Bed Shear Velocity Research Articles

Three-dimensional modeling of hydro-morphodynamic characteristics of mining affected alluvial channel using TELEMAC and GAIA

In this numerical study, TELEMAC-3D and GAIA solvers were coupled to examine the three-dimensional (3D) flow and morphological changes in an alluvial channel due to sand mining. The 3D modeling approach enables a comprehensive analysis of the interactions between bed shear stress, velocity field, secondary flows, and turbulent kinetic energy that affect sediment transport processes near the mining pit. First, the numerical model was applied to two previous experimental studies on straight channels with mining and validated with their published data. Thereafter, model applications are demonstrated to a 180° curved channel with a mining pit at three different locations. The results indicate that the morphological changes in curved channels with a mining pit were relatively more asymmetrical in contrast to straight channels. The most severe bed degradation of 76.8% was observed at the outer bank downstream of the pit located at the end of 180° bend. The analysis of bed shear stress in the curved channel revealed higher values at the outer bank and lower values around the inner bank downstream of the pit location. Additionally, the presence of the mining pit had a significant impact on the structure and location of the secondary flow recirculation cell in the curved channel. The results indicate that turbulent kinetic energy increases significantly in the vicinity of the mining pit in both straight and curved channels. This increased turbulence due to bed topography may account for the enhanced secondary flow and sediment movement observed in the pit region.

Wave dynamics and sediment transport in Great Salt Lake

Great Salt Lake is a natural laboratory to test and refine ideas about the relationship between sediment transport by waves and the characteristics of shoreline carbonate sediments, in particular ooid sands and microbialite mounds. In this chapter, we present a year-long series of wave data collected from July 2021 through June 2022 and use these wave data to assess the performance of a US Army Corps of Engineers wave model previously used to estimate bed shear velocity and intermittency of sediment transport in Great Salt Lake (Smith and others, 2020). We use this model-data comparison to identify the strengths and weaknesses of the existing model for both geological and ecological applications, and areas of improvement for future model development. We also use shallow sediment cores and Unmanned Aerial Vehicle (UAV)-based orthomosaics collected from shorelines near each buoy to assess how the wave climate along two parts of the lake shore influences the stratigraphic record and the surface morphology of the lakebed.

Evaluation of collar efficiency to prevent scouring around cylindrical bridge piers under live bed condition

The present study was carried out to experimentally investigate the effect of single and double collar on development of local scouring around cylindrical bridge piers under live-bed condition. The single collar with diameter of 3 times the pier diameter placed on the streambed level and double collars one on the streambed level and one on a lower elevation were used. Tests were conducted with different flow intensities equal to 1.4, 2.0, 2.4, 2.8 and 4.0 where flow intensity is defined as the ratio of bed shear velocity to shear velocity of bed material at threshold of motion. One experiment was also carried out with flow intensity of 4.7 at which dunes were washed out and transition flow regime prevailed. The duration of the experiments was long enough to assure complete dune formations and multiple traverses of dunes through the pier location. Results showed that the scour depth fluctuated between a maximum and a minimum value due to the bed features migration. A graph was developed to show the efficiency of single and double collars at different positions and under different flow intensities. With two collars in place, the mean and maximum scour depths at the highest flow intensity, reduced by about 53% and 35% respectively. Efficiency of collar was better in lower flow intensities. Finally, based on the present results, a design table is presented for the elevation of the lower collar based on the flow intensity.

Effects of Flow Unsteadiness on the Transport of Bimodal Bed Material

The grain size distribution of the transported bed load was experimentally investigated under unsteady flow conditions with bimodal mixture of sand and gravel in a laboratory flume. Five various triangular hydrographs were generated. A clockwise behavior for the total bed load versus shear velocity was observed meaning that the bed load during rising limb was higher than that of falling limb. It was found that the percent finer at the plateau of bimodal sediment size distribution curve had higher values during the initial and final phases compared to those obtained during the peak time. At all plateaus, the percent finer values related to the hydrograph peak discharge were in the same order of magnitude with that of the bed material. The sand content of the transported bed material initially decreased, then maintained a constant value during a certain time interval and finally returned to its original value. The sand percent of the bed load decreased in the falling limb showing a counterclockwise loop and the duration of the hydrograph did not affect the results considerably. The greater the peak flow rate of the hydrograph, the greater was the hysteresis. The bimodality index was calculated for all transported sediment samples and it was revealed that its initial and final values were less than that of the bed material but it was approximately the same elsewhere. The 5% finer sediment amount was nearly equal during rising and falling limbs. It was revealed that D50 value of the bed load decreased in the rising limb showing a clockwise loop. The hysteresis was not considerably changed according to the hydrograph characteristics. The clockwise type hysteresis was also observed for the size group of D95. The lag increased as the peak flow rate increased. A strong relation was found between the dimensionless total bed load Wt* and the total work index Wk as well as Wk and the ratio WR/WF. The correlations between the dimensionless total bed load and the unsteadiness parameters P, and Pmod were very weak, whereas a high value of determination coefficient was obtained with the unsteadiness parameter Pgt, implying an appreciable interdependence.

The importance of grain‐related shear velocity in predicting multi‐monthly dune growth

AbstractThis study assesses the accuracy of the aeolian transport model proposed by van Rijn and Strypsteen in 2020 in predicting sediment transport rates for dune growth, with a focus on the importance of grain‐related shear velocity. A 9‐month dataset of local and regional wind characteristics and dune growth from a new artificial dune with planted marram grass in an environment with minor supply limitations was analysed. The study site is located in Oosteroever, Belgium. The results revealed that utilizing local measured overall shear velocities resulted in significant overprediction of dune volume changes. Incorporating sub‐models for grain‐related bed roughness and shear velocity improved the predictions of dune growth drastically with high statistical results (r2 = 0.98 and RMSE = 0.64 m3/m). The primary driver contributing to dune growth at the study site was due to oblique onshore moderate winds of 10 m/s, as revealed from a frequency‐magnitude analysis. The model could be used with either local wind measurements or regional data transformed to local beach conditions. The study highlights the importance of considering grain‐related shear velocity in future studies to improve the prediction of sand transport rates and enhance our understanding of dune evolution.

The response of high density turbidity currents and their deposits to an abrupt channel termination at a slope break: Implications for channel–lobe transition zones

ABSTRACTThe transition between the slope and basin floor is typically marked by a slope break, in some cases causing channels to terminate and turbidity currents to undergo a loss of confinement. It is thus essential to understand how these slope breaks and losses of confinement influence the hydrodynamic evolution of turbidity currents and impact their depositional variability within natural scale channel mouth settings. Flume experiments, utilizing Shields scaling, are conducted to study how channel slope angle (3°, 6° and 9°) and initial suspended sediment concentrations (12 to 18% by volume) impact the hydrodynamics and deposit geometries of high density turbidity currents, subject to a simultaneous break of slope and loss of confinement. Measured velocity and concentration profiles indicate that turbidity currents are supercritical, with mean velocities between 0.80 m s−1 and 1.04 m s−1 and depth‐averaged basal concentrations between 9.2% and 23.9%, yielding bed shear velocities between 0.050 m s−1 and 0.064 m s−1. Upon encountering the slope break and loss of confinement, turbidity currents exhibit increases to their densimetric Froude numbers and shear velocities. This is due primarily to two factors: firstly, turbidity currents continue to accelerate during an initial period of velocity lag as their residual momentum gradually dissipates; and, secondly, expansion via flow relaxation collapses their structure towards the bed. The corresponding depositional geometries of these processes reveal that turbidity currents produce elongate channel–lobe transition zones that disconnect channel and basin deposits. The length to width ratios of channel–lobe transition zones decrease as the initial sediment concentrations of turbidity currents increase, while a reduction in the channel slope break angle reduces their length to width ratios. Corresponding, lobe elements are observed to increase in length, width and thickness with increasing initial sediment concentrations, while a reduction in channel slope break angle reduces their dimensions due to enhanced slope deposition.

Development of a Quantitative Approach for Morphodynamic Assessment of Extreme Flood Event in Lokoja

Abstract – This study developed a quantitative approach for the morphodynamic assessment of River Niger at Lokoja. The study involves the collection of twenty-one years daily discharge and water level at the gauging station. The data were collated and outliers were removed. The missing data were fitted using the Least Square Method. The flood generating processes were investigated by computing the bankfull discharge of selected reach as well as collecting river bed samples at six (6) different locations along the river reach. Based on these, the specific gravity and mobile D50 and D90 of the bed materials were obtained. The preliminary investigation of the river morphodynamics was studied by computing the sediment transport parameters such as Shield parameter, bed shear velocity, sediment fall velocity amongst others. These parameters are significantly important due the high flow rate associated with the river. Based on criteria by two well-known sediment transport capacity formula, the river reach is characterized as sandy-bed River in line with Eugelund and Hansen’s Formula (E-H-F). The entire flow generation parameters and mobile river bed materials failed the Meyer and Peter- Muller criteria. Hence, the sediment transport capacity of the river was computed using (E-H-F). The results show that understanding the morphodynamics of the rivers play a significant role in the understanding of flooding.

A Moment-Based Depth-Averaged K-ε Model for Predicting the True Turbulence Intensity over Bedforms

Turbulence models are critical for depth-averaged flow models in at least two ways: (i) as closures for momentum equations and (ii) as indicators of the spatial variability in the turbulence intensity field, which is crucial for sediment transport and bedform evolutions. This paper introduces a novel moment-based depth-averaged k-ε turbulence (MDAKE) model that could be considered as a revised version for the standard k-ε Rastogi–Rodi (SDAKE) model and can be used to estimate the true values for the depth-averaged turbulence kinetic energy in more complex and varied flow conditions with accelerating–decelerating flow fields. The study in hand shows that the SDAKE model tends to overestimate the true depth-averaged turbulent kinetic energy (k¯u) by 50 to 130% in the benchmark case of uniform flow over a flatbed. Further, the SDAKE model assumes that the bed shear velocity is an appropriate scale for the generation terms of both turbulent kinetic energy and dissipation. When bed topographic features vary, a shear flow zone is formed and the assumption is invalid. Since most of the turbulence is generated by shear flow zones away from the bed, the SDAKE model’s estimates for the depth-averaged turbulent kinetic energy field are out of phase with measurements for the flow over a train of bedforms. Therefore, a newly developed depth-averaged KE model based on the moment concept (MDAKE) is presented here. The model replaces bed shear velocity with the integral moment velocity scale (u1). The calibrated MDAKE model is used to predict turbulent kinetic energy over a train of bedforms. The results of the MDAKE model are in phase and generally in reasonable agreement with the measurements.

Quantitative evaluation of the roles of ocean chemistry and climate on ooid size across the Phanerozoic: Global versus local controls

AbstractOoid size in natural systems can be predicted based on the expected equilibrium between precipitation and abrasion rates. Therefore, ooid size distributions may enable quantitative inferences about past ocean and climate conditions from sedimentology that complement insights from geochemistry. A few previous attempts have been made to compile information on ooid sizes across the Phanerozoic, but no systematic ooid size dataset is available and equilibrium models of ooid growth have not been explored comprehensively. In this study, convolutional neural network‐based segmentation was used to automate ooid size measurement and provide a systematic sampling of ooid sizes spanning the Phanerozoic. This data set is coupled with Monte Carlo simulations to quantitatively explore the interplay between three testable physicochemical parameters (long‐term average carbonate saturation state, bed shear velocity and intermittency of transport) in determining equilibrium ooid size. The numerical model shows that a typical‐sized ooid (≤1000 µm) can grow under a wide range of parameter combinations whereas giant ooids (>2000 µm) can only form under a more restricted set of circumstances. Furthermore, the model predicts that the formation of giant ooids is common when conditions favourable for rapid CaCO3 precipitation are achieved. This finding is consistent with the naturally rare occurrences of giant ooids, which developed under exceptional environmental conditions and are primarily associated with intervals of bimineralic seas and elevated sea‐surface temperature (greenhouse or transitional climate). Whereas global controls could help explain secular trends in ooid size, significant spatial variability of ooid size in several time intervals further demonstrates the importance of local environmental parameters in the growth of ooids. Together, spatial and temporal variation in ooid size distributions can complement geochemical proxies in quantitatively reconstructing ancient tropical marine environments.

Sediment suspension affected by submerged rigid vegetation under waves, currents and combined wave–current flows

Laboratory experiments and mathematical analyses were carried out to investigate and quantify the impacts of submerged rigid vegetation on sediment suspension under waves, currents and combined wave–current flows. Mimic canopies constructed from wooden cylinders were used in the experiments with three configurations (sparse, dense and vertically varying density). It was found that more sediment was suspended within the vegetation canopies, where smaller velocities and higher turbulence were observed, indicating that vegetation-induced turbulence rather than mean flow was the main driver of sediment suspension over vegetated beds. Meanwhile, higher sediment concentration near the bed was observed within a denser canopy, especially in the case of vertically varying vegetation density. The near-bed suspended sediment concentration could be described by an exponential formulation using an effective bed shear velocity considering different turbulence components (i.e. vegetation wake turbulence, bed shear turbulence and near-bed coherent structures). The formula was applicable in both vegetated and bare beds with different hydrodynamic conditions. To predict the vertical distributions of sediment suspension, two theoretical models of turbulent diffusion were improved by incorporating the vertically varying turbulent intensity in the water column.

Numerical Study on the Effect of Bank Vegetation on the Hydrodynamics of the American River under Flood Conditions

Vegetation can have an appreciable impact on the hydrodynamics and scour potential in natural rivers, but this effect is generally unaccounted for in high-fidelity computational fluid dynamic models. In this study, we have incorporated trees into the flow domain using two different approaches to study the hydrodynamics of the American River in Northern California under flood conditions. In the first approach, we resolved numerous trees as discrete objects. The second method incorporated a vegetation model into our in-house numerical model to treat the vegetation as a momentum sink along the banks. The flood flow of both cases was modeled using the large-eddy simulation. The computed hydrodynamics results of the cases were compared with a baseline case, which did not include any trees. Although both the tree-resolving and vegetation model approaches compared well with one another with respect to the flow field, they significantly altered the computed river flow dynamics and bed shear stress near the banks and the midwidth of the river compared with that of the no-tree case. Both methods that accounted for the resistance of the trees obtained lower and higher bed shear stresses and velocities along the banks and the midwidth of the river, respectively, than that of the baseline case. This research identified the important role that vegetation plays in natural rivers and provided researchers and engineers with the conceptual tools needed to incorporate vegetation into numerical models to improve the accuracy of the model results.

Sediment oxygen demand enhancement at the sediment/water interface of a shallow pond induced by pressure fluctuations from raindrop impact at the water surface

The increase of Sediment Oxygen Demand (SOD) by raindrop impact at the water surface of shallow ponds was investigated. A model was built to simulate pressure fluctuations at the sediment/water interface driven by raindrops striking the water surface of the pond continuously at constant intervals of a few seconds when the water depth h in the pond is on the order of 5 to 100 cm. Simulated pressure fluctuations at the sediment/water interface were translated into bed shear velocity describing the intensity of near – bed turbulence. Modeled shear velocity increases as the depth of water in the pond increases. Also, shear velocity becomes larger with increased terminal velocity of raindrops which was varied from 400 to 600 cms−1. The DO flux from the water column to the sediment surface, i.e. SOD, was calculated using the obtained shear velocity. Modeled SOD can be solely dependent on the microbial oxygen uptake rate (μ) in the sediment when μ < 500 mg L−1 d−1. While, SOD depends on the shear velocity, which in turn depends on the water depth (h) in the pond when h < 20 cm, the microbial oxygen uptake rate (μ) becomes solely limiting and SOD is no longer water – side controlled when h > 20 cm and μ > 1000 mg L−1 d−1. This simulation result suggests that raindrops impinging on the water surface of the pond can increase the SOD as can increase in height of bed roughness and/or the velocity of water flowing over the sediment surface as a turbulent flow. SOD induced by raindrop impact at the water surface can be equal to that for turbulent flow, or even larger depending on the water depth and microbial oxygen uptake rate.

Seabed disturbance and sediment mobility due to tidal current and waves on the continental shelves of Canada

Waves and tidal currents can interact to produce strong seabed shear stress and mobilization of sediments on continental shelves. Modelled wave and tidal current data for a 3-year period were used in a combined-flow sediment transport model to simulate the seabed shear stresses and the mobilization of uniform medium sand on the continental shelves of Canada. The modelling results are presented to establish the first national framework of seabed disturbance and sediment mobility on the continental shelves of Canada. Strong waves and tidal currents on the Canadian continental shelves produce mean bed shear velocity &gt;5 cm·s−1. Medium sand can be mobilized &gt;50% of the time over many areas on the shelves. The mobilization by tidal currents occurs over 36% and by waves over 50% of the shelf area, demonstrating that mobilization of sediments is dominated by waves on the Canadian continental shelves. Combined shear stresses due to wave and tidal current interaction further increase sediment mobilization to over 68% of the shelf area. The spatial variation of the relative importance of wave and tidal disturbances allows classification of the continental shelves into six disturbance types. Innovative Seabed Disturbance (SDI) and Sediment Mobility (SMI) indices are proposed to quantify the seabed exposure to oceanographic processes and sediment mobilization, incorporating both the magnitude and frequency of these processes. The proposed SDI and SMI, together with the disturbance type classification, can be used as standard parameters to best quantify seabed disturbance and sediment mobility on other shelves of the world.

Bed-Shear Velocity Measurement in Curved Open Channel

Generally, the condition of the rivers in Indonesia are alluvial rivers which had meanders, where the change in the river bed topography often occur. One of the parameters associated with changes in the river bed topography is bed-shear velocity, or Reynolds stress. The bed-shear velocity can be calculated by the Reynolds stress distribution method and the Clauser method which commonly used in straight channels. In fact, on natural channel there is a curve and even a meandering channel. With more complex flow conditions, the use of the Clauser method in curved channels can be questioned, is it still accurate or not. In this paper, both methods will be discussed by comparing the measurement data in the laboratory using 180 curved channel with flat bed. The results of data analysis show that the use of these two methods in curved channels produces an average difference of around 19.81%, where the Clauser method gives greater results and better tendencies. Apart from the differences in the results given, it can be said that the Clauser method as well as the Reynolds stress distribution method can still be used to calculate the bed-shear velocity in the curved channel

A Two‐Layer Turbulence‐Based Model to Predict Suspended Sediment Concentration in Flows With Aquatic Vegetation

AbstractTraditional bed shear stress‐based models (e.g., Rouse model) derived from the classic parabolic profile of eddy viscosity in open‐channel flows fail to accurately predict suspended sediment concentration (SSC) in flows with aquatic vegetation. We developed a two‐layer, turbulence‐based model to predict SSC profiles in emergent vegetated flows. Turbulence generated from vegetation, bed, and coherent structures caused by stem‐bed‐flow interaction are considered into the near‐bed turbulent kinetic energy (TKE) to calculate the effective bed shear velocity, . The model, validated by experimental data, further showed that the thickness height of the near‐bed layer (effective bottom boundary layer), Hb, varies with flow velocity and canopy density. Two additional models are provided to estimate Hb and . The model is expected to provide critical information to future studies on sediment transport, landscape evolution, and water quality management in vegetated streams, wetlands, and estuaries.

Particle dynamics in stormwater treatment areas

In south Florida, USA, Stormwater Treatment Areas (STAs) are used to reduce Phosphorus (P) loading into the northern portion of the Everglades. Phosphorus is well retained in the STAs (e.g. P biological uptake and P-sorption on adequate substrata) but a small, yet significant portion of it, leaves the STAs as particulate P (PP) in the discharge water. Thus, this study was conducted to improve the understanding of mechanisms and factors that affect PP removal efficiency of the STAs. Specifically, this study employed a suite of field and analytical methods to determine the effects of hydraulic conditions on the erosion, entrainment, transport, and settling of particles in the STAs. Prediction of the flux of sediment by numerical models requires estimates of the density, settling velocity, size, and fractal dimension of the particles and estimates of the critical bed shear velocity. We found that the STA particles are porous aggregates as in other similar shallow water bodies, but have a relatively high settling velocity, likely due to the high amount of CaCO3 and relatively low amount of organic matter in the sediment. Correlations between diurnal variations in windspeed and suspended sediment concentrations suggest that wind generated turbulence was responsible for resuspended matter in the water column. However, the wind-generated shear stresses applied to the bed were much smaller that the critical shear stress measured at the bed. These results suggest that much of the suspended material came from entrainment of materials from the surfaces of the surrounding submerged aquatic vegetation rather than erosion and entrainment of sedimented materials from the bed. Using calibrated acoustic backscatter from an acoustic doppler velocimeter, an analogy of Type 2 erosion was applied to estimate the critical shear stress of particles from the stems and leaves of submerged aquatic vegetation. The estimated critical stress was close to zero, supporting the idea that this unconsolidated and easily resuspended material comprises the bulk of the suspended sediment during normal operating conditions.

Interaction of a solitary wave with an array of macro-roughness elements in the presence of steady currents

The present study focuses on the effects of following and opposing steady currents on the interactions of a solitary wave with an array of macro-roughness elements, placed on a berm beach. A series of laboratory experiments and high-fidelity numerical simulations are conducted. The large eddy simulations are carried out using the open source computational fluid dynamics package, OpenFOAM. Wave breaking conditions on the berm are found to be controlled by the intensity of the currents. The opposing currents influence the layer of water rushing up the macro-roughness elements, leading to asymmetric runup patterns. Furthermore, the vortices forming around the elements' sharp edges, resulting from the interactions of the wave with the elements, are modified to a large extent due to the combined wave and current effect. The elliptical vortex tubes become up to ~20% wider under the effect of the following current flow, whereas their size is reduced by up to ~90% when the opposing currents are present. The following currents enhance the bed shear velocity, leading to intensified bed shear stress zones throughout the macro-roughness environment. On the other hand, the intensification of the bed shear velocity and corresponding stress occurs on the seaside in the presence of opposing currents. Overall, the results indicate that the currents entirely change the hydrodynamics of the interactions between the solitary wave and macro-roughness environment.

A Mixed Length Scale Model for Migrating Fluvial Bedforms

AbstractWith the expansion of hydropower, in‐stream converters, flood‐protection infrastructures, and growing concerns on deltas fragile ecosystems, there is a pressing need to evaluate and monitor bedform sediment mass flux. It is critical to estimate real‐time bedform size and migration velocity and provide a theoretical framework to convert easily accessible time histories of bed elevations into spatially evolving patterns. We collected spatiotemporally resolved bathymetries from laboratory flumes and the Colorado River in statistically steady, homogeneous, subcritical flow conditions. Wave number and frequency spectra of bed elevations show compelling evidence of scale‐dependent velocity for the hierarchy of migrating bedforms observed in the laboratory and field. New scaling laws were applied to describe the full range of migration velocities as function of two dimensionless groups based on the bed shear velocity, sediment diameter, and water depth. Further simplification resulted in a mixed length scale model estimating scale‐dependent migration velocities, without requiring bedform classification or identification.

Bedload transport rate prediction: Application of novel hybrid data mining techniques

The accurate prediction of bedload transport in gravel-bed rivers remains a significant challenge in river science. However the potential for data mining algorithms to provide models of bedload transport have yet to be explored. This study provides the first quantification of the predictive power of a range of standalone and hybrid data mining models. Using bedload transport data collected in laboratory flume experiments, the performance of four types of recently developed standalone data mining techniques - the M5P, random tree (RT), random forest (RF) and the reduced error pruning tree (REPT) - are assessed, along with four types of hybrid algorithms trained with a Bagging (BA) data mining algorithm (BA-M5P, BA-RF, BA-RT and BA-REPT). The main findings are four-fold. First, the BA-M5P model had the highest prediction power (R2 = 0.943; RMSE = 0.061 kg m−1 s−1; MAE = 0.040 kg m−1 s−1; NSE = 0.945; PBIAS = −1.60) followed by M5P, BA-RT, RT, BA-RF, RF, BA-REPT, and REPT. All models displayed ‘very good’ performance except the BA-REPT and REPT model, which were ‘satisfactory’. Second, the M5P, BA-RT, and RT models underestimated, and the BA-M5P, BA-RF, RF, BA-REPT and REPT models overestimated, bedload transport rates. Third, flow velocity had the most significant impact on bedload transport rate (PCC = 0.760) followed by shear stress (PCC = 0.709), discharge (PCC = 0.668), bed shear velocity (PCC = 0.663), bed slope (PCC = 0.490), flow depth (PCC = 0.303), median sediment diameter (PCC = 0.247), and relative roughness (PCC = 0.003). Fourth, the maximum depth of tree was the most sensitive operator in decision tree-based algorithms, and batch size, number of execution slots and number of decimal places did not have any impact on model’ prediction power. Overall the results revealed that hybrid data mining techniques provide more accurate predictions of bedload transport rate than standalone data mining models. In particular, M5P models, trained with a Bagging data mining algorithm, have great potential to produce robust predictions of bedload transport in gravel-bed rivers.

Depth-Averaged von Kármán Coefficient in Sediment-Laden Flows Using a Turbulent Kinetic Energy Balance

AbstractPrecise prediction of bed shear stress (τ0) and velocity profile in open channels is critical in various applications. This paper deliberates on the depth-averaged von Karman coefficient in...