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The processes of sediment entrainment, transport, and deposition over bedforms are highly dynamic and temporally and spatially variable. Obtaining measurements to understand these processes has led to ongoing developments in instrumentation for studying near-bed sediment dynamics, with the outputs applied to the development and assessment of sediment transport modelling. In the present study results are reported from three acoustic systems deployed to make observations of bedforms, bedload, suspended concentration and horizontal and vertical velocity components. To evaluate the instruments a series of near-bed boundary layer measurements were collected in a large scale flume facility over a rippled bed of medium sand under regular waves. The observations were conducted as part of Joint Research Activities within the EU funded Hydralab project. The suite of acoustic instruments consisted of a Bedform And Suspended Sediment Imager, BASSI, a three dimensional acoustic ripple profiler, 3D-ARP, and three Acoustic Concentration and Velocity Profilers, ACVP's. Here results are reported from the deployment of the instruments, to illustrate the ongoing developments in acoustics and the expanding capability of the application of acoustics to the study of near-bed flow and sediment dynamics. [ABSTRACT FROM AUTHOR]

Velocity-skewed oscillatory sheet flow transport is studied by an approximate model for instantaneous sediment transport resulting from exponential profiles of sediment concentration and velocity over a mobile bed. The phase lag effect, and asymmetry in wave friction factor, oscillatory flow orbital amplitude, roughness height, bed shear stress and wave boundary layer thickness are modelled so that the net boundary layer stream of pure velocity-skewed oscillatory flow can be obtained. The proposed model is found consistent with the previous classical formulas, and qualitatively refines a series of exponents of velocity power function for the approximation of instantaneous sediment transport rate under different flow conditions. The sediment fluxes can be well predicted with accuracy as that of a two-phase numerical model. The net boundary layer stream and sediment transport rates are also well predicted, especially the negative net stream and rates with large phase residual. The phase residual is shown a useful but insufficient factor in the net sediment transport in pure velocity-skewed flows. In addition, the net boundary layer stream resulting from velocity-skewed wave boundary layer development difference between onshore and offshore flow durations is an essential factor as well. [ABSTRACT FROM AUTHOR]

A series of laboratory experiments and high-fidelity numerical simulations were carried out to investigate the scour induced by a solitary wave around a non-slender, vertical structure of a square cross-section on a sandy berm. Various wave and water level combinations, structure layouts, and dimensions were studied. The flow separation at the sharp edges resulted in counterclockwise rotating out-of-plane vortices that extended from the free surface to the sandy berm. These energetic vortices were found to be the primary driving mechanism of the scouring through entraining, and entrapping the sand particles into their cores, keeping them in suspension, carrying them, and releasing them as the vortices propagate along a spiral trajectory. The analyses also showed that the flow blockage by the structure could result in flow field modulation and exacerbate the scour processes. The structure dimension appeared to be the most influential factor in the scouring process, drastically altering the characteristics of the non-equilibrium scour holes. Irrespective of the structure dimension or layout, the scour depth was greater around the seaside edge of the structure while the scour width was larger on the leeside edge. The uncertainties associated with the maximum non-equilibrium scour depth were quantified via Monte Carlo simulations which showed that the impact of the structure dimension on the maximum scour depth was almost twice more significant than that of the layout. The three-dimensional (3D) Eulerian two-phase flow numerical model, SedWaveFoam, was shown to be able to simulate sediment transport and scour around sharp-edged square structure at a low Keulegan-Carpenter (K C) number. • Interactions between a solitary wave and an impermeable structure placed on an erodible berm were studied experimentally. • Energetic vortices, formed at the corners of the structure, were found to be the primary driving mechanism of the scouring. • Structure dimension was the most influential factor in the scouring process. • Monte Carlo simulation was employed to assess the sensitivity of the maximum non-equilibrium scour depth to flow conditions. • SedWaveFoam model simulated scour around sharp-edged square structure at low Keulegan-Carpenter (KC) number. [ABSTRACT FROM AUTHOR]

Abstract: The present paper reports experiments on the flow field of a grain–water mixture around a flat, thin plate at zero incidence. The velocity measurements are performed using a Particle Image Velocimetry (PIV) technique. The Proper Orthogonal Decomposition (POD) analysis reveals that the degree of organisation of the flow field increases with the Reynolds number. The displacement thickness of the boundary layers generally increases downstream and increases slightly with the Reynolds number, which is based on the length of the plate. The vorticity normal to the plane of the flow has a maximum value at the leading edge and is almost invariant with respect to the Reynolds number; additionally, the non-dimensional profiles in the direction normal to the plate show self-similarity in the streamwise direction for a single test, and the profiles are almost coincident for all tests. The flow divergence is assumed to be an indicator of the variation of the sediment volume concentration; it indicates an increment of the sediment volume concentration near the walls of the plate and a spatial periodicity downstream that is triggered for relatively large Reynolds numbers. The spatial correlation analysis allows the evaluation of the integral length scales that are successively utilised in modelling the non-local rheology of the mixture. The velocity profiles have been modelled based on Savage’s model and Bagnold’s experiments, with further modifications from Ertaş and Halsey (2002) that are represented by pseudo-turbulence modelling of the flow field. Vortices have been detected according to the -criterion given by Jeong and Hussain (1995). The statistics of the vortices indicate that no preferential size is selected and that at a high Reynolds number, the most energetic vortices develop near the leading edge. [Copyright &y& Elsevier]

Abstract: The boundary layer is very important in the relation between wave motion and bed stress, such as sediment transport. It is a known fact that bed stress behavior is highly influenced by the boundary layer beneath the waves. Specifically, the boundary layer underneath wave runup is difficult to assess and thus, it has not yet been widely discussed, although its importance is significant. In this study, the shallow water equation (SWE) prediction of wave motion is improved by being coupled with the k–ω model, as opposed to the conventional empirical method, to approximate bed stress. Subsequently, the First Order Center Scheme and Monotonic Upstream Scheme of Conservation Laws (FORCE MUSCL), which is a finite volume shock-capturing scheme, is applied to extend the SWE range for breaking wave simulation. The proposed simultaneous coupling method (SCM) assumes the depth-averaged velocity from the SWE is equivalent to free stream velocity. In turn, free stream velocity is used to calculate a pressure gradient, which is then used by the k–ω model to approximate bed stress. Finally, this approximation is applied to the momentum equation in the SWE. Two experimental cases will be used to verify the SCM by comparing runup height, surface fluctuation, bed stress, and turbulent intensity values. The SCM shows good comparison to experimental data for all before-mentioned parameters. Further analysis shows that the wave Reynolds number increases as the wave propagates and that the turbulence behavior in the boundary layer gradually changes, such as the increase of turbulent intensity. [Copyright &y& Elsevier]

Abstract: Understanding of sea bottom boundary layer characteristics, especially bottom shear stress acting on the sea bed, is an important step needed in sediment transport modeling for practical application purposes. In the present study, a new generation system for bottom boundary layer under solitary wave is proposed. Applicability of this system is examined by comparing measured and numerical solution velocities. Moreover, transitional behavior from laminar to turbulence was investigated. It is concluded that the critical Reynolds number in the experiments shows good agreement with DNS result of Vittori and Blondeaux (2008) and laboratory data of Sumer et al. (2010), indicating validity of the generation system. Since the present generation system enables continuous measurement to obtain ensemble averaged quantities, it can be effectively utilized for future experimental studies on solitary wave boundary layers, including sediment transport experiments with movable bed. [Copyright &y& Elsevier]

Abstract: Shellfish farming, particularly oyster farms, suffers from strong siltation phenomena which are harmful to the production of shellfish. The lack of knowledge about the impact of an oyster farm on the wave propagation and on the flow remains a significant difficulty for the comprehension of sediment transport processes in coastal zones. These effects are one of the possible sources of sedimentation. The study presented here focuses on describing finely hydrodynamical phenomena (velocity fields, turbulence parameters) around oyster tables. The analysis is based on experimental trials carried out in a flume tank on reduced models of oyster tables. Experiments highlight the flow perturbations in the near field and constitute a database for validation of numerical models developed at the same time. The model based on Navier–Stokes equations offers the possibility to study the impact of more realistic table lengths on the flow and to simulate the perturbation produced by a group of oyster tables. Both experimental and numerical results are presented in this paper. [Copyright &y& Elsevier]

Abstract: Sediment transport models require appropriate representation of near-bed processes. We aim here to explore the parameterizations of bed shear stress, bed load transport rate and near-bed sediment erosion rate under the sheet flow regime. To that end, we employ a one-dimensional two-phase sheet flow model which is able to resolve the intrawave boundary layer and sediment dynamics at a length scale on the order of the sediment grain. We have conducted 79 numerical simulations to cover a range of collinear wave and current conditions and sediment diameters in the range 210–460 . The numerical results confirm that the intrawave bed shear stress leads the free stream velocity, and we assess an explicit expression relating the phase lead to the maximum velocity, wave period and bed roughness. The numerical sheet flow model is also used to provide estimates for the bed load transport rate and to inspect the near-bed sediment erosion. A common bed load transport rate formulation and two typical reference concentration approaches are assessed. A dependence of the bed load transport rate on the sediment grain diameter is observed and parameterized. Finally, the intrawave near-bed vertical sediment flux is further investigated and related to the time derivative of the bed shear stress. [Copyright &y& Elsevier]

Abstract: A new model for the boundary layer development and associated skin friction coefficients and shear stress within the swash zone is presented. The model is developed within a Lagrangian reference frame, following fluid trajectories, and can be applied to both laminar flow and smooth turbulent flow. The model is based on the momentum integral approach for steady, flat-plate boundary layers, with appropriate modifications to account for the unsteady flow regime and flow history. The model results are consistent with previous measurements of bed shear stress and skin friction coefficients within the swash zone. These indicate strong temporal and spatial variation throughout the swash cycle, and a clear distinction between the uprush and backwash phase. This variation has been previously attributed the unsteady flow regime and flow history effects, both of which are accounted for in the new model. Fluid particle trajectories and velocity are computed using the non-linear shallow water wave equations and the boundary layer growth across the entire swash zone is estimated. Predictions of the bed shear stress and skin friction coefficients agree reasonably well with direct bed shear stress measurements reported by Barnes et al. (Barnes, M.P., O’Donaghue, T., Alsina, J.M., Baldock, T.E., 2009. Direct bed shear stress measurements in bore-driven swash. Coastal Engineering 56 (8), 853–867) and, for a given flow velocity, give stresses which are consistent with the bias toward uprush sediment transport which has consistently been observed in measurements. The data and modelling suggest that the backwash boundary layer is initially laminar, which results in the late development of significant bed shear during the backwash, with a transition to a turbulent boundary layer later in the backwash. A new conceptual model for the boundary layer structure at the leading edge of the swash is proposed, which accounts for both the no-slip condition at the bed and the moving wet–dry interface. However, further development of the Lagrangian Boundary Layer Model is required in order to include bore-generated turbulence and to account for variable roughness and mobile beds. [Copyright &y& Elsevier]

Abstract: Direct measurements of bed shear in the swash zone are presented. The data were obtained using a shear plate in medium and large-scale laboratory bore-driven swash and cover a wide range of bed roughness. Data were obtained across the full width of the swash zone and are contrasted with data from the inner surf zone. Estimates of the flow velocities through the full swash cycle were obtained through numerical modelling and calibrated against measured velocity data. The measured stresses and calculated flow velocities were subsequently used to back-calculate instantaneous local skin friction coefficients using the quadratic drag law. The data show rapid temporal variation of the bed shear stress through the leading edge of the uprush, which is typically two–four times greater than the backwash shear stresses at corresponding flow velocity. The measurements indicate strong temporal variation in the skin friction coefficient, particularly in the backwash. The general behaviour of the skin friction coefficient with Reynolds number is consistent with classical theory for certain stages of the swash cycle. A spatial variation in skin friction coefficient is also identified, which is greatest across the surf-swash boundary and likely related to variations in local turbulent intensities. Skin friction coefficients during the uprush are approximately twice those in the backwash at corresponding Reynolds number and cross-shore location. It is suggested that this is a result of the no-slip condition at the tip leading to a continually developing leading edge and boundary layer, into which high velocity fluid and momentum are constantly injected from the flow behind and above the tip region. Finally, the measured stress data are used to determine the asymmetry and cross-shore variation in potential sediment transport predicted by three forms of sediment transport formulae. [Copyright &y& Elsevier]

Abstract: A laboratory flume channel, equipped with an acoustic Doppler flow sensor and a bottom scanning laser, was used for detailed, non-intrusive flow measurements (at 2 cm s−1 and 10 cm s−1) around solitary biogenic structures, combined with high-resolution mapping of the structure shape and position. The structures were replicates of typical macrozoobenthic species commonly found in the Mecklenburg Bight and with a presumed influence on both, the near-bed current regime and sediment transport dynamics: a worm tube, a snail shell, a mussel, a sand mound, a pit, and a cross-stream track furrow. The flow was considerably altered locally by the different protruding structures (worm tube, snail, mussel and mound). They reduced the horizontal approach velocity by 72% to 79% in the wake zone at about 1–2 cm height, and the flow was deflected around the structures with vertical and lateral velocities of up to 10% and 20% of the free-stream velocity respectively in a region adjacent to the structures. The resulting flow separation (at flow Reynolds number of about 4000 and 20,000 respectively) divided an outer deflection region from an inner region with characteristic vortices and the wake region. All protruding structures showed this general pattern, but also produced individual characteristics. Conversely, the depressions (track and pit) only had a weak influence on the local boundary layer flow, combined with a considerable flow reduction within their cavities (between 29% and 53% of the free-stream velocity). A longitudinal vortex formed, below which a stagnant space was found. The average height affected by the structure-related mass flow rate deficit for the two velocities was 1.6 cm and 1.3 cm respectively (80% of height and 64%) for the protruding structures and 0.6 cm and 0.9 cm (90% and 127% of depth) for the depressions. Marine benthic soft-bottom macrozoobenthos species are expected to benefit from the flow modifications they induce, particularly in terms of food particle capture due to altered particle pathways and residence times, but also for the exchange of gases, solutes and spawn. The present results confirm previous studies on flow interaction effects of various biogenic structures, and they add a deeper level of detail for a better understanding of the fine-scale effects. [Copyright &y& Elsevier]

Abstract: Sandy sediments in shallow coastal waters of the Baltic Sea are often characterised by large numbers of biogenic structures which are produced by macrozoobenthos species. A series of experiments was devised to quantify how the interaction of such structures with the near-bed flow regime affects the sediment flux. Most experiments were done with simplified replicates of structures generated by typical species commonly found in the Mecklenburg Bight, starting with solitary structures and regularly-spaced arrays in a range of characteristic population densities, followed by a complex benthic macrofauna community, both artificial and alive. A laboratory flume channel, equipped with an acoustic Doppler flow sensor and a topography scanning laser, was used for high-resolution measurements (2 mm horizontal step size and 0.3 mm vertical resolution) of sand erosion (220 µm median grain size, at 20 cm s−1) and fine particle deposition (8 µm grain size, at 5 cm s−1). Sediment transport threshold values were measured for each layout. As a rule-of-thumb, both the erosion fluxes and the deposition of suspended matter increased considerably at low population densities (below 2%, expressed as percent of the sediment surface covered, i.e. roughness density RD). Above densities of 4%, erosion almost stopped inside the test arrays, and deposition remained well below the level of unpopulated areas. An attempt to extrapolate these findings to field conditions (using field current velocity data from 2001) showed that the net flux switched from erosion to deposition for densities above 5%. These parameters can now be integrated into a numerical sediment transport model coupling waves, currents, sediment dynamics and biological processes, which is currently under construction at the Baltic Sea Research Institute (IOW), Rostock, Germany. [Copyright &y& Elsevier]

Abstract: A simple conceptual formulation to compute seabed shear stress due to asymmetric and skewed waves is presented. This formulation generalizes the sinusoidal wave case and uses a variable friction factor to describe the physics of the boundary layer and to parameterize the effects of wave shape. Predictions of bed shear stresses agree with numerical computations using a standard boundary layer model with a k–ε turbulence closure. The bed shear stress formulation is combined with a Meyer-Peter and Müller-type formula to predict sheet flow bedload transport under asymmetric and skewed waves for a horizontal or sloping bed. The predictions agree with oscillatory water tunnel measurements from the literature. [Copyright &y& Elsevier]

Abstract: Laboratory data of free surface elevation and fluid velocities (cross-shore and vertical velocities) were obtained using a laser-Doppler velocimeter (LDV) for the case of a periodic wave plunging over an impermeable, steep (1:10) slope with a fixed bottom roughness (nominal diameter=2.2mm). The measurements were conducted over 14 cross-shore locations from the outer surf zone to the swash zone with approximately 10 vertical points at each location. The vertical resolution included measurements in the bottom boundary layer and some points above the trough level. Various hydrodynamic quantities, including ensemble-averaged turbulent kinetic energy (TKE) (〈k〉) and turbulence intensity (〈u′2〉 and 〈w′2〉), were estimated to better understand inner surf and swash zone hydrodynamics induced by strongly plunging waves. In the outer region of the bottom boundary layer, the ratio of the time-averaged horizontal turbulence intensity to the time-averaged vertical turbulence intensity agreed well with the case of plane wake turbulence . The average ratio near the bottom was larger which is closer to flows typified by the inner region of a boundary layer . In the surf zone, the ensemble-averaged horizontal fluid velocity (〈u〉) near the bottom leads in phase compared to 〈u〉 in the upper layer, and 〈u〉 at the bore front exceeds the theoretical wave celerity. At the impinge point, a strong return flow occurred which was greater in magnitude than the onshore directed velocity . In the surf zone, 〈k〉 was largest just below trough level with a forward shift in phase of the peak intensity. The turbulence energy was mostly dissipated after the passage of the crest at this location. 〈u〉 near the bottom was leading in phase with a sharp vertical gradient in 〈u〉 indicating that boundary layer processes may have been important. In the swash zone, the vertical gradient of 〈u〉 was relatively small compared to the vertical gradient of 〈u〉 in the surf zone and may be due to the effect that the strong downrush had on turbulent mixing. Finally, the time-averaged estimate of TKE was vertically uniform over the inner surf and swash zone. [Copyright &y& Elsevier]

Abstract: Two-dimensional depth-averaged Boussinesq-type equations were presented with the consideration of slowly varying bathymetry and effects of bottom viscous boundary layer. These Boussinesq-type equations were written in terms of the horizontal velocity components evaluated at an arbitrary elevation in the water depth and the free surface displacement. The leading order effects of the bottom boundary layer were represented by a convolution integral in the depth-integrated continuity equation. To test the validity of the theory, a set of laboratory experiments was performed to measure the viscous damping and shoaling of a solitary wave propagating in a wave tank. The time histories of the free surface profiles were measured at several locations along the centerline of the flume. To compare these laboratory data with theoretical results, the two-dimensional Boussinesq-type equations were integrated across the wave tank, resulting in a set of one-dimensional equations, while the side-wall boundary layers were properly considered. The agreement between the experimental data and numerical results was very good. The bottom shear stress formula was also given and its impact on the sediment transport rate was discussed. [Copyright &y& Elsevier]

Abstract: Oscillatory flow tunnel measurements of velocities and fluxes for sands in oscillatory sheet flow conditions are presented. The experiments involved a range of well-sorted and graded sands in two asymmetric flows. Velocities were measured using an ultrasonic velocity profiler (UVP) capable of measuring deep within the sheet flow layer. Velocity profiles are found to be similar for the same flow but different sand beds and display expected features of oscillatory boundary layer flow. The near-bed velocity leads the main flow velocity by approximately 21° and a small offshore-directed current is generated near the bed. Measures of the boundary layer thickness are in good agreement with those predicted using an equation formulated for the boundary layer thickness over fixed beds. Velocity data have been combined with concentration data to produce time-dependent sand flux profiles covering the sheet flow and suspension regions. There are fundamental differences in the transport processes of sands of different size and grading, caused by unsteady effects which dominate in the case of fine sand and are largely absent in the case of coarse sand. (1) Time-averaged flux is onshore-directed (positive) in the case of coarse sand and is confined to a region immediately above the bed; in contrast, time-averaged flux in the case of fine sand extends high above the bed, is offshore-directed (negative) in the sheet flow layer and becomes onshore-directed in the suspension layer. (2) Net transport in the case of coarse sand is directed onshore. As the percentage of fine sand in the bed increases, offshore transport becomes increasingly dominant as the percentage of fine sand increases. (3) Net transport in the suspension layer is onshore while net transport in the sheet-flow layer may be onshore or offshore depending on sand size and grading. [Copyright &y& Elsevier]

A process-based sediment transport model is presented that combines the knowledge of sediment transport in rivers and estuaries with the understanding of physical processes specific for the shelf seas. Due to formation of bottom Ekman spiral, the near-bottom current and hence the sediment transport deviate from the direction of surface current. The model takes into account velocity veering induced by Ekman spiral and estimates both direction and rate of transport of suspended particulate matter (SPM) generated by a steady or slowly varying current, through suspension, relocation and deposition of sediment in a shallow sea. The model uses a combination of analytical and numerical methods: analytical integration, in the vertical, and numerical integration, in the horizontal. The model predicts also vertical erosion/deposition fluxes at the seabed. The deviation angles and other parameters of SPM transport are computed for a range of water depths 5–50 m, particle settling velocities 0.1–6 cm/s, and current speeds 0.4–1.2 m/s. The model converges automatically to traditional engineering-style formulations, in extreme case of strong current in very shallow water, where velocity veering is of minor importance. [Copyright &y& Elsevier]

For moderate Shields number flows, the characteristic minimum sediment transport prediction error is estimated to be of the order of a factor of 2, even in stationary and horizontally homogeneous flows over a flat bottom. For oscillatory flows over ripples the same error is judged to be comparable to a factor of 4.In actual flows when the flow, sediments and bottom shape have to be predicted, moderate estimation errors for the near bottom turbulent stress results in characteristic minimum sediment transport error that is probably at least of the order of a factor of 10.The equations for the large-scale average flow require nonstandard parameterizations of the smaller scale ripple flow and boundary conditions. Only weakly founded closure relations are available for this. The error of the large-scale sediment transport can therefore not be quantified without extensive data comparisons. As extrapolated from the simpler estimates, it appears plausible that it could be significantly larger than a factor of 10.When the sediment transport variability is large, both in reality and in models, many models can probably be adjusted to fit the few data available. This may not be relevant for judging the prediction accuracy. [Copyright &y& Elsevier]

Extensive research on the stability and morphodynamics of aqueous bedforms over the past four decades reveals the existance of seven bedform states (ripples, lower stage plane beds, pebble clusters, bedload sheets, dunes, upper stage plane beds and antidunes). Their stability and morphology is a function of mean flow velocity/non-dimensional bed shear stress and sediment-size. These bedform states are distinguishable from one other by their morphology, dimension, and sediment transport rate. Each bedform state is characterized by distinct physical process(es), and transitional bedform states (washed-out-ripples and dunes) are consequences of their temporal, spatial and dimensional variabilities. The physical processes associated with various aqueous bedform states and transitional bedforms are discussed in this paper, in order to gain insights into their stability and morphodynamics in different sediment-sizes. [Copyright &y& Elsevier]

Understanding the boundary layer flow structure at the tip of a swash flow is important for improving predictions of wave run-up, coastal flooding and sediment transport processes on beaches, but this is difficult to investigate experimentally. Recently, there has been debate regarding the mechanics of boundary layer growth during the uprush flow. Here, an extensively validated RANS model is used to investigate the swash tip dynamics during a dam-break driven swash event. The model enables the analysis of the spatial and temporal variation of important parameters, in particular the water surface gradients, the bed shear stress, and the non-uniformity of the velocity profile. The rate of flow convergence of surface particles toward the tip, and the ratio of the depth-averaged flow velocity and celerity of the swash tip are also obtained. The flow depth varies with distance behind the wave tip approximately as a power law, with a power of 1/2–3/4. The surface elevation dips offshore at distances greater than 0.2 m behind the front. The shear stress decreases quite slowly in the spatial region immediately behind the wave tip, and is in very good agreement with the flat-plate boundary layer model of Barnes and Baldock (2010). The model results indicate that the boundary layer structure is well-developed or depth-limited at the wave tip, and fits a power-law velocity profile with an exponent of order 1/3, consistent with a rough bed. The normalised vertical variation in the velocity profile is very uniform in the region 1 m behind the wave tip, and matches that for a 1/3 power law. Alternate logarithmic fits to the velocity profile yield consistent values of bed roughness at different locations, but corresponding to a grain size that is about twice that used in the experiment. The rate of flow convergence of surface particles toward the wave tip is also consistent with a fully developed boundary layer and a 1/3 power law. • RANS model used to investigate boundary layer structure at a swash tip. • The model provides high resolution spatial data. • The boundary layer is fully-developed at the wave tip, with a 1/3 power law velocity profile. • Bed shears stress predicted by a flat-plate boundary layer model agrees very well with the RANS model. • The rate of flow convergence of surface particles toward the front is consistent with the power-law profile. [ABSTRACT FROM AUTHOR]