Bed Shear Stress Measurements Research Articles

Wave bottom boundary layer processes below irregular surfzone breaking waves with light-weight sheet flow particle transport

The present work investigates the structure of the near-bed flow below irregular surfzone breaking waves inducing light-weight sheet flow particle transport. The experiments are carried out in the LEGI flume under steady equilibrium conditions between the wave forcing and the underlying bed morphology. Synchronized ACVP and video images provide detailed information about the mean wave and current characteristics and the coupled flow regimes across the entire wave breaking region including the outer and the inner surfzones. An analysis of the impact of breaking eddies in the Wave Boundary Layer (WBL) is undertaken at the beginning of the inner surfzone. Subsequently, the intrawave variation of several contributions of the total shearing force per unit area and the net values of the Reynolds stress related to phase-averaged velocities are analyzed. It is found that is the dominant term. The turbulent Reynolds stress, the low frequency, and the mean terms are at least 1 order of magnitude lower. Due to the irregular wave forcing, the net values are separated into the net wave-by-wave Reynolds stress and the wave Reynolds stress averaged over the entire irregular wave sequence. All these measured bed shear stress terms are then compared to estimations obtained with two different parameterized models in order to evaluate their prediction performances. The values of the model parameters are discussed in comparison to those found in the literature. Finally, the vertical profile of net Reynolds shear stress exhibits a nearly constant value across the sheet-flow layer.

Laboratory observations of flow and sediment transport induced by plunging regular waves

[1] Two parallel experiments involving the evolution and runup induced by plunging regular waves near the shoreline of a sloping bed are considered: (1) a rigid-bed experiment, allowing direct (hot film) measurements of bed shear stresses and (2) a sediment-bed experiment, allowing for the measurement of pore-water pressures as well as observation of sediment suspension and bed morphological changes. Both experiments utilize the same initial bed profile and wave forcing. The experiments show that the mean bed shear stresses experienced onshore of incipient breaking are amplified by nearly a factor of 2 relative to prebreaking conditions, whereas their corresponding turbulent fluctuations are amplified even more strongly, by a factor of 5–6. The plunging processes lead to a series of vortices, whose formation may be explained as the result of shear layer instability. Measurements show that these vortices can significantly enhance peaks in the offshore-directed bed shear stresses. Moreover, near-bed pore pressure measurements indicate that these vortices cause large upward-directed pressure gradients, which in turn produce a corresponding series of suspended sediment plumes shoreward of the initial breaking event. These findings are related to the induced morphological changes over both short and long time scales. The present results are also compared and contrasted with previous experiments utilizing a similar methodology, but involving plunging solitary waves.

Numerical and experimental investigation of flow and scour around a half-buried sphere

The paper describes the results of a numerical and experimental investigation of flow and scour around a half-buried sphere exposed to a steady current. Hot-film bed shear stress and Laser Doppler Anemometer measurements were made with a half sphere mounted on the smooth bed in an open channel. The hydrodynamic model is a 3-D general purpose N–S flow solver. The k-omega SST turbulence model was used for closure. The flow model was used to study the horseshoe vortex and lee-wake vortex flow processes around the sphere. The flow model was coupled with a morphologic model to calculate scour around the half-buried sphere in currents. The morphologic model includes a sediment-transport description, and a description of surface-layer sand slides for bed slopes exceeding the angle of repose. The sediment transport description includes, for the first time, the effect of externally-generated turbulence (induced by the horseshoe-vortex flow and the lee-wake flow processes) on sediment transport. The results show that the scour depth increases and time scale decreases when the effect of externally-generated turbulence is incorporated in the calculations. Empirical expressions representing the numerically obtained data on the equilibrium scour depth and the time scale are presented. The results show that the equilibrium maximum scour depth in the live-bed regime can be approximated by 0.5 D in which D is the sphere diameter.

Wave forcing over an intertidal mussel bed

The Mosselwad project studies the stability and opportunities for restoration of mussel beds in the Wadden Sea. In this context we seek to predict mussel bed stability with respect to hydrodynamic forcing. To make accurate predictions with models, field experiments are needed to determine relevant processes and to establish representative estimates for model parameters. These parameter values were determined by a six week campaign on a relatively young mussel bed in the Wadden Sea. During this period wave height, period, propagation velocity, dissipation and flow velocities were measured. From these measurements values for the total rate of energy dissipation and the rate of wave energy dissipation were estimated. Results show a large increase in measured bed shear stress over the mussel bed compared with the uncovered parts of the intertidal flat. This is caused by the large roughness of the mussels. The turbulent kinetic energy was high above the covered parts of the bed. From the dissipation rate of TKE values for the corresponding bed shear stress and roughness height were estimated. These estimates were subsequently applied to calibrate a wave model which was used to determine the spatial distribution of the wave forcing. Model results show that the bed shear stress decreases over the mussel bed but increases behind the bed. Furthermore, a model study on the situation before the mussel bed settled shows that a minimum in wave forcing coincides with the seaward edge of the bed. This suggests that the bed is currently located in the optimal location with respect to wave forcing.

Measurement and modeling of bed shear stress under solitary waves

Direct measurements of bed shear stresses (using a shear cell apparatus) generated by non-breaking solitary waves are presented. The measurements were carried out over a smooth bed in laminar and transitional flow regimes (~ 10 4 < R e < ~ 10 5). Measurements were carried out where the wave height to water depth (h/d) ratio varied between 0.12 and 0.68; maximum near bed velocity varied between 0.16 m/s and 0.51 m/s and the maximum total shear stress (sum of skin shear stress and Froude–Krylov force) varied between 0.386 Pa and 2.06 Pa. The total stress is important in determining the stability of submarine sediment and in sheet flow regimes. Analytical modeling was carried out to predict total and skin shear stresses using convolution integration methods forced with the free stream velocity and incorporating a range of eddy viscosity models. Wave friction factors were estimated from skin shear stress at different instances over the wave (viz., time of maximum positive total shear stress, maximum skin shear stress and at the time of maximum velocity) using both the maximum velocity and the instantaneous velocity at that phase of the wave cycle. Similarly, force coefficients obtained from total stress were estimated at time of maximum positive and negative total stress and at maximum velocity. Maximum positive total shear stress was approximately 1.5 times larger than minimum negative total stress. Modeled and measured positive bed shear stresses are well correlated using the best convolution model, but the model underestimates the data by about 4%. Friction factors are dependent on the choice of normalizing using the maximum velocity, as is conventional, or the instantaneous velocity. These differ because the stress is not in phase with the velocity in general. Friction factors are consistent with previous data for monochromatic waves, and vary inversely with the square-root of the Reynolds number. The total shear stress leads the free stream fluid velocity by approximately 50°, whereas the skin friction shear stress leads by about 30°, which is similar to that reported by earlier researchers.

BED SHEAR STRESS IN UNSTEADY FLOW

Standard engineering methods of estimating bed shear stress using friction factors can fail spectacularly in unsteady hydrodynamic conditions. This paper demonstrates this fact using direct measurements of bed shear stresses under irregular waves using a shear plate apparatus. The measurements are explained in terms of the influence of the horizontal pressure gradient and the shear stresses acting on the surface of the plate. The horizontal fluid velocity at the edge of the boundary layer and the water surface elevation and slope were also measured. The paper demonstrates that the water surface measurements can be used to obtain accurate estimates of the forces on the bed, by employing Fourier analysis techniques or an innovative convolution integral method. The experimental results indicate that an offshore bed shear stress may be recorded while the free stream velocity remains onshore at all times. This demonstrates the failure of the standard engineering friction factor method in this scenario, since negative friction factors would be required. Important questions are raised regarding the appropriate definition for the bed shear stress when the vertical gradient of the shear stress is large. It is shown that it is problematic to define a single value for a "bed† shear stress in the presence of a strong horizontal pressure gradient. It is also argued that the natural driver for any model used to predict bed shear stress is the pressure gradient (or its proxy the free stream acceleration), rather than the velocity. This allows for accurate calculation of both acceleration effects (more rapid acceleration leads to a thinner boundary layer and higher shear stress) and also the direct action of the horizontal pressure gradient.

Flow and sediment transport induced by a plunging solitary wave

[1] Two parallel experiments involving the evolution and runup of plunging solitary waves on a sloping bed were conducted: (1) a rigid-bed experiment, allowing direct (hot film) measurements of bed shear stresses and (2) a sediment-bed experiment, allowing for the measurement of pore water pressures and for observation of the morphological changes. The two experimental conditions were kept as similar as possible. The experiments showed that the complete sequence of the plunging solitary wave involves the following processes: shoaling and wave breaking; runup; rundown and hydraulic jump; and trailing wave. The bed shear stress measurements showed that the mean bed shear stress increases tremendously (with respect to that in the approaching wave boundary layer), by as much as a factor of 8, in the runup and rundown stages, and that the RMS value of the fluctuating component of the bed shear stress is also affected, by as much as a factor of 2, in the runup and hydraulic jump stages. The pore water pressure measurements showed that the sediment at (or near) the surface of the bed experiences upward directed pressure gradient forces during the down-rush phase. The magnitude of this force can reach values as much as approximately 30% of the submerged weight of the sediment. The experiments further showed that the sediment transport occurs in the sheet flow regime for a substantial portion of the beach covering the area where the entire sequence of the wave breaking takes place. The bed morphology is explained qualitatively in terms of the measured bed shear stress and the pressure gradient forces.

Coherent structures in wave boundary layers. Part 2. Solitary motion

This study continues the investigation of wave boundary layers reported by Carstensen, Sumer &amp; Fredsøe (J. Fluid Mech., 2010, part 1 of this paper). The present paper summarizes the results of an experimental investigation of turbulent solitary wave boundary layers, simulated by solitary motion in an oscillating water tunnel. Two kinds of measurements were made: bed shear stress measurements and velocity measurements. The experiments show that the solitary-motion boundary layer experiences three kinds of flow regimes as the Reynolds number is increased: (i) laminar regime; (ii) laminar regime where the boundary-layer flow experiences a regular array of vortex tubes near the bed over a short period of time during the deceleration stage; and (iii) transitional regime characterized with turbulent spots, revealed by single/multiple, or, sometimes, quite dense spikes in the bed shear stress traces. Supplementary synchronized flow visualization tests confirmed the presence of the previously mentioned flow features. Information related to flow resistance are also given in the paper.

Coherent structures in wave boundary layers. Part 1. Oscillatory motion

This work concerns oscillatory boundary layers over smooth beds. It comprises combined visual and quantitative techniques including bed shear stress measurements. The experiments were carried out in an oscillating water tunnel. The experiments reveal two significant coherent flow structures: (i) Vortex tubes, essentially two-dimensional vortices close to the bed extending across the width of the boundary-layer flow, caused by an inflectional-point shear layer instability. The imprint of these vortices in the bed shear stress is a series of small, insignificant kinks and dips. (ii) Turbulent spots, isolated arrowhead-shaped areas close to the bed in an otherwise laminar boundary layer where the flow ‘bursts’ with violent oscillations. The emergence of the turbulent spots marks the onset of turbulence. Turbulent spots cause single or multiple violent spikes in the bed shear stress signal, which has profound implications for sediment transport (in both the laboratory and the field). The experiments also show that similar coherent flow structures exist in the case of combined oscillatory flow and current.

A Lagrangian model for boundary layer growth and bed shear stress in the swash zone

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.

Direct bed shear stress measurements in bore-driven swash

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.

Computing Nonhydrostatic Shallow-Water Flow over Steep Terrain

Flood and dambreak hazards are not limited to moderate terrain, yet most shallow-water models assume that flow occurs over gentle slopes. Shallow-water flow over rugged or steep terrain often generates significant nonhydrostatic pressures, violating the assumption of hydrostatic pressure made in most shallow-water codes. In this paper, we adapt a previously published nonhydrostatic granular flow model to simulate shallow-water flow, and we solve conservation equations using a finite volume approach and an Harten, Lax, Van Leer, and Einfeldt approximate Riemann solver that is modified for a sloping bed and transient wetting and drying conditions. To simulate bed friction, we use the law of the wall. We test the model by comparison with an analytical solution and with results of experiments in flumes that have steep (31°) or shallow (0.3°) slopes. The law of the wall provides an accurate prediction of the effect of bed roughness on mean flow velocity over two orders of magnitude of bed roughness. Our nonhydrostatic, law-of-the-wall flow simulation accurately reproduces flume measurements of front propagation speed, flow depth, and bed-shear stress for conditions of large bed roughness.

Application of laser anemometry for measuring critical bed shear stress of sediment core samples

This work details the application of the Laser Doppler Anemometry (LDA) technique for the direct measurement of the critical bed shear stress of natural sediment beds. This property was determined from variations in the velocity profiles obtained at the interface, for various Reynolds numbers. The onset of erosion was identified as a sudden transition in the local stress. Samples of sediment were collected from Cávado (Portugal) and Westerschelde (the Netherlands) estuaries. Experiments were carried out in laboratory using a circular mini flume, 126.8 mm in diameter, enabling the reproduction of the flow characteristics close to the sediment. It was found that the deformation at the sediment surface is a very important factor affecting the bed shear stress. That deformation is affected by the mud characteristics and composition, namely the particle size. It was also verified that the erosion process is not continuous, the sediment being eroded in layers. From the various experiments, it was concluded that the LDA technique is appropriate for measuring the critical bed shear stress of sediments.

Flow around Cylinders in Open Channels

This paper presents the results of an experimental study of flow around cylindrical objects in an open channel. Cylindrical objects of equal diameter and four heights were tested under similar flow conditions producing four different levels of submergence, including a surface piercing bridge-pier-like cylinder. Different flow elements and their locations were identified using a set of flow visualization tests. Observations made from the flow visualization tests were then verified by measurements of bed-shear stress and deflected flow velocity around the cylinders. Horse-shoe vortex systems were found to appear closer to the submerged cylinders compared to a surface piercing cylinder. The increase in dimensionless bed-shear stress is found to be inversely related to the level of submergence of the cylinders. Bed-shear stress results presented in this paper will be valuable for a qualitative understanding of the scour potential of flow around submerged cylinders. Mean velocity profiles in the deflected flow...

Direct Bed Shear Stress Measurements in Laboratory Swash

Direct Bed Shear Stress Measurements in Laboratory Swash

Dynamics of intertidal gravel dunes

This paper examines the dynamics of intertidal gravel dunes subjected to high‐energy unsteady and reversing tidal currents in the Severn Estuary, UK. The dunes were composed of shale particles with median grain size, D50, around 4 mm and had mean heights and wavelengths of 60 cm and 7 m, respectively. Acoustic instruments were deployed above a dune to measure the streamwise profile and flow turbulence. Radar was used to map a section of the dune field on two occasions. Measurements during the peak spring ebb tides showed that when the measured bed shear stress exceeded the threshold for entrainment of the coarse surface armor, sediments were eroded from the upper surface of the dune. The dune prograded in the direction of the ebb flow a distance O(1 m), and some eroded sediments were deposited on the stoss slope downstream. The dune was then reworked during the following flood tide to reestablish approximately the same pre‐ebb profile shape and location. Radar data showed also that the exposed dunes at low water occupied approximately the same location over a period of 4 days during peak spring tides. The relationship between the depth‐mean current and the net volume of dune sediments moved was found to conform to a power law. The predicted critical bed shear stress, τcrit, for D50 = 4 mm was approximately 1 N/m2. However, owing to a coarse armor layer on the surface of the dune, a measured τcrit value O(4 N/m2) was required to initiate dune erosion. Although the Van Rijn formula was found to overestimate both the height and wavelength of dunes at this site, the dunes appear to be equilibrium bed forms controlled by local hydraulics and sediment supply. Sediment transport predicted by bed load formula were within a factor of two of the observed mass transport of dune sediments for ebb tides.

Bayesian analysis for erosion modelling of sediments in combined sewer systems

Previous research has confirmed that the sediments at the bed of combined sewer systems are the main source of particulate and organic pollution during rain events contributing to combined sewer overflows. However, existing urban stormwater models utilize inappropriate sediment transport formulas initially developed from alluvial hydrodynamics. Recently, a model has been formulated and profoundly assessed based on laboratory experiments to simulate the erosion of sediments in sewer pipes taking into account the increase in strength with depth in the weak layer of deposits. In order to objectively evaluate this model, this paper presents a Bayesian analysis of the model using field data collected in sewer pipes in Paris under known hydraulic conditions. The test has been performed using a MCMC sampling method for calibration and uncertainty assessment. Results demonstrate the capacity of the model to reproduce erosion as a direct response to the increase in bed shear stress. This is due to the model description of the erosional strength in the deposits and to the shape of the measured bed shear stress. However, large uncertainties in some of the model parameters suggest that the model could be over-parameterised and necessitates a large amount of informative data for its calibration.

Numerical and experimental investigation of flow and scour around a circular pile

The flow around a vertical circular pile exposed to a steady current is studied numerically and experimentally. The numerical model is a three-dimensional model. The model validation was achieved against new experimental data (which include two-component laser-Doppler anemometry (LDA) flow measurements and the hot-film bed shear stress measurements, and reported in the present paper) and the data of others, and a k-w turbulence model was used for closure. The model does not have a free-surface facility and therefore is applicable only to cases where the Froude number is small (Fr < 0(0.2)). The flow model was used to study the horseshoe vortex and lee-wake vortex flow processes around the pile. The influence on the horseshoe vortex of three parameters, namely the boundary-layer thickness, the Reynolds number and the bed roughness, was investigated. In the latter investigation, the steady solution of the model was chosen. A study of the influence of the unsteady solution on the previously mentioned flow processes was also carried out. The ranges of the parameters covered in the numerical simulations are: The boundary-layer-thickness-to-pile-diameter ratio is varied from 2 x 10 -2 to 10 2 , the pile Reynolds number from 10 2 to 2 × 10 6 , and the pile diameter-to-roughness ratio from 2 to about 10 3 . The amplification of the bed shear stress around the pile (including the areas under the horseshoe vortex and the lee-wake region) was obtained for various values of the previously mentioned parameters. The steady-state flow model was coupled with a morphologic model to calculate scour around a vertical circular pile exposed to a steady current in the case of non-cohesive sediment. The morphologic model includes (i) a two-dimensional bed load sediment-transport description, and (ii) a description of surface-layer sand slides for bed slopes exceeding the angle of repose. The results show that the present numerical simulation captures all the main features of the scour process. The equilibrium scour depth obtained from the simulation agrees well with the experiments for the upstream scour hole. Some discrepancy (up to 30 %) was observed, however, for the downstream scour hole. The calculations show that the amplification of the bed shear stress around the pile in the equilibrium state of the scour process is reduced considerably with respect to that experienced at the initial stage where the bed is plane.

Shear Stress in Smooth Rectangular Open-Channel Flows

The average bed and sidewall shear stresses in smooth rectangular open-channel flows are determined after solving the continuity and momentum equations. The analysis shows that the shear stresses are function of three components: (1) gravitational; (2) secondary flows; and (3) interfacial shear stress. An analytical solution in terms of series expansion is obtained for the case of constant eddy viscosity without secondary currents. In comparison with laboratory measurements, it slightly overestimates the average bed shear stress measurements but underestimates the average sidewall shear stress by 17% when the width–depth ratio becomes large. A second approximation is formulated after introducing two empirical correction factors. The second approximation agrees very well ( R2 >0.99 and average relative error less than 6%) with experimental measurements over a wide range of width–depth ratios.

Velocity distribution in non-prismatic compound channels

River-flow modelling relies on accurate prediction of the stage–discharge relationship. Additionally, the lateral distribution of the longitudinal velocity component should be estimated for sediment transport investigations. In compound channels, the shear stress at the interface between the floodplains and the main channel strongly affects both conveyance and velocity distribution. This effect is reinforced when mass transfer occurs between subsections due to channel non-prismaticity. The stage–discharge relationship and the velocity distribution in prismatic compound channels can be computed using the lateral distribution method (LDM). The present paper investigates an extension of the LDM to non-prismatic channels. The physical meaning of the so-called secondary-current term is discussed. Numerical results are compared with previous velocity measurements in a symmetrically narrowing compound channel and to new bed shear-stress measurements in the same geometry.