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. 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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 0.10). 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 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. 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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. 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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. 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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