ice covered period, snowpack on the top of ice
cover can decrease benthic light availability in rivers of all sizes, thereby reducing the
availability of suitable habitat for photosynthetic organisms or visual predators (Sharma et al.,
2020).
In cold regions, river ice processes have been attracted more attentions from researchers
especially in restoration efforts. In the Peace-Athabasca Delta in Canada, one of the world’s
largest inland freshwater deltas, winter flooding caused by ice jams is of crucial importance
for biodiversity (Prowse & Conly, 1998). Human impacts, such as flow regulation,
channelization, agriculturalization and water pollution can both favour and disfavour riverine
vegetation dynamics. It is possible for rivers to mitigate some effects of anticipated changes
on river ice and vegetation dynamics by slowing flows and increasing water depth, thus
reducing the risk of massive ice formation underwater (Dynesius & Nilsson, 1994; Nilsson et
al., 2005; Ranzi et al., 2002; Takács et al., 2013).
Researchers now propose replanting and restoring projects in rivers, especially those
used for agriculture, flood control and emergency spillways. To the authors’ knowledge, no
studies have been conducted on how ice cover and vegetation influence deformation of
riverbeds as well as flow resistance. It is thus prerequisite to examine the connection between
vegetation and ice covers thoroughly in order to guarantee successful restoration projects. This
innovative research will be essential for the proper management of rivers, the restoration of
riverbeds, and the revitalization of cold-weather river ecosystems.

93

4.2 Material and methods
4.2.1 Equipment for Experiments
Experiments have been carried out in a large-scale outdoor flume. This flume is 38-m
long, 2.0-m wide, and 1.3-m deep, as shown in Figure 2.1. The longitudinal slope of the flume
bed is 0.2%. A transparent viewing window made of plexiglass is opened on the flume sidewall
along each of the sand boxes which makes it possible to observe the process of scouring and
deposition around vegetation elements. Two water depths of 20 cm and 30 cm have been used
for this experimental study by adjusting the tailgates at the end of the flume. These water depths
were chosen based on a real situation in nature since the submerged vegetation typically grows
in shallow regions of rivers. The desired constant flow rate, which is 100 cm3/s in this study,
was obtained by adjusting these three valves.
A down-looking Acoustic Doppler Velocimeter (ADV) 10-MHz developed by Nortek
was used to measure the instantaneous three-dimensional velocity components with a sampling
rate of 25 Hz and a sampling volume of 0.25 cc. The duration of each measurement was 2 min,
acquiring 3000 instantaneous velocity data at each measurement point. The vertical distance
between two consecutive points for each velocity profile was 10 mm.
The equilibrium state of the scour process in the presence of vegetation in channel bed
will achieve after 48 hours (Nabaei et al., 2021). To make sure that the exact flow rate has
been obtained over the duration of 48 hours, a SonTek-IQ Plus was used. This precise and
robust apparatuse was also used to measure the average velocity and water depth with the
advanced post-processing functions (SonTek-IQ Series, 2017).

4.2.2 Vegetation settings
Figure 4.1 shows the positions for measurement using an ADV (called as ADV positions)
in channel bed for two different vegetation arrangement patterns, namely, the squared and

94

staggered configurations. Data collated at 24 ADV positions around vegetation elements
provide robust information for detecting flow structure and turbulence intensity. To determine
the wake structure behind each vegetation element, the velocity profile was taken at three
points in the wakes of some vegetation elements, as shown in Figure 4.1.

Figure 4.1: Schematic top view of a vegetation zone in sand boxes. Black pronged shape shows the positions of
individual vegetation elements. Circles represent locations of ADV measurement in the wake of vegetation
elements. Star shapes depict the ADV location between two vegetation elements, and diamond shapes show the
ADV location in the center of four vegetation elements which have been placed in a squared-configuration
pattern. The spacing distance between adjacent vegetation elements is shown in the figure.

In the presence of a finite vegetation patch, channel resistance and conveyance are
modified at least locally, resulting in a deviation from uniform flow conditions (Siniscalchi et
al., 2012). In this study, since the channel has a longitudinal slope of 0.2% and the bed material
is nonuniform sand, flow in the channel in the presence of vegetation is non-uniform flow.
The vegetation density in this study is summarized in Table 4.1.
Table 4.1: Vegetation density parameters in this study
Configuration of vegetation elements

Square non-bending,
Square deflected
Staggered non-bending
Staggered deflected
Square non-bending

Vegetation density

Canopy density

a(

(λ= ah)

)

0.12

0.624

0.09
0.23

1.2

0.17

0.256

0.05

95

Square deflected
Staggered non-bending
Staggered deflected

0.03
0.1

0.506

0.07

From Table 4.1, the range of the canopy density λ=ah is 0.03 < λ ≈<0.23. Some
researchers claimed that, for 0.1< λ ≈<0.2, the eddies in the mixing layer penetrate toward the
bed. In this study, the vortices (eddies) in the middle layer of the flow named as mixing layer
penetrate toward the bed and are responsible for turbulence patterns across the vegetation and
benefits the resuspension of sediment (Huai et al., 2021; Nepf and Ghisalberti, 2008).
Therefore, no penetration depth needs to be calculated in the present study because the eddies
reach the bed.
Barahimi & Sui, 2023 found that the dense deflected vegetation (λ ≥ 0.1) results in the
decrease in sediment transport in streams by reducing the velocity near the bed more than nonbending vegetation and sparse densities. Therefore, it is suggested that dense vegetation
provides better protection for beds subject to erosion and scour.
In the present study, for the case of the densest vegetation configuration, the ratio of the
total thickness of all vegetation elements across the channel to the channel width, D/W, is
smaller than 0.5. Thus, the effect of channel blockage on the wake structure can be negligible.
The vegetation Reynolds number is defined as:
=
where,

4.1

is the mean flow velocity, d is the stem diameter and

is the kinematic viscosity of

water. Both calculated flow Reynolds number and Froude number indicated that flow for all
experimental runs was fully turbulent and subcritical.
To start each experimental run, one valve with a low discharge of 5 L/s was gradually
opened while the tailgate at the downstream end of the flume was closed to avoid sediment
96

being washed away. From the holding tank, water was gently discharged through the spillway
into the flume. To maintain the desired flow rate, all three valves were fully opened once the
desired water level was reached. Some of measured hydraulic data are presented in
.
Table 4.2: Some of hydraulic data for canopy density of λ = ah=0.624
Sand
(mm)

Size

Surface
condition

Water
(cm)

Depth

open
0.50

0.60

0.98

0.50

0.60

0.98

U (cm/s)

∗ (cm/s)

11.36

0.07

2.39

10.45

0.06

2.51

rough

11.10

0.06

2.44

open

13.37

0.08

2.96

10.97

0.06

2.45

rough

10.14

0.08

3.08

open

10.20

0.06

2.86

9.58

0.06

2.90

rough

9.97

0.06

2.92

open

16.82

0.12

3.44

11.75

0.08

3.42

rough

9.99

0.07

3.58

open

16.21

0.11

2.86

12.51

0.09

2.66

rough

10.70

0.08

2.56

open

16.56

0.12

3.97

14.79

0.10

3.84

13.16

0.09

3.82

smooth

smooth

smooth

smooth

smooth

smooth

30

30

30

20

20

20

rough

4.2.3 Sediment used in experiments
Three non-uniform natural sands have been used in this study. The median particle size
(

) of these sediments is 0.50 mm, 0.60 mm and 0.98 mm, respectively. The standard

97

deviation ( =

⁄

) used to analyze the uniformity of the distributions where

are 84% and 16% finer particle diameters, respectively. The smaller the

and

value, the well-

sorted the sediment is (Blott & Pye, 2001). The standard deviation for sands with median grain
size of 0.50 mm, 0.60 mm and 0.98 mm is 1.97, 2.39, and 1.41 respectively. Clearly, the sands
used in this experiment are poorly-sorted sands. The grain size distribution has been obtained
using a mechanical shaker and seven different-sized sieves. Sieve analyses (ASTM D422-63)
have been performed to obtain the grain size distribution of these three non-uniform sands, as
showed in Figure 4.2.

Figure 4.2: Grain size distribution of bed materials

4.2.4 Ice cover conditions
To simulate an ice-covered flow condition, Styrofoam panels were used to model ice
cover on water surface. While an experiment was running, the model ice cover (Styrofoam
panels) was floated on the water surface. Two types of ice cover have been used in the present
study, namely smooth and rough covers. The smooth ice cover is modeled by Styrofoam panels
without any treatment, while the rough ice cover was prepared by attaching small Styrofoam
cubes to the bottom surface of the smooth ice cover. Each Styrofoam cube has dimensions of
25 mm x 25 mm x 25mm, and spacing distance between 2 adjacent cubes is 35mm. The
roughness of an ice jam – whether it contains loose or dense slush or solid ice blocks – as well
98

as its thickness, determines its resistance to flow and is therefore important for the flooding
potential (Beltaos, 2008).
The hydraulic radius (R) is different in the case of ice-covered flow, since an additional
solid boundary is added to the water surface. As a result, an empirical equation introduced by
(Tang and Davar, 1985) which is for the estimation of the hydraulic radius has been adopted
for a variety of covered flow regimes, from open water to fully covered. Hydraulic radius for
ice covered surface can be stated for channels with rectangular cross sections:
=

(

4.2

)

where, a is the percentage of the cover on the water surface.

4.3 Results
4.3.1 Manning’s coefficient
Although hydraulic resistance can be parametrized using the Darcy-Weisbach friction
factor, the Chezy or Manning's roughness coefficient is preferred (Ferguson, 2010). In order
to determine the hydraulic resistance of flow under an ice-covered flow condition, Manning's
coefficient of solid boundaries must be calculated. To develop reliable stage-discharge
relationships and accurately predict water level under an ice-jammed flow condition, it is
essential to preciously estimate Manning's coefficient (White, 2003). And then, it can be used
to predict sediment transport and deformation of channel bed (Tsai & Ettema, 1994).
In the present study, following equations through three different methods reviewed by
(Li, 2012) was used to calculate the Manning’s coefficient for smooth and rough ice cover.
Method 1: in this method, the roughness height of the ice cover,
through:

99

, will be determined

= 30 exp [−(1 −
where,

⁄

)]

4.3

is the thickness of the ice-affected layer,

an ice-covered flow condition,

is the maximum velocity of flow under

is the depth-averaged velocity of the ice-affected layer. The

ice-affected layer is extended from the underside surface of the ice cover to the location of the
maximum velocity. The Manning’s coefficient of the ice affected layer can be determined by:
=

(

( ⁄

)

.

(

)
⁄

4.4

)

where, g is gravitational acceleration. The term ⁄

does not change significantly over a wide

range of flow conditions. Therefore, Equation 4.4 can be written as (Li, 2012):
4.5

= 0.039

Method 2: the roughness of an ice cover can be determined by fitting the logarithmic law
of the wall to the adjacent data of the ice cover (Sirianni et al., 2022):
=

∗

ln +

∗

ln( )

4.6

where,

is the mean flow velocity at the distance of y from the underside surface of an ice

cover,

∗ is the shear velocity determined using equation for the boundary layer method, and

κ is the von Karman constant (κ=0.41). A regression fitting curve to the velocity profile where
the law of the wall is valid, gives a slope and intercept. By comparing the regression equation
and Equation 4.6,

can be determined. Figure 4.3 shows the regression fitting to the linear

region of the velocity profile where the law of the wall applies (from the water surface to the
location of the maximum velocity in the ice-affected region).

100

Figure 4.3: An example of linear regression for the rough ice cover using the law of the wall approximation

Method 3, a semi-logarithmic line is fitted to the ice-affected velocity data. This fitting
line yields the slope a, and intercept b. Assuming the law of the wall is valid for the ice-affected
layer:
⁄ ∗ = 2.3

log (30 ⁄ )

It can be shown that

= 5.7 ∗ and

4.7
= [1.478 − log ( )], thus

is calculated

using:
= 10 .

⁄

Then, kS is converted to

4.8
using Equation 4.5.

Table 4.3 shows the calculated Manning’s coefficient using the above-mentioned three
methods for different bed materials and different cover conditions. The Manning’s coefficient
for rough ice cover is close to the findings of (Carey, 1996; Huai et al., 2019; Wu et al., 2014).
By using the measured discharge through the ice and field data related to the observed
characteristics of the underside of the ice cover, the calculated Manning roughness coefficient
by Carey (1996) was between 0.01~0.0281. From his calculation, a constant roughness of
0.0251 was used for the winter period (Carey, 1996). Valela et al. (2021) claimed that the
equivalent Manning’s roughness values range from near zero (smooth) to 0.08 (very rough).

101

Table 4.3: Manning’s coefficient using three methods for different bed materials and different ice cover
conditions
Sand D50=0.50 mm

Sand D50=0.60 mm

Sand D50=0.98 mm

Ice cover type

smooth

rough

smooth

rough

smooth

rough

Method 1

0.0489

0.0455

0.0495

0.0470

0.0471

0.0488

Method 2

0.0299

0.0326

0.0251

0.0307

0.0110

0.0250

Method 3

0.0299

0.0310

0.0286

0.0341

0.0111

0.0228

Average Method 2 and 3

0.0299

0.0318

0.02685

0.0324

0.01105

0.0239

As Table 4.3 displays, the Manning's coefficient of an ice-covered flow is dependent not
only on the roughness of the ice cover, but also on the roughness of the bed materials. Methods
two and three yielded results that were reasonably close to the results of previous researchers.
These two methods are based on laboratory data and the law of the wall, and are reliable even
under ice-covered flow conditions. Thus, in the last row of Table 4.3, the average Manning's
coefficient of methods two and three has been calculated. Method one, however, seems to have
overestimated results that are different from the other two methods. In the first method, the
value of the average velocity in Equation 4.3 is used to calculate the roughness height kS. The
presence of vegetation in a flow causes a huge change in the average velocity of the profile.
This discrepancy between calculated Manning’s coefficients should be related to the presence
of vegetation.
Equation 4.5 can be used to determine the roughness coefficient of the channel bed with
different bed materials. The roughness height can be substituted for the median grain size in
this case (Hager, 2010). Therefore, the roughness coefficient of sand bed,

, is estimated as

0.0110 for sand bed of D50 = 0.5 mm, 0.0113 for sand bed of D50 = 0.6 mm, and 0.0123 for
sand bed of D50 = 0.98 mm, respectively.

102

4.3.2 Scour and deposition patterns and armour layer
Several factors influence local scouring around vegetation elements, such as the
characteristics of fluid, bed material, and vegetation elements (Breusers et al., 1977). For nonuniform bed material, variables for describing the armour layer should be also considered in
studies of the scouring process in the vicinity of the in-stream infrastructures. As claimed by
Wang et al. (2008) that the incipient motion of sediment under ice-covered flow conditions is
different from that under open channel flow conditions since the maximum flow velocity will
move closer to the channel bed. Besides, they found that the deeper the flow depth under an
ice cover, the higher the flow velocity needed for the incipient motion of bed material. Streams
with non-uniform bed materials are typically protected by bed armoring layers. This
phenomenon is mainly caused by selective erosion processes in which the bed shear stress on
finer sediment particles exceeds the critical shear stress for movement during the erosion
process. Consequently, finer sediment particles are transported, and coarser sediment particles
are left behind. There is an association between incipient motion of sediment particle and the
development of an armour layer around bridge piers and vegetation stems. For the same bed
material, it found that the depth of scour holes with an armour layer around bridge piers is less
than that without an armour layer 1(Namaee & Sui, 2019c; Wu et al., 2014).
Experiments showed that, inside the scour hole around the vegetation stem, the armour
layer evolved gradually as the experiments progressed. The progress of incipient motion, the
scour hole around the vegetation stem and deposition dune downstream of the vegetation stem,
has been observed through the Plexiglas sidewall of the flume. The scour holes were initiated
at the root of vegetation stems, primarily at the leading edge of the vegetation patch due to the
effect of blockage of flow caused by vegetation patch and the uplift force. The major part of
the scouring was observed at the front face of each vegetation element (starts at about 2cm
103

upstream of each vegetation element). Then, the scour hole encompassed each vegetation stem
and extended to the front and sides of the vegetation element. Generally, each scour hole was
extended along the sides of vegetation rather than in the front. As a result, a horseshoe-shape
scour hole around each vegetation element developed. The finer bed materials eroded from
back, sides and in front of each vegetation stem, and left the coarser materials inside the scour
hole around each vegetation element. The deposition dune formed at about a distance of 3-cm
downstream of each vegetation stem, with a sensible deposition ridge. The deposition dunes
keep developing in size until a steady-state is reached (Shahmohammadi et al., 2018). Due to
the slope stability caused by the formation of the armour layer, the maximum depth of scour
holes remains quite constant once the armour layer was formed inside scour holes. After each
experimental run, samples of the armour layer within scour holes and samples at the surface of
deposition dunes were collected. The median sizes of these samples are presented in Table 4.4,
Table 4.5, Table 4.6. These tables show median grain size values for both armor layers within
scour holes and at the surface of deposition dunes under conditions of different sand bed
material, vegetation density, vegetation pattern under rough ice-covered flow.
Table 4.4: Median grain size of armour layer inside scour holes and at the surface of deposition dunes (sand bed
material: D50=0.50mm, rough ice-covered flow)
Configuration

of

Canopy density

Grain size of armour

Grain size of deposition

vegetation elements

(λ= ah)

layer (D50A)

dune (D50D)

Square deflected

0.09

0.6564

0.3161

Staggered deflected

0.17

0.6314

0.3076

Square deflected

0.04

0.6958

0.3843

Staggered deflected

0.07

0.6825

0.3209

Table 4.5: Median grain size of armour layer inside scour holes and at the surface of deposition dunes (sand bed
material: D50=0.60mm, rough ice-covered flow)
104

Configuration

of

Canopy density

Grain size of armour

Grain size of deposition

vegetation elements

(λ= ah)

layer (D50A)

dune (D50D)

Square deflected

0.09

0.7119

0.5941

Staggered deflected

0.17

0.7674

0.5669

Square deflected

0.04

0.7674

0.5797

Staggered deflected

0.07

0.7172

0.5671

Table 4.6: Median grain size of armour layer inside scour holes and at the surface of deposition dunes (sand bed
material:D50=0.98mm, rough ice-covered flow)
Configuration

of

Canopy density

Grain size of armour

Grain size of deposition

vegetation elements

(λ= ah)

layer (D50A)

dune (D50D)

Square deflected

0.09

1.8292

-

Staggered deflected

0.17

1.4879

-

Square deflected

0.04

1.8575

-

Staggered deflected

0.07

1.7270

-

Results indicate that the median grain size of the deposition dune (

) is clearly finer

than that of the bed material used. On the other hand, the median grain size of the armor layer
formed inside scour holes (

) is clearly coarser than that of bed material used in each

experimental run. As the vegetation density increases, the dimension of scour holes including
length, width and depth decreases. Besides, with the increase in the vegetation density, the
median grain size of the armour layer (

) decreases correspondingly. This result is true as

well for the deposition dune formed downstream of each vegetation element. When the
vegetation elements were placed in a staggered configuration, the median grain size of the
armour layer inside scour holes is finer than that by arranging vegetation elements in a squared
configuration. These results have been observed for the finer bed materials of D50=50 mm and

105

D50=60 mm. However, for the coarse sand bed of D50=0.98 mm, scour holes were too shallow
to be observed, since the weight of most particles exceed the uplifting force. Also, for the
coarse sand bed of D50=0.98 mm, no deposition dunes have been developed at the downstream
of vegetation elements. Figure 4.4 shows the grain size distribution curves for armour layer
inside scour holes around vegetation elements (
vegetation elements (

) and deposition dunes downstream of

).

Figure 4.4: Grain size distribution of the sediment particles under rough ice-covered flow condition (a) armour
layer inside scour holes, and (b) deposition dunes

Figure 4.5 shows the bed deformation under a rough ice-covered flow condition in the
presence of vegetation arranged in square and staggered configuration, respectively. In this
figure, the x axis represents the longitudinal direction of the flow where the vegetation patch
was embedded in the middle of each sand box and the y axis shows the width of the channel
(2 m). As the legend in Figure 4.5 showed, the darker blue represents the scouring of bed
material and the darker red indicates the deposition of bed material. In the presence of a sparse
vegetation with the vegetation density of λ = ah < 0.1, the vegetation drag is smaller compared
to the bed roughness. The introduction of sparse vegetation can augment the turbulence
intensity due to the additional turbulence caused by stem wakes. In this case, the turbulence
106

near the bed will be increased as the stem density increases. As a result, sediment particles
around vegetation stems initiate motion as the near bed turbulence increases. On the other
hand, in the presence of dense vegetation with the vegetation density of λ = ah > 0.1, the
vegetation drag is clearly higher compared to the bed stress. An increase in the vegetation
density will lead to the decrease in the near-bed turbulence and increase in the sedimentation
process (Leonard & Croft, 2006; Shi et al., 1996). As a result, in the presence of dense
vegetation, vegetation can contribute positively to incipient motion of bed material. Due to the
forced movement of the flow through vegetation patch, the bed shear stress and flow field
become spatially heterogeneous around each vegetation stem as pointed out by (Nepf, 2012).
The incipient motion of sediment particles varies with vegetation's position and is controlled
by local conditions of flow (Cheng et al., 2020).

(a)

(b)

Figure 4.5: . Images describing scour and deposition in the presence of vegetation under rough ice cover
condition: (a) square configuration of vegetation (b) staggered configuration of vegetation

Regardless of the roughness of an ice cover on water surface and the grain size of bed
material, the maximum depth of scour holes always occurred at the upstream, front face of
107

vegetation stems. Under ice-covered flow conditions, the scour hole is deeper and longer than
that under an open flow condition. Besides, under ice-covered flow conditions, the maximum
heights of deposition dunes are clearly greater than that under an open channel flow condition.
The maximum depth of scour hole under a rough ice-covered flow condition is clearly greater
compared to that under a smooth ice-covered flow condition. The reason for this result is that
as the rough ice cover increase the resistance of flow beneath rough ice cover, and shift the
maximum flow velocity toward the channel bed. Consequently, the velocity gradient and shear
stress near the bed increase, and cause more scouring. This finding is in agreement with
previous studies (Jafari and Sui, 2021; Namaee and Sui, 2019a, 2019b, 2019c; Sirianni et al.,
2022; Valela et al., 2021). For example, Burrell and Beltaos (2019) reported that if the ice
cover is uneven such as a reconsolidated ice cover after midwinter jamming or flow is
channelized by slush deposits under a solid ice sheet, significant erosion and transport of
sediment can occur. Results also indicate that, the higher the vegetation density, the more
expanded area of deposition. The effect of vegetation density on erosion and deposition in a
flow is significant. The amount of deposited sediment downstream of the vegetation elements
increases with the increase in vegetation density. This finding confirms the result of Tinoco
and Coco (2016). However, as shown in Figure 4.5, both the length and depth of scour holes
decrease as the vegetation density increases.

4.3.3 Equations for calculating the maximum scour depth (yS)
4.3.3.1 The maximum relative scour depth (yS/H) vs. Froude number (Fr)
Figure 4.6 depicts the relationship between the maximum relative scour depth ( /H)
and flow Froude number (Fr). As Fr increases, the maximum relative scour depth ( /H)

108

increases. Moreover, when Fr is constant, the maximum relative scour depth ( /H) is greater
under ice-covered conditions compared to that under open flow conditions. For open channel
flow, a higher Froude number is required to initiate sediment transportation compared to an
ice-covered flow, indicating that a lower shear stress is necessary for sediment movement
under an ice-covered condition.

Figure 4.6: Relation between the maximum relative scour depth (y /H) and Froude number (Fr)

4.3.3.2 The maximum relative scour depth (yS/H) vs. roughness of ice cover (ni/nb)
As previously mentioned, Equation 4.5 can be used to determine the roughness
coefficient of the channel bed material (nb). The roughness height can be substituted for the
median grain size in this case (Hager, 2010). Therefore, the roughness coefficient of sand bed,
, is estimated as 0.0110 for sand bed of D50 = 0.5 mm, 0.0113 for sand bed of D50 = 0.6
mm, and 0.0123 for sand bed of D50 = 0.98 mm, respectively. Thus, from Table 4.3, the relative
Manning’s roughness (ni/nb) can be gained. The relative Manning’s roughness (ni/nb) increases
with the increase in the roughness of ice cover (ni) and with decrease in the particle size of bed
material, as depicted in Figure 4.7. Results indicate that with increase in the relative Manning’s
roughness (ni/nb), the maximum relative scour depth (yS/H) increases correspondingly.
109

Figure 4.7: Relation between the maximum relative scour depth (y S/H) with the relative Manning’s coefficient
(n /n )

4.3.3.3 The maximum relative scour depth (yS/H) vs. the vegetation density λ
The density of vegetation patch used in this study is shown in Table 4.1. According to
Figure 4.8, the increasing trend in scour depth correlates directly with the increase in the
vegetation density from 0.03 to 0.1 under ice cover conditions. However, under open flow
condition, this increasing trend is from the vegetation density of 0.03 to 0.09. In this regime,
the vegetation density is categorized as sparse vegetation distribution. This regime indicates
an increased near-bed turbulence as vegetation density increases. However, for dense
vegetation in the bed (λ>0.1), as shown in Figure 4.8, as vegetation density increases, the
maximum relative scour depth (yS/H) decreases.

Figure 4.8: Relation between the maximum relative scour depth (y S/H) with the vegetation density (λ)
110

4.3.3.4 Equations for determining the maximum relative scour depth (yS/H)
As discussed above, considering all factors affecting the depth of scour holes around
vegetation elements, following general formula can be used to compute the maximum depth
of scour holes:
= ( , , ,
In which,

,

,

,W, h,

,

)

4.9

is the maximum depth of scour hole around vegetation elements,

Manning roughness coefficient of channel bed,

is the

is Manning roughness coefficient of ice

cover; h is the bending height of vegetation; W is the channel width, D50 is the median grain
size of bed material, D50A is the median grain size of armour layer, D50D is the median grain
size of deposition, and H is water depth. The maximum relative depth of a scour hole can be
expressed as following:
= (

,

The values of

,

,

⁄

is so small that it can be disregarded. The ratio of

has a very weak connection to

, , ,

)

4.10
⁄

⁄ , so it can be also neglected. This is because the deposition

has not been observed when the sand D50=0.98 mm is used as the bed material (this will be
discussed further in section 3.2). Consequently, Equation 4.10 can be simplified as following
to determine the maximum relative scour depth ( ⁄ ) around vegetation elements.
= (

)

4.11

( ) ( )

In the case of open channel flow, the ratio of roughness coefficient of ice cover to that
of channel bed roughness is not taken into account in Equation 4.11. However, the median
grain size of bed material (D50) in Equation 4.11 can be used to represent the impact of different
sand beds on the scour depth. Following Equations 4.12 and 4.13 have been developed to

111

compute the maximum relative scour depth ( ⁄ ) for ice-covered and open flow conditions,
respectively.
Ice covered flow condition:
= 1.095(

) .

.

.

( )

.

( ) .
4.12

= 0.73

Open flow condition:
= 0.302(

) .

.

( )

.

( ) .
4.13

= 0.74
According to Equation 4.12, under ice-covered conditions, the relative Manning’s
roughness coefficient (ni/nb) possesses the greatest power among all variables. In other words,
the relative Manning’s roughness coefficient (ni/nb) is determinative in the scouring process
around vegetation elements. This confirms the results of field observations since the greatest
scour depth was under the roughest ice cover and the smallest bed materials. The flow Froude
number is another important variable affecting the depth of scour holes. In open channel flow,
however, flow Froude number is the most important variable affecting the depth of scour holes.
It has been noticed that the scour hole around vegetation elements had a larger depth when
vegetation elements are placed in a squared-configuration compared to that with a staggeredconfiguration, due to the decrease in velocity when vegetation elements are arranged in a
staggered-configuration. The ratio of

⁄

has a negative power, which means that as the

grain size of the bed material increases, scour depth around vegetation elements decreases with
maintaining a constant water depth. Besides, the finer the bed material, the deeper the scour
hole. Figure 4.9 showed the calculated relative scour depth ( /H) compared to those observed
112

under ice-covered and open flow conditions. As showed in Figure 4.9, the calculated relative
scour depth ( /H) agreed well with those observed from laboratory experiments under both
open channel and ice-covered flow conditions.

(a)

(b)
Figure 4.9: Comparison of calculated relative scour depth (y /H) to those observed from experiments (a) under
ice-covered flow conditions (b) open flow conditions

113

4.4 Conclusions
Based on 144 experiments carried out in a large-scale flume, this study aims to better
understand the impact of submerged vegetation in channel bed under ice-covered flow
conditions on bed deformation. Most of data were collected in the wake zones behind
vegetation elements under different cover conditions including open channel, smooth and
rough covered flow conditions. Results showed that both vegetation density and arrangement
patterns of vegetation in channel bed as well as the cover conditions have substantial effects
on channel bed deformation. The following conclusions were drawn from this study:
1) Based on data collected from experiments, equations have been developed to predict the
maximum relative depth of scour hole around vegetation considering various independent
variables. Result showed that the most significant variable affecting the depth of scour
holes around vegetation elements under ice-covered flow conditions is the ratio of the ice
cover roughness to the bed roughness (ni/nb). However, under an Open channel flow
condition, flow Froude number is the most important variable affecting the depth of scour
holes.
2) Three methods were used to calculate the Manning’s coefficient of an ice cover. Methods
two and three yielded results that were reasonably close to results reported by other
researchers. These two methods are based on the law of the wall and are reliable even under
ice-covered flow condition and laboratory data. Method one, however, seems to have
overestimated results that are different from those of other two methods. The reason for
this discrepancy can be related to the presence of vegetation in the bed since the value of
the average velocity is used to calculate the roughness height. However, the presence of

114

vegetation in the bed causes a huge change in the average velocity under an ice-covered
flow condition.
3) The grain size of the deposition dunes downstream of vegetation elements (D50D) consists
of finer sediment particles than that of the initial sand bed (D50). On the other hand, the
grain size of armor layer formed inside scour holes (D50A) is coarser than that of the initial
sand bed (D50D). As the vegetation density increases, the dimension of the scour hole
including length, width and depth decreases. With the increase in the vegetation density,
the median grain size of the armour layer (D50A) decreases correspondingly. This result is
valid for the deposition dune formed downstream of each vegetation element. When
vegetation elements are arranged in a staggered configuration, the median grain size of the
armour layer (D50A) is finer than that arranged in a squared configuration. These results
have been observed for the finer sand beds of D50=50 mm and D50=60 mm. However, for
the coarse sand bed of D50=0.98 mm, the scour holes around vegetation elements are too
shallow to be observed, since the weight of most particles exceed the uplifting force. Also,
for the coarse sand bed of D50=0.98 mm, no deposition dunes have been developed around
vegetation elements.
4) The maximum scour depths always occurred at the upstream, front face of vegetation
elements. Under ice-covered flow conditions, the scour hole is deeper and longer than that
under an open flow condition. Under an ice-covered flow condition, the maximum
deposition height is clearly greater than that under an open flow condition. The depth of
scour holes is greater under a rough covered flow condition compared to that under a
smooth covered condition. In the presence of vegetation in the bed, the depth of scour holes
will be affected significantly by both vegetation density and vegetation arrangement

115

patterns. It is found that the denser the vegetation in the bed, the higher the deposition
dunes developed at the downstream of vegetation elements. The amount of deposited
sediment downstream of vegetation elements increases with the increase in the vegetation
density. However, both the length and depth of scour holes decrease as vegetation density
increases.
5) Results of laboratory experiments and formulae suggest that the maximum depth of scour
holes increases with the increase in flow Froude number (Fr), ratio of cover roughness
coefficient to that of channel bed (ni/nb), and vegetation density (λ). In contrast, the
maximum depth of scour holes decreases with the increase in the median grain size (D50/H)
and submergence ratio of vegetation (H/h).

4.5 Bibliography
Andrews, S. N., Buhariwalla, C. F., Fleet-Pardy, B., Dadswell, M. J., Linnansaari, T., & Curry, R. A.
(2019). Left out in the cold: The understudied overwintering ecology of striped bass in
Canada. Environmental Biology of Fishes, 102(3), 499–518. https://doi.org/10.1007/s10641019-0847-2
Andrews, S. N., O’Sullivan, A. M., Helminen, J., Arluison, D. F., Samways, K. M., Linnansaari, T.,
& Curry, R. A. (2020). Development of Active Numerating Side-scan for a High-Density
Overwintering Location for Endemic Shortnose Sturgeon (Acipenser brevirostrum) in the
Saint John River, New Brunswick. Diversity, 12(1), 23. https://doi.org/10.3390/d12010023
Barahimi, M., & Sui, J. (2023). Effects of Submerged Vegetation Arrangement Patterns and Density
on Flow Structure. Water, 15(1), 176. https://doi.org/10.3390/w15010176
Beltaos, S. (2008). Progress in the study and management of river ice jams. 51, 2–19.
Beltaos, S., & Burrell, B. C. (2021). Effects of River-Ice Breakup on Sediment Transport and
Implications to Stream Environments: A Review. Water, 13(18), 2541.
https://doi.org/10.3390/w13182541
Blott, S. J., & Pye, K. (2001). GRADISTAT: A grain size distribution and statistics package for the
analysis of unconsolidated sediments. Earth Surface Processes and Landforms, 26(11),
1237–1248. https://doi.org/10.1002/esp.261
Breusers, H. N. C., Nicollet, G., & Shen, H. W. (1977). Local Scour Around Cylindrical Piers.
Journal of Hydraulic Research, 15(3), 211–252. https://doi.org/10.1080/00221687709499645

116

Brown, R. S., Hubert, W. A., & Daly, S. F. (2011). A Primer on Winter, Ice, and Fish: What Fisheries
Biologists Should Know about Winter Ice Processes and Stream-Dwelling Fish. Fisheries,
36(1), 8–26. https://doi.org/10.1577/03632415.2011.10389052
Burrell, B. C., & Beltaos, S. (2019). Effects and Implications of River Ice Breakup on SuspendedSediment Concentrations: A synthesis. CGU HS Committee on River Ice Processes and the
Environment, Ottawa, Ontario, Canada.
Carey, K. L. (1996). Observed configuration and computed roughness of the underside of river ice,.
550, B192-B198.
Casson, N. J., Contosta, A. R., Burakowski, E. A., Campbell, J. L., Crandall, M. S., Creed, I. F.,
Eimers, M. C., Garlick, S., Lutz, D. A., Morison, M. Q., Morzillo, A. T., & Nelson, S. J.
(2019). Winter Weather Whiplash: Impacts of Meteorological Events Misaligned With
Natural and Human Systems in Seasonally Snow‐Covered Regions. Earth’s Future, 7(12),
1434–1450. https://doi.org/10.1029/2019EF001224
Chassiot, L., Lajeunesse, P., & Bernier, J.-F. (2020). Riverbank erosion in cold environments:
Review and outlook. Earth-Science Reviews, 207, 103231.
https://doi.org/10.1016/j.earscirev.2020.103231
Cheng, N.-S., Wei, M., & Lu, Y. (2020). Critical Flow Velocity for Incipient Sediment Motion in
Open Channel Flow with Rigid Emergent Vegetation. Journal of Engineering Mechanics,
146(11), 04020123. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001857
Dynesius, M., & Nilsson, C. (1994). Fragmentation and Flow Regulation of River Systems in the
Northern Third of the World. Science, 266(5186), 753–762.
https://doi.org/10.1126/science.266.5186.753
Engström, J., Jansson, R., Nilsson, C., & Weber, C. (2011). Effects of river ice on riparian vegetation:
Ice and riparian vegetation. Freshwater Biology, 56(6), 1095–1105.
https://doi.org/10.1111/j.1365-2427.2010.02553.x
Ettema, R. (2002). Review of Alluvial-channel Responses to River Ice. Journal of Cold Regions
Engineering, 16(4), 191–217. https://doi.org/10.1061/(ASCE)0887-381X(2002)16:4(191)
Ettema, R., Braileanu, F., & Muste, M. (2000). Method for estimating sediment transport in icecovered channels. 14(3).
Ferguson, R. (2010). Time to abandon the Manning equation? Earth Surface Processes and
Landforms, 35(15), 1873–1876. https://doi.org/10.1002/esp.2091
Hager, W. H. (2010). Wastewater Hydraulics. Springer Berlin Heidelberg.
https://doi.org/10.1007/978-3-642-11383-3
Huai, W., Li, S., Katul, G. G., Liu, M., & Yang, Z. (2021). Flow dynamics and sediment transport in
vegetated rivers: A review. Journal of Hydrodynamics, 33(3), 400–420.
https://doi.org/10.1007/s42241-021-0043-7

117

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
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), 1844.
https://doi.org/10.3390/w13131844
Katz, S. L., Izmest’eva, L. R., Hampton, S. E., Ozersky, T., Shchapov, K., Moore, M. V.,
Shimaraeva, S. V., & Silow, E. A. (2015). The “ M elosira years” of Lake B aikal: Winter
environmental conditions at ice onset predict under‐ice algal blooms in spring. Limnology
and Oceanography, 60(6), 1950–1964. https://doi.org/10.1002/lno.10143
Lau, L., & Krishnappan, B. (1985). Sediment transport under ice cover. 111(6).
Lawson, E.F. Chacho, B.E. Brockett, J.L. Wuebben, C.M. Collins, S.A. Arcone, & A.J. Delaney.
(1986). Morphology, hydraulics and sediment transport of an ice-covered river (CRREL
Report 86-11). Office of the Chief of Engineers.
Leonard, L. A., & Croft, A. L. (2006). The effect of standing biomass on flow velocity and turbulence
in Spartina alterniflora canopies, Estuarine. 69(3–4), 325–336.
https://doi.org/10.1016/j.ecss.2006.05.004
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
Lind, L., Nilsson, C., Polvi, L. E., & Weber, C. (2014). The role of ice dynamics in shaping
vegetation in flowing waters: Ice dynamics and vegetation in flowing waters. Biological
Reviews, 89(4), 791–804. https://doi.org/10.1111/brv.12077
Nabaei, S. F., Afzalimehr, H., Sui, J., Kumar, B., & Nabaei, S. H. (2021). Investigation of the Effect
of Vegetation on Flow Structures and Turbulence Anisotropy around Semi-Elliptical
Abutment. Water, 13(21), 3108. https://doi.org/10.3390/w13213108
Namaee, M., & Sui, J. (2019a). 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, 102811.
https://doi.org/10.1016/j.coldregions.2019.102811
Namaee, M., & Sui, J. (2019b). Impact of armour layer on the depth of scour hole around side-by-side
bridge piers under ice-covered flow condition. Journal of Hydrology and Hydromechanics,
67(3), 240–251. https://doi.org/10.2478/johh-2019-0010
Namaee, M., & Sui, J. (2019c). Local scour around two side-by-side cylindrical bridge piers under
ice-covered conditions. International Journal of Sediment Research, 34(4), 355–367.
https://doi.org/10.1016/j.ijsrc.2018.11.007
Nepf, H. (2012). Flow and transport in regions with aquatic vegetation. Annu Rev Fluid Mech, 44(1),
123–142. https://doi.org/10.1146/annurev-fluid-120710-101048

118

Nepf, Heidi, & Ghisalberti, M. (2008). Flow and transport in channels with submerged vegetation.
Acta Geophys, 56(3). https://doi.org/10.2478/s11600-11008-10017-y
Nilsson, C., Lepori, F., Malmqvist, B., Törnlund, E., Hjerdt, N., Helfield, J. M., Palm, D., Östergren,
J., Jansson, R., Brännäs, E., & Lundqvist, H. (2005). Forecasting Environmental Responses to
Restoration of Rivers Used as Log Floatways: An Interdisciplinary Challenge. Ecosystems,
8(7), 779–800. https://doi.org/10.1007/s10021-005-0030-9
Prowse, T. D., & Conly, F. M. (1998). Effects of climatic variability and flow regulation on ice-jam
flooding of a northern delta. Hydrological Processes, 12(10–11), 1589–1610.
https://doi.org/10.1002/(SICI)1099-1085(199808/09)12:10/11<1589::AIDHYP683>3.0.CO;2-G
Ranzi, R., Bochicchio, M., & Bacchi, B. (2002). Effects on floods of recent afforestation and
urbanisation in the Mella River (Italian Alps). Hydrology and Earth System Sciences, 6(2),
239–254. https://doi.org/10.5194/hess-6-239-2002
Renman, G. (1989). Distribution of littoral macrophytes in a North Swedish riverside lagoon in
relation to bottom freezing. Aquatic Botany, 33(3–4), 243–256. https://doi.org/10.1016/03043770(89)90040-5
Rood, S. B., Goater, L. A., Mahoney, J. M., Pearce, C. M., & Smith, D. G. (2007). Floods, fire, and
ice: Disturbance ecology of riparian cottonwoodsThe review is one of a selection of papers
published in the Special Issue on Poplar Research in Canada. Canadian Journal of Botany,
85(11), 1019–1032. https://doi.org/10.1139/B07-073
Scrimgeour, G. J., Prowse, T. D., Culp, J. M., & Chambers, P. A. (1994). Ecological effects of river
ice break-up: A review and perspective. Freshwater Biology, 32(2), 261–275.
https://doi.org/10.1111/j.1365-2427.1994.tb01125.x
Shahmohammadi, R., Afzalimehr, H., & Sui, J. (2018). Impacts of turbulent flow over a channel bed
with a vegetation patch on the incipient motion of sediment. Canadian Journal of Civil
Engineering, 45(9), 803–816. https://doi.org/10.1139/cjce-2017-0474
Sharma, S., Meyer, M. F., Culpepper, J., Yang, X., Hampton, S., Berger, S. A., Brousil, M. R.,
Fradkin, S. C., Higgins, S. N., Jankowski, K. J., Kirillin, G., Smits, A. P., Whitaker, E. C.,
Yousef, F., & Zhang, S. (2020). Integrating Perspectives to Understand Lake Ice Dynamics in
a Changing World. Journal of Geophysical Research: Biogeosciences, 125(8).
https://doi.org/10.1029/2020JG005799
Shi, Z., Pethick, J. S., Burd, F., & Murphy, B. (1996). Velocity profiles in a salt marsh canopy. GeoMar. Lett, 16(4), 319–323. https://doi.org/10.1007/BF01245563
Siniscalchi, F., Nikora, V. I., & Aberle, J. (2012). Plant patch hydrodynamics in streams: Mean flow,
turbulence, and drag forces: PLANT PATCH HYDRODYNAMICS. Water Resources
Research, 48(1). https://doi.org/10.1029/2011WR011050
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

119

Smith, T. B., & Ettema, R. (1995). Ice-cover influence on flow and bed-load transport in dune-bed
channels (Technical Report No. 374). National Science Foundation.
SonTek-IQ Series. (2017). 135.
Sui, J., Hicks, F. E., & Menounos, B. (2006). Observations of riverbed scour under a developing
hanging ice dam. Canadian Journal of Civil Engineering, 33(2), 214–218.
https://doi.org/10.1139/l05-094
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)0733-9429(2002)128:8(781)
Sui, J., Wang, D., & Karney, B. W. (2000). Suspended sediment concentration and deformation of
riverbed in a frazil jammed reach. Canadian Journal of Civil Engineering, 27(6), 1120–1129.
https://doi.org/10.1139/l00-038
Sui, J., Wang, J., Balachandar, R., Sun, Z., & Wang, D. (2008). Accumulation of frazil ice along a
river bend. Canadian Journal of Civil Engineering, 35(2), 158–169.
https://doi.org/10.1139/L07-093
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/S1001-6279(10)60026-1
Takács, K., Kern, Z., & Nagy, B. (2013). Impacts of anthropogenic effects on river ice regime:
Examples from Eastern Central Europe. Quaternary International, 293, 275–282.
https://doi.org/10.1016/j.quaint.2012.12.010
Tang, T. C. C., & Davar, K. S. (1985). Resistance to flow in partially-covered channels.
Thellman, A., Jankowski, K. J., Hayden, B., Yang, X., Dolan, W., Smits, A. P., & O’Sullivan, A. M.
(2021). The Ecology of River Ice. Journal of Geophysical Research: Biogeosciences, 126(9).
https://doi.org/10.1029/2021JG006275
Tinoco, R. O., & Coco, G. (2016). A laboratory study on sediment resuspension within arrays of rigid
cylinders. Advances in Water Resources, 92, 1–9.
https://doi.org/10.1016/j.advwatres.2016.04.003
Toniolo, H., Vas, D., Prokein, P., Kenmitz, R., Lamb, E., & Brailey, D. (2013). Hydraulic
Characteristics and Suspended Sediment Loads during Spring Breakup in Several Streams
Located on the National Petroleum Reserve in Alaska, USA. Natural Resources, 04(02),
220–228. https://doi.org/10.4236/nr.2013.42028
Tsai, W.-F., & Ettema, R. (1994). Ice cover influence on transverse bed slopes in a curved alluvial
channel. Journal of Hydraulic Research, 32(4), 561–581.
https://doi.org/10.1080/00221686.1994.9728355
120

Twiss, M. R., McKay, R. M. L., Bourbonniere, R. A., Bullerjahn, G. S., Carrick, H. J., Smith, R. E.
H., Winter, J. G., D’souza, N. A., Furey, P. C., Lashaway, A. R., Saxton, M. A., & Wilhelm,
S. W. (2012). Diatoms abound in ice-covered Lake Erie: An investigation of offshore winter
limnology in Lake Erie over the period 2007 to 2010. Journal of Great Lakes Research,
38(1), 18–30. https://doi.org/10.1016/j.jglr.2011.12.008
Valela, C., Sirianni, D. A. B., Nistor, I., Rennie, C. D., & Almansour, H. (2021). Bridge Pier Scour
under Ice Cover. Water, 13(4), 536. https://doi.org/10.3390/w13040536
Vandermause, R., & Ettema, R. (2017). Aerial Monitoring of Vegetation to Identify Ice-related Bank
Erosion Along the Middle Reach of the Susitna River, Alaska. Hydraulics of Ice Covered
Rivers. CGU HS Committee on River Ice Processes and the Environment, Whitehorse,
Yukon, Canada,.
Walling, D. E. (2006). Human impact on land–ocean sediment transfer by the world’s rivers.
Geomorphology, 79(3–4), 192–216. https://doi.org/10.1016/j.geomorph.2006.06.019
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/S1001-6058(08)60036-0
White, K. D. (2003). Review of prediction methods for breakup ice jams. Canadian Journal of Civil
Engineering, 30(1), 89–100. https://doi.org/10.1139/l02-047
Wu, P., Hirshfield, F., Sui, J., Wang, J., & Chen, P. (2014). Impacts of ice cover on local scour
around semi-circular bridge abutment. Journal of Hydrodynamics, 26(1), 10–18.
https://doi.org/10.1016/S1001-6058(14)60002-0

121

5. Flow structure and shear stress in the presence of both ice cover on water surface
and leafless vegetation in channel bed
5.1 Introduction
In winter, many streams and rivers experience ice-covered flow conditions. During
winter period, more periods of mild weather are predicted to lead to multiple freeze-ups and
break-ups of ice in watercourses (Stickler et al., 2010). As a result, the in-stream infrastructure
may be affected, and organisms living along streams and rivers be influenced (Prowse &
Beltaos, 2002).
The arrangement and type of riparian and aquatic vegetation is in connection with the
roughness of ice cover and accumulation (Dayton et al., 1969; Engström et al., 2011; Ettema,
2002; Lind et al., 2014). Ice formation can also be affected by flow regulation and
channelization. As a result of anchor ice, species richness may increase through the
disfavouring of a few dominant species and the favoring of less-competitive, disturbancetolerant species or a reduction of diversity in riparian areas where fluvial and ice disturbance
exceeds plant capacity. It is found that riparian under ice covered condition resulted in greater
species richness than non-ice conditions (Engström et al., 2011). In case of scraping vegetation
by ice, gaps open for colonization. By enhancing small scale spatial heterogeneity, this type of
gap dynamics may promote bryophyte diversity (Virtanen et al., 2001). Because aquatic
bryophytes influence the abundance and composition of invertebrates (Englund, 1991), which
can also affect fish communities, ice disturbance may have broad implications for the aquatic
ecosystem as a whole (Lind et al., 2014).
The turbulence in vegetated area is characterized by high turbulence intermittency within the
vegetation and the absorption of momentum by foliage's aerodynamic drag (Finnigan, 2000).

122

Within the vegetation, sweeps take up less time than ejections, but contribute more to
momentum flux than ejections (Su et al., 1998).
It has been a major focus of environmental fluid mechanics for decades to identify
organized coherent structures in turbulent flows over vegetative canopies due to the role these
structures play in mass and energy exchange (Finnigan & Shaw, 2000; Shaw & Schumann,
1992; Yue et al., 2007). In the presence of an ice cover on water surface, flow structure in
vegetated channel is very complex due to the interaction of ice cover, aquatic vegetation, and
deformation of channel bed. The interaction of submerged vegetation with ice cover on river
surfaces is poorly understood, and research work has been hardly reported. To address this
research topic, the present study has been conducted based on laboratory experiments under
different surface cover conditions in the presence of different arrangement patterns of
vegetation elements in channel bed. Quadrant analysis is employed to determine the effects of
submerged vegetation, roughness of ice cover on velocity profiles, Reynolds shear stress, and
turbulence kinetic energy.
5.2 Material and methods
5.2.1 Facilities for experiments
Experiments have been carried out in a large-scale outdoor flume which is 38-m long,
2.0-m wide, and 1.3-m deep, as shown in Figure 5.1. The longitudinal slope of the flume bed
is 0.2%. There are two sandboxes which are spaced 10.2 meters apart from each other. Two
flow depths of 20 cm and 30 cm have been used for this experimental study by adjusting the
tailgates at the end of the flume. The desired constant flow rate of 100 cm3/s in this study was
obtained by adjusting these three valves.
In this experimental study, a down-looking Acoustic Doppler Velocimeter (ADV) 10MHz developed by Nortek was used to measure the instantaneous three-dimensional velocities.
123

The duration of each measurement event was 2 minutes, acquiring 3000 instantaneous velocity
data at each measurement point. For each velocity profile, the vertical distance between two
consecutive measurement points was 10 mm. The method for filtering measured data proposed
by Goring & Nikora (2002) was selected in this study. The WinADV software was used for
data filtering.

Figure 5.1: The layout of the experimental flume (vertical and plan views)

To make sure that the exact flow rate has been obtained over data collection, a SonTekIQ Plus was used. This precise and robust apparatuse was also used to measure the average
velocity and water depth with the advanced post-processing functions (SonTek-IQ Series,
2017).

5.2.2 Vegetation settings
Figure 5.2 shows the positions for measurement using an ADV (ADV positions) in
channel bed with two different arrangement patterns of vegetation elements, namely, the
square and staggered configurations.

124

Figure 5.2: Schematic top view of a vegetation zone in sand boxes. Black pronged shape shows the positions of
individual vegetation elements. Circles represent locations of ADV measurement in the wake of vegetation
elements. Star shapes depict the ADV location between two vegetation elements, and diamond shapes show the
ADV location in the center of four vegetation elements which have been placed in a square pattern. The spacing
distance between adjacent vegetation elements is shown in the figure.

In the presence of a finite vegetation patch, channel resistance and conveyance are
modified, at least locally, resulting in a deviation from uniform flow conditions (Siniscalchi et
al., 2012). In addition, the channel has a longitudinal slope of 0.2% and the bed material is
non-uniform sand, which leads to non-uniform flow in the experiments.
The vegetation density in this study is summarized in Table 5.1. One can see from Table
5.1, the range of the canopy density λ=ah is 0.04 < λ ≈<0.17.

Table 5.1: Vegetation density parameters in this study

Configuration of vegetation

Vegetation density

Canopy density

elements

a (

λ= ah

Square deflected

0.624

0.09

Staggered deflected

1.2

0.17

Square deflected

0.256

0.04

Staggered deflected

0.506

0.07

)

125

5.2.3 Sediment used in experiments
Three different sands have been used in this study. The median particle size (

) of

non-uniform sediments used in this study is 0.50 mm, 0.60 mm and 0.98 mm, respectively.
The standard deviation ( =
where

and

⁄

) used to analyze the uniformity of the distributions

are 84% and 16% finer particle diameters, respectively. The smaller the

value of , the well-sorted the sediment is (Blott & Pye, 2001). The standard deviation for
sands with median grain size of 0.50 mm, 0.60 mm and 0.98 mm in this study is 1.97, 2.39,
and 1.41 respectively. Thus, the grain size of sands used in this experiment are poorly sorted
sand. The grain size distribution has been obtained using a mechanical shaker and seven
different-sized sieves. Sieve analyses (ASTM D422-63) have been performed to obtain the
grain size distribution of these three non-uniform sediments used as bed material in this study,
as shown in Figure 5.3.

Figure 5.3: Grain size distribution of bed materials

5.2.4 Ice cover conditions
To simulate an ice-covered flow condition, Styrofoam panels were used to model ice
cover on water surface. While an experiment was running, the model ice cover floated on the
water surface. Two types of model ice cover have been used in the present study, namely
smooth and rough covers. The smooth ice cover is modeled by Styrofoam panels without any
126

treatment, while the rough ice cover was prepared by attaching small Styrofoam cubes to the
bottom surface of the smooth ice cover. Each Styrofoam cube has dimensions of 25mm x 25
mm x 25 mm, and spacing distance between 2 adjacent cubes is 35mm. The roughness of an
ice cover is very important for the flow structure. As claimed by Beltaos (2008), the roughness
of an ice jam - whether it contains loose or dense slush or solid ice blocks - as well as its
thickness, determines its resistance to flow and is thus important for the flooding potential.
The hydraulic radius (R) is different in the case of ice-covered flow since an additional
solid boundary is added to the flow. As a result, an empirical equation introduced by Tang &
Davar (1985) which is for the estimation of the hydraulic radius has been adopted for a variety
of covered flow regimes, from open water to fully covered. Hydraulic radius in ice cover
surface can be stated as follows for rectangular channels:
=

(

5. 1

)

where, a is the percentage of the cover on the water surface.

5.3 Results
5.3.1 Velocity profiles
The location of the maximum streamwise velocity under an ice cover is dependent on
the relative roughness of the two boundaries, namely roughness coefficients of channel bed
and ice cover. The maximum streamwise velocity will tend to the surface that poses the least
resistance to the flow (Ghareh Aghaji Zare et al., 2016; Namaee & Sui, 2020; Sui et al., 2010;
Wu et al., 2016). With a higher roughness of an ice cover such as ice jam, the maximum
velocity will be shifted closer to the river bed, resulting in a higher bed shear stress that is
believed to produce more scour (Wu et al., 2016).

127

Figure 5.4 shows the velocity profiles in the streamwise direction under open channel, smooth
and rough ice-covered flow conditions in downstream of vegetation patch. In Figure 5.4, the
vegetation density is λ=0.08. Figure 5.5 shows that streamwise velocity profiles in the bare
channel (without the presence of vegetation in the bed). The flow depth in the first sand box is
30 cm, and two sands of D50= 0.50 mm and D50= 0.98 mm were used in this sand box. The
water depth in the second sandbox is 33 cm since it is located 10.2 m downstream of the first
sandbox with the channel bed longitudinal slope of 0.2%. The sand of D 50= 0.60 mm is used
in the second sand box. Obviously, the velocity profiles in Figure 5.4 differ from those without
the presence of vegetation in channel bed (Figure 5.5). The velocity profiles in Figure 5.4
represent the results of the interactions of ice cover, turbulent flow, vegetation in channel bed
and sand bed.
Generally, in the presence of vegetation in the bed (Figure 5.4), the velocity profiles
collected behind vegetation stems under an ice-covered flow condition have two peak values.
One is located at the sheath section of the vegetation elements and another one is above the
vegetation top. At the sheath section, the frontal width of each vegetation element is the least
and the spanwise strip at the sheath section is more porous than that in the middle-vegetated
layer. This means, the strip at the sheath section can handle larger flow than that in the middlevegetated layer (Chen et al., 2011). The second peak value of streamwise velocity is located in
the zone between the ice cover and vegetation canopy. For flow over the sand bed of D50= 0.60
mm, the decreasing trend between two peak values of streamwise velocity is more sensible.
This may be mainly resulted by the positions of the branches but not much related to the sand
bed. However, for flows over sand beds of both D50=0.50 mm and D50=0.98 mm, this
decreasing trend between two peak values of streamwise velocity has not been observed.

128

Additionally, the decreasing trend between two peak values of streamwise velocity is more
sensible under the rough covered flow condition compared to that under the smooth covered
condition. Results indicate that the presence of the rough ice cover largely retards streamwise
velocity in the zone between the flow depth of z/H=0.2 and the cover. These retardation effects
caused by both smooth and rough ice cover make the bulk velocity be less compared to that
under an open flow condition.
In open channel flow, vegetation deflection in the channel bed can be viewed as a passive
“drag-reduction” mechanism exhibited by vegetation. Result shows that, in the presence of
vegetation in the bed under an open flow condition, the streamwise velocity profiles generally
have a “S” shaped curve. One can see from Figure 5.4, in the wake zone behind the vegetation,
the inflection points at the top of the deflected vegetation are sensible. This finding is in good
agreement with that of other researchers that velocity profiles in flows with submerged
vegetation contain an inflection point near the top of the vegetation (Nepf, 2012). Results of
present study showed that there is an increase in velocity on top of the canopy of the deflected
vegetation at a depth of around z/H = 0.3 compared to the velocity in the inner layer of
vegetation, where z is the distance from the initial sand bed, and H is the flow depth under
ice cover. The difference between the drag magnitude in the non-vegetated zone and that in
the vegetated zone causes the Kelvin–Helmholtz (KH) vortices at the interface between
vegetation and non-vegetation layers. The KH vortices promote mass and momentum transport
both within and above the canopy of vegetation. For channel bed with sands of D 50=0.50mm
and 0.60 mm, the streamwise velocity next to bed started to increase as going off the bed.
However, for channel bed with sand of D50=0.98 mm, the zero value of velocity was recorded
in the zone from the bed to z/H=0.05. This means the bed material cannot be eroded easily

129

under this flow condition. Since the sand D50=0.98 mm is much coarser compared to sands
D50=0.50 mm and 0.60 mm, the flow was unable to move this bed material (D50=0.98 mm)
greatly. From Figure 5.4, it can be concluded that the finer the bed material, the greater the
velocity near the bed and the deeper the scour hole around vegetation elements.

Figure 5.4: Streamwise velocity under different surface conditions behind vegetation with the vegetation density
of λ=0.09 and water depth = 30 cm: (a) D50=0.50 mm (b) D50=0.60 mm and (c) D 50=0.98 mm

The streamwise velocity (u) profile under an open flow condition can be described as a
logarithmic function with the maximum velocity near water surface. However, under an icecovered flow condition, the velocity profile resembles a pipe flow with the maximum velocity
occurring at approximately mid-depth (Sui et al., 2010). Figure 5.5 display the velocity profiles
under different cover conditions without the presence of vegetation in channel bed. In open
channel flow, flow velocity increases from the bed toward water surface. Under a covered flow
condition, the velocity decrease toward the ice cover. This decreasing trend is more sensible
under the rough cover compared to that under the smooth cover. Also, the decresing trend of
velocity under an covered condition is more sensible in the channel with the sand of D50=0.50
mm followed by sand bed of D50=0.60 mm and then sand bed of D50=0.98 mm.

130

Figure 5.6 presents the stream-wise velocity profiles for the different sand bed under
different surface conditions in downstream of vegetation with the vegetation density of λ=0.09
under 20 cm water depth. The general trend of velocity profiles in flow with the depth of 20
cm are more complicated (wavier profiles) compared to that for a deeper water depth of 30 cm.
Under an open flow condition, in the presence of vegetation in the bed, the general trend of
“S” shaped velocity profiles has been retained for the flow depth of 20 cm, and the maximum
velocity reached in the zone above the vegetation canopy. However, under both smooth and
rough covered flow conditions, the wavy velocity profiles have been observed. The most
unpredictable velocity profile pattern has been observed in flows with sand bed of D50=0.60
mm under both smooth and rough covered conditions. The reason for that may be related to
the positions of the vegetation that make the velocity profile wavy. For flows with the sand
beds of D50=0.50 mm and D50=0.98 mm, the two peak velocity values were sensible at the
sheath section of vegetation and the location slightly above the top of the vegetation. The
decreasing trend of the streamwise velocity values near the ice cover is sensible. Keeping the
same flow depth and discharge, the bulk velocity in open channel is not larger than that under
ice-covered flow conditions with the sand beds of D50=0.50 mm and D50=0.60 mm. The reason
for this can be attributed to the interaction of vegetation and ice cover that makes the flows
more turbulent. For sand beds of D50=0.50mm and D50=0.60 mm, the streamwise velocity next
to the bed started to increase as going off the bed. However, for sand bed of D50=0.98 mm, the
zero value velocities were recorded in the region from the bed to z/H=0.05. This means that
the bed material cannot be easily initiated to move under that flow condition. Since sand bed
of D50=0.98 mm consists of coarser materials compared to sand beds of both D50=0.50 mm
and D50=0.60 mm, the flow is unable to erode sand particles greatly.

131

Figure 5.5: Streamwise velocity under different surface condtions in a bare channel (water depth = 30 cm): (a)
D50=0.50 mm (b) D50=0.60 mm and (c) D50=0.98 mm

Figure 5.6: Streamwise velocity profiles behind vegetation under different cover condtions with the vegetation
density λ=0.09, water depth =20 cm: (a) D50=0.50 mm (b) D50=0.60 mm and (c) D 50=0.98 mm

Figure 5.7: Streamwise velocity profiles under different surface condtions without vegetation in the channel
bed, water depth = 20 cm: (a) D50=0.50 mm (b) D50=0.60 mm and (c) D50=0.98 mm

132

Figure 5.8 shows the velocity profiles behind vegetation elements in a staggered
configuration with density of 0.17. As you can see, the velocity follow the distribution pattern
with two peak values, same as that for the square configuration of vegetation elements. One
of the peak velocity occurred at the sheath section around z/H=0.1 and another one at around
z/H 0.4. Between the two peak velocities, the velocity values has been reduced by vegetation
canopy. Toward the ice cover, the decreasing trend of flow velocity has been observed as
expected. By comparing Figure 5.4 and Figure 5.8, no much difference in the velocity
distribution pattern has been observed between square and staggered configuration of
vegetation elements. Also, regardless of vegetation configuration and grain size of bed
material, the peak stream-wise velocity at the sheath section is less than the peak velocity of
the second one above the canopy top.

Figure 5.8: Streamwise velocity profiles behind vegetation with density of 0.17 in staggered configuration of
vegetation elements (water depth= 30 cm): (a) D50=0.50 mm (b) D50=0.60 mm and (c) D50=0.98 mm

5.3.2 Shear Stress
The presence of an ice cover on water surface greatly influences the flow and sediment
transport dynamics of a river, since the presence of an ice covers almost double the wetted
perimeter of the flow cross section (Lau & Krishnappan, 1985). Smith, & Ettema (1995)
showed that the flow depth increases with the increase in the cover roughness, but the bulk
133

velocity correspondingly decreases with the cover roughness. In general, under the same
discharge, the appearance of an ice cover results in the decrease in the bulk velocity and,
consequently, reduces shear stress on the bed and increases flow depth (Smith, & Ettema,
1995). On the other hand, for the same flow depth and average velocity, Hains et al. (2004)
claimed that the addition of a floating ice cover increases turbulent shear stress three-folds on
the bed. In addition, the location of the maximum velocity is shifted downwards within the
flow depth, an increased stream-wise velocity gradient occurs near the bed, which can induce
greater bed shear stresses and more scour can occur, correspondingly (Wu et al., 2016).
In the presence of vegetation in the bed, Barahimi & Sui (2023) studied the effects of
vegetation density on flow structures based on data collected from the same flume under an
open flow condition. It is found that within the range of vegetation density of 0.04<λ≈< 0.23,
as the vegetation density increases, both negative and positive values of Reynolds shear stress
(RSS) throughout the flow depth increase. However, for dense vegetation (λ>0.1), as the
vegetation density increases, the influence of the bed shear stress decreases. Based on that, the
submerged vegetation in the bed can be viewed as an extra layer of riverbed, implying that the
dense vegetation has shielded riverbed roughness from its effects. When vegetation elements
are arranged in a staggered pattern, the RSS profiles are similar to those in the wake zone of
the vegetation elements arranged in a squared pattern with increased RSS values (Barahimi &
Sui, 2023).
From Figure 5.9 and Figure 5.10, one can see that the bed shear stress under the rough
covered flow condition is more than those under the smooth covered and open channel flow
conditions. It is consistent with the results of the above-mentioned researchers because the
water depth in laboratory flume has been kept as constant after adding an ice cover on water

134

surface. Using the surface roughness as a parameter, Faruque (2009) found that turbulent
events are more likely to occur, causing a greater change in Reynolds shear stress distributions,
which may affect sediment transport. Figure 5.9 and Figure 5.10 indicate that the upper portion
of the RSS profiles generally is smaller under ice-covered flow conditions in comparison to
open channel flow condition. For the channel bed with the sand of D50= 0.98 mm, the near-bed
stress was almost the same regardless of the surface cover (open channel, smooth covered, and
rough covered flow) conditions. The stress profiles which have a wavy pattern are affected by
both the layout of vegetation elements and ice-covered conditions. As shown in Figure 5.9, the
values of -u'w' are negative in the middle layer, showing an upward vertical transport of
momentum with negative velocity gradients (see Figure 5.4). Zones of negative Reynolds
stresses within the vegetation indicates modifications in the longitudinal velocity profile and
associated turbulent fluxes. These modifications were linked to the vegetation morphology and
the extent of reconfiguration. In this region, because the area of frontal projected vegetation is
the largest, wake is produced behind each vegetation element that attenuates the streamwise
velocity and causes a region of negative RSS. As pointed out by Nezu (2005), the RSS value
is zero and negative near water surface in flows without presence of vegetation and ice cover.
However, the resistance caused by ice cover and extra turbulence created by vegetation in
channel bed, results in the positive RSS value near ice cover surface (see Figure 5.9 and Figure
5.10). Based on the comparison between different surface cover conditions and different sizes
of bed material, the latter contributes more to the RSS than the former.

135

Figure 5.9: Normalized Reynolds Shear Stress downstream of vegetation elements under different surface cover
conditions (flow depth = 30 cm): (a) D50=0.50 mm (b) D50=0.60 mm (c) D50=0.98 mm

Figure 5.10: Normalized Reynolds Shear Stress downstream of vegetation elements under different surface
cover conditions (flow depth = 20 cm): (a) D50=0.50 mm (b) D50=0.60 mm (c) D50=0.98 mm

5.3.3 Turbulent kinetic energy (TKE)
The generation of vortices in the wake zone behind vegetation stem drains energy from
the mean flow and feeds it into turbulent kinetic energy (TKE). Most sediment transport
models are based on shear stress in a bare channel bed since the turbulence is related to the bed
stress. However, in vegetated channels, the turbulence level is related to the vegetative drag
and has little or no link to the bed shear stress (Nepf, 1999). The local turbulent kinetic energy
was defined as:

136

= 1⁄2(
where, ′, ′, and

+

+

5. 2

)

′ represent the root-mean-square (RMS) velocity fluctuations, indicating

the mean energy per unit mass related to turbulent eddies in streamwise, spanwise (or lateral)
and vertical directions, respectively.
Figure 5.11 shows the TKE behind dense vegetation elements in the flow of 30-cm deep
under open channel and ice-covered conditions. Generally, the profiles of the TKE behind
vegetation elements have two peak values, one peak at the sheath section and the second one
above the vegetation bending height as well as a decreasing trend of the TKE under both
smooth and rough ice-covered flow conditions. For the square vegetation configuration,
regardless of grain size of bed material, the peak TKE value at the sheath section is normally
more than the peak TKE of the second one above the canopy top. However, in an open channel
flow, the TKE is kept constant throughout the water depth with a mild decrease near water
surface generally.
In the region near the bed 0.05 < z/H < 0.1, the TKE reaches its maximum regardless the
particle sizes of bed material. In this region, flow can pass through the sheath sections of the
vegetation since the blockage effects of the vegetation is reduced. Besides, the stem-scale
turbulence is attributed to the boost the TKE in this region. In the region from the flow depth
of z/H = 0.05 to z/H = 0.1, the effects of turbulence caused by the bed enhance the TKE. In the
region of 0.1 < z/H < 0.25~0.3, the blockage effects of the vegetation reach its maximum and
reduce the cross section for passing flow, and thus cause a decrease in the TKE. At the flow
depth of around z/H = 0.3 which is the transition zone from the vegetated zone to unvegetated
zone, the TKE has the opportunity to enhance itself. Finally, near the bottom surface of ice
cover, due to the no slipping rule, the TKE decreases. However, under an open channel flow

137

condition, the TKE near water surface follows the same trend as lower layers and did not show
any noticeable change.
The above-mentioned trend is true regardless of the particle size of bed material used in
this study. However, for the sand bed of D50=0.60 mm, this trend is relative milder. It can be
explained that the sand bed of D50=0.60 mm was used in the second sand box which is far from
the flume entrance. In addition, due to slope of the flume bed (0.2%), the depth of the flow in
this sandbox is 33 cm instead of 30 cm in the first sandbox.

Figure 5.11: Comparison of Turbulent Kinetic Energy (TKE) behind dense (λ=0.9) deflected vegetation in
square configuration under different surface cover conditions, (a) D 50=0.50 mm (b) D50=0.60 mm and (c)
D50=0.98 mm

Figure 5.12 shows the TKE with the presence of staggered vegetation in the bed with
density of 0.17 under ice covered-flow conditions. The similar trend of TKE was observed in
staggered configuration of the vegetation with two peaks at sheath section and above the
deflected vegetation canopy. However, by comparing Figure 5.11 and Figure 5.12, one can
notice a lower values of TKE throughout the water depth for case of staggered vegetation
layout. Besides, TKE values for case of staggered configuration have an increasing trend
toward the ice cover. The vegetation in staggered configuration has the higher density (λ=0.17)
compared to square configuration (λ=0.09). The higher vegetation density (staggered
138

vegetation layout) causes the TKE values to decrease. For case of staggered configuration,
TKE values near both smooth and rough ice cover has the opportunity to be enhanced again.
For case of square configuration, however, TKE values had been decreased toward ice cover.

Figure 5.12: Comparison of Turbulent Kinetic Energy (TKE) behind dense (λ=0.17) deflected vegetation in
staggered configuration, (a) D50=0.50 mm (b) D50=0.60 mm and (c) D50=0.98 mm

5.3.4 Quadrant analysis
As a method for assessing the structure of turbulent stresses, Willmarth and Lu (1972)
introduced the quadrant method. Using this method, the theory of coherent structures,
momentum transfer, and dissipation was significantly advanced. Quadrant methods are
conventionally applied to study the temporal fluctuations of velocity components w' and u',
especially their distribution between four quadrants (Dey, 2014; Dey & Nath, 2010).
A quadrant analysis is defined as decomposing the Reynolds stress into four quadrant
planes based on the signs of the longitudinal velocity fluctuation (u’) and the vertical velocity
fluctuation (w’) as (i = 1-4):
i = 1 represents the outward motion (u’ >0 and w’ > 0)
i = 2 represents the ejection motion (u’ < 0 and w’ > 0)
i = 3 represents the inward motion (u’ < 0 and w’ < 0)
i = 4 represents the sweep motion (u’ > 0 and w’ < 0)

139

The hole parameter (H') was defined to distinguish the drastic factor ( -u' w' ) involved
at each quadrant and to bring out u' and w' by increasing the sampling time. The hole size
parameter is a hyperbolic region that is threshold level (Dey & Nath, 2010). The hole parameter
H’=0 indicated that Hʹ curve included every value.
1 if (u' , w ) is in quadrant i and if | u' w' | H ( u u )
I ( i , H ') (u , w) = 
0 otherwise

0.5

( ww) 0.5

5. 3

At one point, the contribution of -u' w' from the ith quadrant excluding a hyperbolic
hole region of size H' is obtained from following equation (Yue et al., 2007):
T

1
u' w' i ,H ' = lim  u' (t ) w' (t ) I i , H ' u ' , w'dt
T 0

5. 4

in which, T is the time interval and square brackets indicates a conditional average, If (uˊ,wˊ)
exists in the ith quadrant, = 1, and otherwise

= 0.

Each event is responsible for momentum transport caused by the turbulence. This
analysis was applied to examine the contribution of each quadrant to the Reynolds shear stress
for ice covered flow, sand bed and submerged vegetation. To determine the contribution of
each quadrant to the Reynolds stress, a computer program was written in MATLAB.
In the case of the same mean flow properties, both the type and arrangement of vegetation
elements on channel bed can influence turbulence structure (Strom & Papanicolaou, 2007).
Figure 5.13 shows the contribution of each quadrant (in percentage) versus the relative
water depth in the presence of sparse vegetation with the density of λ=0.09 in the bed. Under
an open channel condition, when the flow depth is z/H>0.05, sweep and ejection events are the
most dominant contribution among others (see Figure 5.13). The most frequently occurring
event is ejection followed by sweep, indicating that the transfer of momentum and kinetic
energy between non-vegetated zone and vegetated zone is mostly carried by ejection followed
140

by sweep events. In the presence of a dense vegetation patch in the bed, results of quadrant
analysis of vegetation turbulence consistently shows that the sweep events contribute the most
to the downward momentum transfer, suggesting that the fast moving gusts penetrate the
vegetation as pointed out by (Afzalimehr et al., 2017; Huai et al., 2019; Lu & Dai, 2016). The
result of the present study is in agreement with the previous research, since the vegetation
density used in the present study is categorized as either the sparse vegetation or transition
from sparse vegetation to less dense vegetation. The values of sweep and ejection events cause
the negative sign of u'w', resulting in positive Reynolds shear stress (-u'w') for flow in open
channel, as shown in Figure 5.10. Results showed that, under an open flow condition, both
inward and outward events are dominant near the bed in the scouring region in front of
vegetation elements (Figure 5.13 a) and the Reynolds shear stress has a negative value (Figure
5.10).
Under ice-covered flow conditions, the contributions of both inward and outward events
have been increased and, in most cases, exceed the contributions of the sweep and ejection
events. Both the inward and outward events are the upward components of the shear stress,
and the inward and outward events contribute to the bed scour around vegetation stems.
However, in most of the cases, the inward event appears most frequently in the scouring region
around vegetation stem. The contribution of the inward event from the bed to the top of
vegetation is more obvious under the rough covered flow condition compared to that under the
smooth covered condition, confirming the larger and deeper scour holes around vegetation
stems under the rough covered flow condition. As shown in Figure 5.10, the profiles of
Reynolds shear stress under the rough covered flow condition show more negative values

141

compared to that under the smooth covered flow condition, confirming the stronger inward
and outward events under the rough covered flow condition.

Figure 5.13: Percentage of velocity fluctuations (u' and w') for each quadrant behind vegetation elements (a)
open channel flow, (b) smooth covered flow (c) rough covered flow.

142

5.4 Conclusions
Based on the experiments carried out in a large-scale outdoor flume, this study aims to
better understand the impact of submerged vegetation in channel bed under ice-covered flow
conditions on flow structure. Most of data have been collected in the wake zones behind
vegetation elements under different surface cover conditions including open channel, smooth
covered and rough covered flow conditions. Results showed that vegetation density, hydraulic
and surface cover conditions have substantial effects on velocity structure, Reynolds shear
stress, and turbulent kinetic energy (TKE). The following conclusions are drawn from this
study:
1) In the presence of vegetation in the bed under ice-covered flow condition, the general trend
of velocity profiles is characterized by two peak values. One peak velocity is located at
the sheath part of the vegetation patch. At the sheath part of the vegetation patch, the
frontal width of each vegetation element is the least, namely the net cross section for
passing flow is larger comparing to that in the middle layer of vegetation patch, and thus
it can handle larger flows. The second peak velocity value is located in the region between
ice cover and the top of vegetation canopy. Regardless of vegetation configuration and
grain size of bed material, the peak stream-wise velocity at the sheath section is less than
the peak velocity of the second one above the canopy top. The decreasing trend is more
sensible under the rough covered condition compared to that under the smooth covered
condition. The presence of a rough ice cover on water surface largely retards streamwise
velocity in the zone between z/H=0.2 and the ice cover. This retardation effects resulted
from both smooth and rough ice cover make the bulk velocity be less compared to that
under an open flow condition.

143

2) The RSS values are negative in the middle layer of the vegetation patch, showing an
upward vertical transfer of momentum with negative velocity gradients. In this region,
because the area of the frontal projected vegetation is the largest, wake is produced behind
each vegetation element that attenuates the streamwise velocity and causes a negative
region of the RSS. Without the presence of vegetation in the bed and ice cover on water
surface, the RSS is zero and negative near water surface. However, with the presence of
vegetation in the bed and ice cover on water surface, the resistance caused by ice cover
and extra turbulence created by vegetation leads to the positive RSS value near ice cover.
3) Results of quadrant analysis showed, under ice-covered conditions, the contributions of
inward and outward events have been increased and, in most cases, their contributions
exceed that of the sweep and ejection events. The inward and outward events are the
upward components of the shear stress and the bed scour around vegetation stems has been
created by means of these events. However, in most of the cases, the inward event appears
most frequently in the scouring region around vegetation stem. The contribution of the
inward event from the bed to the top of vegetation is more obvious under the rough covered
flow condition compared to that under the smooth covered condition, confirming the larger
and deeper scour holes around vegetation stems under the rough covered flow condition.
4) Generally, the profiles of the TKE behind vegetation elements have one peak at the sheath
section and the other one above the vegetation bending height as well as a decreasing trend
of the TKE under both smooth and rough ice-covered flow conditions. However, in an
open channel flow, the TKE is kept constant or experienced a mild decrease near water
surface.

144

5) In the presence of vegetation in the bed arranged in staggered configuration, lower values
of TKE throughout the flow depth have been observed. A trend of increasing TKE values
has also been noticed towards the ice cover. The vegetation elements arranged in staggered
configuration has the higher density (λ=0.17) compared to that of square configuration
(λ=0.09). Clearly, higher vegetation density (staggered configuration) causes the TKE
values to decrease. For case of staggered configuration, TKE values near both smooth and
rough ice cover has the opportunity to be enhanced again. For case of square configuration,
however, TKE values had been decreased toward ice cover.

5.5 Bibliography
Afzalimehr, H., Barahimi, M., & Sui, J. (2017). Non-uniform flow over cobble bed with submerged
vegetation strip. Proceedings of the Institution of Civil Engineers - Water Management,
172(2), 86–101. https://doi.org/10.1680/jwama.17.00039
Barahimi, M., & Sui, J. (2023). Effects of Submerged Vegetation Arrangement Patterns and Density
on Flow Structure. Water, 15(1), 176. https://doi.org/10.3390/w15010176
Beltaos, S. (2008). Progress in the study and management of river ice jams. 51, 2–19.
Blott, S. J., & Pye, K. (2001). GRADISTAT: A grain size distribution and statistics package for the
analysis of unconsolidated sediments. Earth Surface Processes and Landforms, 26(11),
1237–1248. https://doi.org/10.1002/esp.261
Chen, S.-C., Kuo, Y.-M., & Li, Y.-H. (2011). Flow characteristics within different configurations of
submerged flexible vegetation. Journal of Hydrology, 398(1–2), 124–134.
https://doi.org/10.1016/j.jhydrol.2010.12.018
Dayton, P. K., Robilliard, G. A., & DeVries, A. L. (1969). Anchor Ice Formation in McMurdo Sound,
Antarctica, and Its Biological Effects. Science, 163(3864), 273–274.
https://doi.org/10.1126/science.163.3864.273
Dey, S. (2014). Fluvial hydrodynamics. Springer.
Dey, S., & Nath, T. K. (2010). Turbulence Characteristics in Flows Subjected to Boundary Injection
and Suction. Journal of Engineering Mechanics, 136(7), 877–888.
https://doi.org/10.1061/(ASCE)EM.1943-7889.0000124

145

Englund, G. (1991). Effects of Disturbance on Stream Moss and Invertebrate Community Structure.
Journal of the North American Benthological Society, 10(2), 143–153.
https://doi.org/10.2307/1467574
Engström, J., Jansson, R., Nilsson, C., & Weber, C. (2011). Effects of river ice on riparian vegetation:
Ice and riparian vegetation. Freshwater Biology, 56(6), 1095–1105.
https://doi.org/10.1111/j.1365-2427.2010.02553.x
Ettema, R. (2002). Review of Alluvial-channel Responses to River Ice. Journal of Cold Regions
Engineering, 16(4), 191–217. https://doi.org/10.1061/(ASCE)0887-381X(2002)16:4(191)
Faruque, Md. A. (2009). Smooth and Rough Wall Open Channel Flow Including Effects of Seepage
and Ice Cover [Doctoral Thesis]. University of Windsor.
Finnigan, J. (2000). Turbulence in Plant Canopies. Annual Review of Fluid Mechanics, 32(1), 519–
571. https://doi.org/10.1146/annurev.fluid.32.1.519
Finnigan, J., & Shaw, R. H. (2000). A Wind-Tunnel Study of Airflow in Waving Wheat: An EOF
Analysis of the Structure of the Large-Eddy Motion. Boundary-Layer Meteorology, 96(1–2),
211–255. https://doi.org/10.1023/A:1002618621171
Ghareh Aghaji Zare, S., Moore, S. A., Rennie, C. D., Seidou, O., Ahmari, H., & Malenchak, J.
(2016). Estimation of composite hydraulic resistance in ice-covered alluvial streams:
ESTIMATION OF COMPOSITE HYDRAULIC RESISTANCE. Water Resources Research,
52(2), 1306–1327. https://doi.org/10.1002/2015WR018096
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)07339429(2002)128:1(117)
Hains, D., Zabilansky, L.J., & Weisman, R.N. (2004). An experimental study of ice effects on scour at
bridge piers. Cold Regions Engineering and Construction Conference and Expo, Edmonton,
Alberta, Canad.
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
Lau, L., & Krishnappan, B. (1985). Sediment transport under ice cover. 111(6).
Lind, L., Nilsson, C., Polvi, L. E., & Weber, C. (2014). The role of ice dynamics in shaping
vegetation in flowing waters: Ice dynamics and vegetation in flowing waters. Biological
Reviews, 89(4), 791–804. https://doi.org/10.1111/brv.12077
Lu, J., & Dai, H. (2016). Effect of submerged vegetation on solute transport in an open channel using
large eddy simulation. Advances in Water Resources, 97, 87–99.
https://doi.org/10.1016/j.advwatres.2016.09.003
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(1),
70–82. https://doi.org/10.2478/johh-2019-0029
146

Nepf, H. (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. (2012). Flow and transport in regions with aquatic vegetation. Annu Rev Fluid Mech, 44(1),
123–142. https://doi.org/10.1146/annurev-fluid-120710-101048
Nezu, I. (2005). Open-Channel Flow Turbulence and Its Research Prospect in the 21st Century.
Journal of Hydraulic Engineering, 131(4), 229–246. https://doi.org/10.1061/(ASCE)07339429(2005)131:4(229)
Prowse, T. D., & Beltaos, S. (2002). Climatic control of river-ice hydrology: A review. Hydrological
Processes, 16(4), 805–822. https://doi.org/10.1002/hyp.369
Shaw, R. H., & Schumann, U. (1992). Large-eddy simulation of turbulent flow above and within a
forest. Boundary-Layer Meteorology, 61(1–2), 47–64. https://doi.org/10.1007/BF02033994
Siniscalchi, F., Nikora, V. I., & Aberle, J. (2012). Plant patch hydrodynamics in streams: Mean flow,
turbulence, and drag forces: PLANT PATCH HYDRODYNAMICS. Water Resources
Research, 48(1). https://doi.org/10.1029/2011WR011050
Smith, T. B., & Ettema, R. (1995). Ice-cover influence on flow and bed-load transport in dune-bed
channels (Technical Report No. 374). National Science Foundation.
SonTek-IQ Series. (2017). 135.
Stickler, M., Alfredsen, K. T., Linnansaari, T., & Fjeldstad, H.-P. (2010). The influence of dynamic
ice formation on hydraulic heterogeneity in steep streams: WINTER DYNAMICS AND
STREAM HETEROGENEITY. River Research and Applications, 26(9), 1187–1197.
https://doi.org/10.1002/rra.1331
Strom, K. B., & Papanicolaou, A. N. (2007). ADV Measurements around a Cluster Microform in a
Shallow Mountain Stream. Journal of Hydraulic Engineering, 133(12), 1379–1389.
https://doi.org/10.1061/(ASCE)0733-9429(2007)133:12(1379)
Su, H.-B., Shaw, R. H., Paw, K. T., Moeng, C.-H., & Sullivan, P. P. (1998). Turbulent Statistics of
Neutrally Stratified Flow Within and Above a Sparse Forest from Large-Eddy Simulation and
Field Observations. Boundary-Layer Meteorology, 88(3), 363–397.
https://doi.org/10.1023/A:1001108411184
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/S1001-6279(10)60026-1
Tang, T. C. C., & Davar, K. S. (1985). Resistance to flow in partially-covered channels.
Virtanen, R., Muotka, T., & Saksa, M. (2001). Species richness-standing crop relationship in stream
bryophyte communities: Patterns across multiple scales: Species richness in stream bryophyte
communities. Journal of Ecology, 89(1), 14–20. https://doi.org/10.1046/j.13652745.2001.00513.x

147

Willmarth, W. W., & Lu, S. S. (1972). Structure of the Reynolds stress near the wall. Journal of Fluid
Mechanics, 55(1), 65–92. https://doi.org/10.1017/S002211207200165X
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.1943-7900.0001063
Yue, W., Meneveau, C., Parlange, M. B., Zhu, W., Van Hout, R., & Katz, J. (2007). A comparative
quadrant analysis of turbulence in a plant canopy: QUADRANT ANALYSIS PLANT
CANOPY. Water Resources Research, 43(5). https://doi.org/10.1029/2006WR005583

148

6. GENERAL CONCLUSIONS
Through 144 experiments in a large-scale flume, this study aims to gain a better
understanding of the effects of submerged vegetation morphology, density, and arrangement
on flow velocity, Turbulence Kinetic Energy (TKE), bed deformation, scouring, and Reynolds
shear stress under ice cover surface and open channel conditions. Majority of data were
collected in the wake zones behind vegetation elements, between two vegetation elements, and
in the center of a square formed by four vegetation elements. Section 6.2, 6.3, and 6.4
respectively present the conclusions derived from Chapter 3, Chapter 4, and Chapter 5. These
conclusions summarize the key findings and outcomes obtained from each chapter, providing
a concise overview of the research results.
6.1 Synthesis
Chapter 3 primarily investigates the impact of submerged vegetation density,
arrangement, and morphology on flow structure, addressing various related hypotheses. It
explores how these factors influence flow patterns and characteristics, such as velocity
distribution, turbulence, and shear stress. The chapter found the effects of dense and sparse
vegetation on flow retardation, wake zone dimensions, and the sheltering effect. It also
examines the role of vegetation bending and staggered arrangement in intensifying inflection
points and flow-vegetation interaction.
Chapter 4 shifts the focus to sediment transport, scouring, and deposition of bed materials
in scenarios where an ice cover is present on top of the water and vegetation exists on the bed,
addressing the sediment related hypotheses. It investigates the combined influence of ice cover,
vegetation, and bed morphology on the movement of sediment, including the formation of
scour holes and the deposition of sediment particles.
149

In Chapter 5, the main emphasis lies on studying the interaction between ice cover,
different roughness elements on the water surface, and the presence of vegetation on the bed
with flow structure. The chapter explores how the presence of ice cover and vegetation affects
flow characteristics, including velocity profiles, turbulence generation, and Reynolds Shear
Stress (RSS). The chapter also investigates quadrant analysis, and the role of ice and vegetation
in altering turbulence.
Collected data for different flow conditions have been attached in appendix.
6.2 Conclusions of chapter 3
1) This study found that the vegetation density in the bed has significant effects on flow
velocity. The results indicate that when vegetation is dense (with λ=0.09 and λ=0.17), the
velocity between two vegetation elements is lower compared to the velocity at the center
of the square formed by four vegetation elements. The reduced velocity between two
vegetation elements can be attributed to the obstructive nature of closely spaced
vegetation, which hinders the flow. In contrast, the velocity at the center of the square is
higher due to the narrower wake zone formed behind each vegetation element. The highdensity vegetation reduces the local flow cross-sectional area, leading to a quicker
dissipation of turbulence and flow disturbance within a shorter distance. In contrast, when
considering sparse vegetation with lower densities (λ=0.04 and λ=0.07), streamwise
velocity between two vegetation elements was found to be higher than the velocity at the
center of the square formed by four vegetation elements. It suggests that when the canopy
density was low, the wake zone behind the vegetation elements was longer and wider. The
study revealed an inverse relationship between canopy density and the dimensions of the
wake zone.

150

2) As the spacing distance between deflected vegetation elements decreases (indicating an
increase in canopy density), the study found that the streamwise velocity experiences
significant retardation at a flow depth of z/H≅0.3, slightly below the inflection point. With
a sparser vegetation canopy, the inflectional region tends to diminish or disappear. This is
because the shear length scale associated with the velocity field increases as the canopy
becomes sparser. Furthermore, the study observed that the inflection point was not
observed in non-bending vegetation. This suggests that the bending behavior of the
vegetation elements plays a role in the formation of the inflection point. Additionally, the
arrangement of vegetation elements also influenced the velocity profiles. Specifically,
velocity profiles showed more pronounced inflection points in the case of a staggered
arrangement of vegetation elements compared to a square arrangement.
3) The study indicates that dense deflected vegetation, characterized by vegetation densities
(λ) equal to or greater than 0.1, reduces the velocity near the bed more effectively
compared to non-bending vegetation and sparse densities. By reducing the velocity near
the bed, the dense vegetation acts as a protective barrier, mitigating erosion and scouring
processes. This suggests that dense deflected vegetation provides better protection for
stream beds that are susceptible to sediment movement and erosion.
4) The study reveals that behind submerged vegetation, the Turbulence Kinetic Energy
(TKE) starts at zero at the bed (z/H=0). However, between two vegetation elements and
at the center of the square formed by four vegetation elements, the TKE has a value greater
than zero (TKE>0). This phenomenon is a well-known effect of submerged vegetation on
turbulence and is commonly referred to as the sheltering or dampening effect. The
sheltering effect was found to be more pronounced in denser vegetation, where the shorter

151

distance between vegetation elements enhances the effect. The TKE distribution in the
wake of the vegetation demonstrates that the maximum Root Mean Square (RMS) values
for the turbulent velocities (u', v', and w') occur either at the sheath section of the
vegetation (at a depth of z/H=0.1) or above the top of the vegetation (at depths z/H≥0.4).
In the sheath section, where the frontal projected area is relatively small, the flow can
mostly pass through the sheath section. This results in enhanced turbulence at the scale of
individual stems within the sheath section. In the region slightly above the channel bed
and extending towards the vegetation top, the presence of Von Karman Street vortexes
contributes to an overall enhancement of TKE compared to unvegetated channels. These
vortexes are formed due to the interaction between the flow and the vegetation elements
and contribute to the increased turbulence levels in this region.
5) In the wake zone behind deflected vegetation, the study observed that the maximum value
of Reynolds Shear Stress (RSS) occurred at an elevation slightly higher above the top of
the vegetation. This indicates the presence of Kelvin-Helmholtz (KH) instability at the top
of the deflected vegetation and slightly above it (at depths z/H≥0.4). Above the top of the
vegetation, the RSS continues to increase. The shift of the maximum RSS above the top
of the vegetation is attributed to the presence of branches, which alter the peak of RSS and
cause it to occur at a higher location above the top of the vegetation. This suggests that the
branching structure of the vegetation contributes to the modified distribution of RSS in
the wake zone. Within the range of vegetation densities studied (0.04 < λ ≈<0.23), it was
observed that as the vegetation density increases, both negative and positive values of RSS
throughout the flow depth also increase. However, for dense vegetation (λ>0.1), an
interesting trend was observed where the influence of bed shear stress decreases as the

152

vegetation density increases. This implies that dense vegetation acts as an additional layer,
effectively shielding the riverbed roughness from its effects. Moreover, when the
vegetation elements are arranged in a staggered layout, the RSS distribution is similar to
that observed in the wake zone of vegetation with a squared layout. However, the RSS
values are intensified in the case of staggered layout, indicating a stronger influence of the
flow-vegetation interaction.
6) In the presence of non-bending vegetation in the channel bed, the velocity distribution
exhibits distinct patterns depending on the flow depth. For a flow depth of 20 cm, a high
velocity gradient is observed from the depth of z/H=0 to z/H=0.1, where the velocity
reaches its peak. Above the depth of z/H=0.1, there is a noticeable decreasing trend in
velocity towards the water surface. This indicates that the highest velocity occurs at a
shallow depth, near the bed, and decreases as we move towards the water surface.
However, for a deeper flow with a depth of 30 cm, the peak velocity occurs at a higher
location within the flow depth. Specifically, the peak velocity is observed at a depth greater
than z/H=0.1. Above this depth, there is a relatively constant velocity value that extends
towards the water surface. This suggests that in deeper flows, the peak velocity is found
at a greater depth, and there is a more uniform velocity profile towards the water surface.
6.3 Conclusions of chapter 4
1) The experiments conducted in this study have allowed for the development of equations
that can predict the maximum relative depth of scour holes around vegetation elements.
These equations take into account various independent variables to accurately estimate the
depth of scour. The results obtained from the experiments indicate that the most significant
variable influencing the depth of scour holes under ice-covered flow conditions is the ratio
of the ice cover roughness to the bed roughness (ni/nb). In such conditions, the presence of
153

ice cover greatly affects the flow dynamics and interaction with the vegetation, making the
ratio of ice cover roughness to bed roughness a crucial factor in determining the depth of
scour. However, when considering open channel flow conditions, the most important
variable influencing the depth of scour holes is the flow Froude number.
2) In the study, three different methods were employed to calculate the Manning's coefficient
of an ice cover. Two of these methods, referred to as methods two and three, produced
results that were reasonably consistent with those reported by other researchers. These two
methods rely on the law of the wall and have proven to be reliable even under ice-covered
flow conditions, as evidenced by laboratory data. However, the first method used in the
study yielded results that were significantly different from those obtained through the
other two methods. The discrepancy observed in this case can be attributed to the presence
of vegetation in the bed. Method one involves utilizing the average velocity to calculate
the roughness height, which is a crucial parameter in determining the Manning's
coefficient. However, under an ice-covered flow condition, the presence of vegetation in
the bed can cause a substantial alteration in the average velocity.
3) The grain size of the deposition dunes downstream of vegetation elements (D50D) consists
of finer sediment particles than that of the initial sand bed (D50). On the other hand, the
grain size of armor layer formed inside scour holes (D50A) is coarser than that of the initial
sand bed (D50D). As the vegetation density increases, the dimension of the scour hole
including length, width and depth decreases. With the increase in the vegetation density,
the median grain size of the armour layer (D50A) decreases correspondingly. This result is
valid for the deposition dune formed downstream of each vegetation element. When
vegetation elements are arranged in a staggered configuration, the median grain size of the

154

armour layer (D50A) is finer than that arranged in a squared configuration. These results
have been observed for the finer sand beds of D50=50 mm and D50=60 mm. However, for
the coarse sand bed of D50=0.98 mm, the scour holes around vegetation elements are too
shallow to be observed, since the weight of most particles exceed the uplifting force. Also,
for the coarse sand bed of D50=0.98 mm, no deposition dunes have been developed around
vegetation elements.
4) In the conducted experiments, it was consistently observed that the maximum scour depths
occurred at the upstream, front face of the vegetation elements. Comparing ice-covered
flow conditions to open flow conditions, it was found that the scour holes were deeper and
longer under ice-covered flow. Similarly, the maximum deposition height was notably
greater under ice-covered flow compared to open flow. Furthermore, the presence of rough
ice cover resulted in greater depths of scour holes compared to smooth ice cover
conditions. The roughness of the ice cover had a significant influence on the extent of
scouring. When considering the effect of vegetation in the bed, it was found that both
vegetation density and arrangement patterns had a significant impact on the depth of scour
holes. Denser vegetation in the bed led to the development of higher deposition dunes
downstream of the vegetation elements. As vegetation density increased, the area of
deposited sediment downstream of the vegetation elements also increased. However,
contrary to expectations, the length and depth of scour holes decreased as vegetation
density increased.
5) The laboratory experiments and derived formulae provided insights into the factors
influencing the maximum depth of scour holes. The results indicate that several variables
have a significant impact on the depth of scour holes. Firstly, the flow Froude number (Fr)

155

was found to be positively correlated with the maximum depth of scour holes. As the flow
Froude number increases, the energy of the flow increases, leading to more significant
erosion and deeper scour holes. Secondly, the ratio of the cover roughness coefficient to
that of the channel bed (ni/nb) was identified as a factor influencing the maximum depth
of scour holes. An increase in this ratio results in a rougher cover, which leads to increased
turbulence and enhanced scouring, resulting in deeper scour holes. Thirdly, vegetation
density (λ) was found to have a positive relationship with the maximum depth of scour
holes. As vegetation density increases, the presence of vegetation impedes the flow and
increases flow resistance, causing more significant scouring and deeper holes. However,
this results is true for sparse vegetation. In dense vegetation, as vegetation density
increases, the scour around vegetation decreases. On the other hand, the median grain size
(D50/H) was found to have a negative correlation with the maximum depth of scour holes.
As the median grain size increases relative to the flow depth, the sediment particles
become coarser and more resistant to erosion, resulting in shallower scour holes. Lastly,
the submergence ratio of vegetation (H/h) also showed a negative relationship with the
maximum depth of scour holes. A higher submergence ratio indicates that the vegetation
is more fully submerged in the flow, reducing its impact on flow dynamics and decreasing
the scouring effect.
6.4 Conclusions of chapter 5
1) In the presence of vegetation in the bed under ice-covered flow conditions, the velocity
profiles exhibit a distinct pattern characterized by two peak values. The first peak velocity
is observed at the sheath part of the vegetation patch. This region corresponds to the
narrowest frontal width of each vegetation element, allowing for a larger net cross section
and accommodating higher flow rates. The second peak velocity is located in the region
156

between the ice cover and the top of the vegetation canopy. Regardless of the configuration
of vegetation elements and the grain size of the bed material, the peak streamwise velocity
at the sheath section is consistently lower than the peak velocity observed above the canopy
top. This trend persists across different vegetation arrangements and bed material
characteristics. The rate of decrease in velocity between the two peaks is more pronounced
under rough ice cover conditions compared to smooth ice cover conditions. The presence
of a rough ice cover on the water surface significantly retards the streamwise velocity
within the zone between z/H=0.2 (where z is the elevation above the bed and H is the flow
depth) and the ice cover. This deceleration effect, resulting from both smooth and rough
ice covers, leads to a reduction in the bulk velocity compared to that observed under open
flow conditions.
2) The RSS values are negative in the middle layer of the vegetation patch, showing an
upward vertical transfer of momentum with negative velocity gradients. In this region,
because the area of the frontal projected vegetation is the largest, wake is produced behind
each vegetation element that attenuates the streamwise velocity and causes a negative
region of the RSS. Without the presence of vegetation in open surface water, the RSS is
zero and negative near water surface. However, with the presence of vegetation in the bed
and ice cover on water surface, the resistance caused by ice cover and extra turbulence
created by vegetation leads to the positive RSS value near ice cover.
3) The quadrant analysis conducted revealed interesting findings under ice-covered flow
conditions. The results showed that the contributions of inward and outward events in the
flow increased, and in many cases, surpassed the contributions of sweep and ejection
events. Inward and outward events refer to the upward components of shear stress, and

157

they play a significant role in the formation of bed scour around vegetation stems. It was
observed that these events were primarily responsible for creating scouring effects.
Interestingly, the inward event appeared most frequently in the scouring region around
vegetation stems. Moreover, it was noted that the contribution of the inward event from
the bed to the top of the vegetation was more pronounced under rough ice cover conditions
compared to smooth ice cover conditions. This finding further supports the observation of
larger and deeper scour holes around vegetation stems under rough ice-covered flow
conditions.
4) In general, the profiles of Turbulence Kinetic Energy (TKE) behind vegetation elements
exhibit a distinct pattern under both smooth and rough ice-covered flow conditions. These
profiles typically display two peaks: one at the sheath section and the other above the
bending height of the vegetation. Under smooth and rough ice-covered flow conditions,
there is a decreasing trend in TKE along the vertical direction. This indicates a reduction
in turbulence intensity with increasing distance from the bed. The peak TKE values
observed at the sheath section and above the vegetation bending height reflect areas of
enhanced turbulence generation and mixing. However, in open channel flow without ice
cover, the behavior of TKE near the water surface differs. In this case, the TKE profile
either remains relatively constant or exhibits a slight decrease in the vicinity of the water
surface. This suggests that the turbulence intensity is relatively maintained or experiences
a mild reduction near the water surface in open channel flow conditions.
5) In the presence of vegetation in the bed arranged in a staggered configuration, lower values
of Turbulence Kinetic Energy (TKE) have been observed throughout the flow depth. This
indicates a decrease in turbulence intensity in the presence of denser vegetation (λ=0.17)

158

compared to a square configuration with lower vegetation density (λ=0.09). The staggered
configuration results in a higher overall vegetation density. Moreover, a noticeable trend
of increasing TKE values has been observed towards the ice cover. This suggests that in
the case of the staggered configuration, the TKE values near both smooth and rough ice
cover have the potential to be enhanced again. On the other hand, for the square
configuration, the TKE values have shown a decrease towards the ice cover.
6.5 Significance of Study
This section will wrap up the contribution of the conclusions discussed in the above
sections and its application.
There is an inverse relationship between canopy density and the dimensions of the wake
zone that can have practical applications in river management. Rivers with high flow velocities
can erode riverbanks and cause damage to nearby infrastructure. By strategically planting
dense vegetation along the riverbanks, vegetation can act as a barrier, reducing the flow
velocity and consequently the erosive potential. Riparian zones, the areas alongside rivers and
streams, are critical habitats for various vegetation and animal species. By increasing
vegetation density through restoration efforts, the dimensions of the wake zone can be reduced.
This can create more favorable microclimates and improve conditions for aquatic organisms
by decreasing the impact of turbulent flow. Additionally, the reduced wake zone dimensions
behind the dense vegetation can limit the resuspension of sediments, leading to clearer and
cleaner water.
River managers can consider the results related to the deflected and non-bending
vegetation when selecting vegetation species for riverbank stabilization or flow control.
Choosing vegetation species that exhibit bending behavior can potentially enhance the

159

formation of inflection points, which can be beneficial for managing flow patterns, reducing
velocities, and promoting sediment deposition.
The arrangement of vegetation elements influences velocity profiles, with more
pronounced inflection points observed in a staggered arrangement compared to a square
arrangement. River managers can utilize this information to design and plan vegetation
arrangements in river management projects. For example, a staggered arrangement may be
preferred if the objective is to create more pronounced inflection points and control flow
velocities.
Another conclusion says that as the vegetation density increases, the dimension of the
scour hole decreases. By increasing vegetation density, such as through the planting of shrubs,
or grasses, the dimensions of scour holes can be minimized. This can help protect riverbanks,
infrastructure, and adjacent land from erosion and destabilization caused by strong currents or
flood events. As the dimensions of the scour hole decrease, sheltered areas with reduced flow
velocities are created, providing refuge and spawning grounds for fish and other aquatic
species.
River managers can apply the results that found with the increase in the vegetation
density, the median grain size of the armour layer (D50A) decreases correspondingly, to control
sediment transport and deposition. Vegetation acts as a natural barrier that can trap sediments
and stabilize the riverbed. The reduced median grain size of the armour layer can enhance
sediment retention, thereby reducing downstream sediment loads and potential impacts on
water quality and aquatic habitats. The decreased median grain size of the armour layer can
also contribute to the creation of more suitable substrate for aquatic habitat, further enhancing
biodiversity and ecosystem health.
160

Other results indicated that the presence of rough ice cover resulted in greater depths of
scour holes around vegetation compared to smooth ice cover conditions. River managers can
take this into account when designing and implementing restoration projects. Proper
engineering and protective measures can be incorporated to mitigate the potential damage
caused by the increased scouring associated with rough ice covers.
6.6 Limitation of the current study
The experimental studies conducted in this research were accompanied by certain limitations.
Despite our efforts to minimize these limitations by implementing various measures, some of
them were unavoidable.
One notable limitation was related to the Acoustic Doppler Velocimeter (ADV) used, which
was unable to collect data from a depth of 10 cm below its transmitter. Consequently, the data
pertaining to the top 10 cm below the water surface was not captured. Another limitation can
be attributed to the discharge available for the experiment, which was limited by the power of
the water pump. The pump, along with the three valves, could provide a maximum flow rate
of 110 liters/second. Additionally, a further limitation was encountered due to the placement
of the second sand box. It was situated at a distance from the entrance, and due to the slope of
the flume, the water depth in the second sand box was consistently 3 cm higher than that in the
first sand box.
6.7 Future directions
Based on the conclusions drawn from the thesis, here are some potential areas for future work:
1) Study of vegetation dynamics: The thesis primarily examined the effects of stationary
vegetation elements. Future research can investigate the dynamics of real submerged

161

vegetation, including the response of vegetation to flow conditions (monami), the growth and
development of vegetation over time, and the interactions between vegetation and sediment
transport.
2) Numerical modeling: The experimental findings can be used to validate and improve
numerical models that simulate flow dynamics and sediment transport in the presence of
submerged vegetation. This can help in developing more accurate predictive models that
consider the effects of vegetation on flow velocity, turbulence, and scouring.
3) Field measurements and validation: While the thesis focused experiments in a large-scale
flume, conducting field measurements in natural channels with submerged vegetation can
provide valuable insights into real-world scenarios. Field observations can help validate the
findings from the laboratory experiments and provide a better understanding of the complex
interactions between vegetation and flow dynamics in natural environments.
4) Climate change implications: Investigating the influence of climate change on the
interaction between submerged vegetation and flow dynamics can be a significant area of
future research. Changes in sediment size, water depth, and ice cover dynamics can impact the
growth and distribution of submerged vegetation, which in turn can affect flow patterns and
sediment transport processes.
5) Interaction with other flow structures: Further investigation can be conducted to examine
the interaction between submerged vegetation and other flow structures, such as bedforms,
instream structures, or hydraulic infrastructure. Understanding how vegetation interacts with
these structures can provide insights into their combined effects on flow patterns and sediment
transport.

162

6) Experimental studies under different flow conditions: The thesis mainly considered open
channel and ice-covered flow conditions. Conducting experiments under different flow
regimes, such as unsteady flow, wavy flow or flood events, can provide a more comprehensive
understanding of how submerged vegetation interacts with varying flow conditions and
sediment transport dynamics.

163

APPENDIX
Table I.1: Experimental data collected for D50=0.98 mm

Surface
condition

Open

smooth

rough

water
depth
20.5
21
21
20.5
20
19.5
20
20.5
29.5
30
29.5
31
30
30
29
28
21.5
22
22
21.5
21
20.5
21
21.5
30.5
31
30.5
32
31
31
30
29
22
21
21.5
22
21.5
22
20
19.5

arrangement

morphology

Fr

D50/H Sr=H/h

square
square
square
square
staggered
staggered
staggered
staggered
square
square
square
square
staggered
staggered
staggered
staggered
square
square
square
square
staggered
staggered
staggered
staggered
square
square
square
square
staggered
staggered
staggered
staggered
square
square
square
square
staggered
staggered
staggered
staggered

non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected

0.108
0.100
0.135
0.063
0.060
0.061
0.093
0.083
0.056
0.056
0.057
0.053
0.054
0.057
0.049
0.067
0.123
0.120
0.119
0.114
0.135
0.124
0.122
0.083
0.054
0.062
0.059
0.052
0.051
0.067
0.061
0.059
0.138
0.130
0.121
0.093
0.125
0.115
0.115
0.114

0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.005
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.004
0.005
0.004
0.004
0.005
0.005
0.005
0.005
0.005
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.004
0.005
0.005
0.004
0.005
0.004
0.005
0.005

164

1.620
2.625
1.659
2.563
1.580
2.438
1.580
2.563
1.554
2.500
1.554
2.583
1.580
2.500
1.527
2.333
1.699
2.750
1.738
2.688
1.659
2.563
1.659
2.688
1.606
2.583
1.606
2.667
1.633
2.583
1.580
2.417
1.738
2.625
1.699
2.750
1.699
2.750
1.580
2.438

density
(λ)
0.120
0.090
0.050
0.030
0.230
0.170
0.100
0.070
0.120
0.090
0.050
0.030
0.230
0.170
0.100
0.070
0.120
0.090
0.050
0.040
0.230
0.170
0.100
0.070
0.120
0.090
0.050
0.040
0.230
0.170
0.100
0.070
0.120
0.090
0.050
0.040
0.230
0.170
0.100
0.070

ni/nb

0.898
0.898
0.898
0.898
0.898
0.898
0.898
0.898
0.898
0.898
0.898
0.898
0.898
0.898
0.898
0.898
1.943
1.943
1.943
1.943
1.943
1.943
1.943
1.943

Cont.
water
depth
30.5
30.5
31
29.5
29.5
31
30
30

arrangement

morphology

Fr

D50/H Sr=H/h

square
square
square
square
staggered
staggered
staggered
staggered

non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected

0.058
0.075
0.061
0.060
0.070
0.071
0.065
0.066

0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003

165

1.606
2.542
1.633
2.458
1.554
2.583
1.580
2.500

density
(λ)
0.120
0.090
0.050
0.040
0.230
0.170
0.100
0.070

ni/nb
1.943
1.943
1.943
1.943
1.943
1.943
1.943
1.943

Table I.2: Experimental data collected for D50=0.60 mm

Surface
condition

Open

smooth

rough

water
depth
23
23
23.5
22
22
21.5
23
22
32
33.5
33.5
31
32
32.5
31
32
24
24
24.5
23
23
22.5
24
23
33
34.5
34.5
32
33
33.5
32
33
23.5
24
23
23.5
22
23.5
24
23.5

arrangement

morphology

Fr

square
square
square
square
staggered
staggered
staggered
staggered
square
square
square
square
staggered
staggered
staggered
staggered
square
square
square
square
staggered
staggered
staggered
staggered
square
square
square
square
staggered
staggered
staggered
staggered
square
square
square
square
staggered
staggered
staggered
staggered

non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected

0.085
0.086
0.079
0.073
0.093
0.067
0.072
0.088
0.045
0.062
0.049
0.053
0.045
0.053
0.052
0.052
0.120
0.112
0.101
0.084
0.081
0.080
0.092
0.081
0.053
0.073
0.052
0.053
0.053
0.047
0.048
0.061
0.118
0.083
0.103
0.100
0.108
0.114
0.107
0.099

166

D50/
H
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.003
0.003
0.002
0.003
0.003
0.003
0.003
0.003
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003

Sr=H/
h
1.580
2.500
1.614
2.391
1.511
2.337
1.580
2.391
1.532
2.538
1.604
2.348
1.532
2.462
1.484
2.424
1.649
2.609
1.683
2.500
1.580
2.446
1.649
2.500
1.580
2.614
1.652
2.424
1.580
2.538
1.532
2.500
1.614
2.609
1.580
2.554
1.511
2.554
1.649
2.554

density
(λ)
0.120
0.090
0.050
0.030
0.230
0.170
0.100
0.070
0.120
0.090
0.050
0.030
0.230
0.170
0.100
0.070
0.120
0.090
0.050
0.040
0.230
0.170
0.100
0.070
0.120
0.090
0.050
0.040
0.230
0.170
0.100
0.070
0.120
0.090
0.050
0.040
0.230
0.170
0.100
0.070

ni/nb

2.376
2.376
2.376
2.376
2.376
2.376
2.376
2.376
2.376
2.376
2.376
2.376
2.376
2.376
2.376
2.376
2.867
2.867
2.867
2.867
2.867
2.867
2.867
2.867

Cont.

rough

water
depth
34
35
34
33
33.5
33.5
32.5
33

arrangement

morphology

Fr

square
square
square
square
staggered
staggered
staggered
staggered

non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected

0.060
0.066
0.063
0.055
0.059
0.049
0.054
0.063

167

D50/
H
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002

Sr=H/
h
1.628
2.652
1.628
2.500
1.604
2.538
1.556
2.500

density
(λ)
0.120
0.090
0.050
0.040
0.230
0.170
0.100
0.070

ni/nb
2.867
2.867
2.867
2.867
2.867
2.867
2.867
2.867

Table I.3: Experimental data collected for D50=0.50 mm

Surface
condition

Open

smooth

rough

water
depth
19
18.5
18
20
19.5
20
19
19
28.5
29
29
30
29.5
29.5
30
29
19.5
20
20
21
21
22
21
20
29.5
29.5
29.5
30
31
31
30
31
20
19.5
19
21
20.5
21

arrangement

morphology

Fr

D50/H

Sr=H/h

square
square
square
square
staggered
staggered
staggered
staggered
square
square
square
square
staggered
staggered
staggered
staggered
square
square
square
square
staggered
staggered
staggered
staggered
square
square
square
square
staggered
staggered
staggered
staggered
square
square
square
square
staggered
staggered

non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected

0.120
0.083
0.098
0.084
0.078
0.067
0.072
0.090
0.067
0.057
0.067
0.064
0.063
0.060
0.060
0.059
0.123
0.110
0.115
0.101
0.140
0.074
0.111
0.073
0.059
0.069
0.067
0.066
0.075
0.064
0.069
0.062
0.167
0.096
0.122
0.104
0.114
0.093

0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.003
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.003
0.003
0.003
0.002
0.002
0.002
0.002
0.003
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.003
0.003
0.003
0.002
0.002
0.002

1.501
2.313
1.422
2.500
1.541
2.500
1.501
2.375
1.501
2.417
1.527
2.500
1.554
2.458
1.580
2.417
1.541
2.500
1.580
2.625
1.659
2.750
1.659
2.500
1.554
2.458
1.554
2.500
1.633
2.583
1.580
2.583
1.580
2.438
1.501
2.625
1.620
2.625

168

density
(λ)
0.120
0.090
0.050
0.030
0.230
0.170
0.100
0.070
0.120
0.090
0.050
0.030
0.230
0.170
0.100
0.070
0.120
0.090
0.050
0.040
0.230
0.170
0.100
0.070
0.120
0.090
0.050
0.040
0.230
0.170
0.100
0.070
0.120
0.090
0.050
0.040
0.230
0.170

ni/nb

2.718
2.718
2.718
2.718
2.718
2.718
2.718
2.718
2.718
2.718
2.718
2.718
2.718
2.718
2.718
2.718
2.891
2.891
2.891
2.891
2.891
2.891

Cont.

20
20
29.5
30
30
31
30.5
30.5
31
30

staggered
staggered
square
square
square
square
staggered
staggered
staggered
staggered

non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected
non-bending
deflected

169

0.101
0.092
0.062
0.088
0.087
0.076
0.069
0.070
0.076
0.075

0.003
0.003
0.002
0.002
0.002
0.002
0.002
0.002
0.002
0.002

1.580
2.500
1.554
2.500
1.580
2.583
1.606
2.542
1.633
2.500

0.100
0.070
0.120
0.090
0.050
0.040
0.230
0.170
0.100
0.070

2.891
2.891
2.891
2.891
2.891
2.891
2.891
2.891
2.891
2.891