Bed Shear Stress

Bed shear stress is a fundamental variable in river studies to link flow conditions to sediment transport. It is, however, difficult to estimate this variable accurately, particularly in complex flow fields. This study compares shear stress estimated from the log profile, the depth-slope product and outputs from a two-dimensional hydraulic model. Vertical velocity profile observations from Megech River (one of the main water sources flowing into Lake Tana, upper Blue Nile Basin, Ethiopia) using SEBA Mini current meter M1attached with SEBA Signal counter Z6-SEBA HAD under typical field conditions are used to evaluate the precision of different methods for estimating local boundary shear stress from velocity measurements. A comparison of the shear stress distributions derived using the two-dimensional hydraulic model and with those estimated using the 1D reach-averaged equation (i.e. the depth-slope product) shows a close correspondence. Mean shear stresses determined using local depth and mean channel slope are roughly comparable to those determined for the same data using local predictions of both depth and energy slope. As the overall mean shear stress provides a useful index of flow strength, this comparison suggests a good level of confidence in using the reach averaged one-dimensional equation, for which data can easily be collected from cross sectional surveys. However, the variance of the modelled shear stress distribution shows some differences to that calculated using the mean channel slope. Although such numerical models are limited to channel types adhering to model assumptions and yield predictions only accurate to ̴ 20-30%, they can provide a useful tool for river-rehabilitation design and assessment, including spatially diverse habitat heterogeneity and sediment transport studies.

With the assumption that the bed shear stress fluctuates in a lognormal fashion, the probability density function (pdf) of the standardised bed shear stress is derived as a function of the relative shear stress intensity. The pdf is more skewed with larger relative intensities, but approaches a Gaussian function when the relative intensity is small. The computed pdf agrees well with the reported experimental data for flows over a smooth boundary. The higher-order moments of the bed shear stress, skewness and kurtosis, are shown analytically to be also dependent on the relative intensity. The theoretical dependencies are then compared to a number of measurements available in the literature. The Reynolds number effect on the relative intensity is also discussed.

Whether or not a sediment particle is entrained from a channel bed is associated with both average bed shear stress and shear stress fluctuation, the latter being flow-dependent and also related to bed irregularities. In the first part of this study, a preliminary analysis of possible fluctuations induced by bed roughness is presented for the case of an immobile plane bed comprised of unisized sediments. The result shows that the roughness-induced variation is generally comparable to that associated with near-bed turbulence, and both variations can be approximated as log-normal in terms of probability density distribution. The bed particle mobility is then analyzed by considering the effects of shear stress fluctuations. The relevant computations demonstrate that with increasing shear stress fluctuations, the probability of the mobility of a bed particle may be enhanced or weakened. For the case of low sediment entrainment, the probability is increased by turbulence. However, the probability may be reduced by the shear stress fluctuation if the average bed shear stress becomes relatively higher. This study shows that the critical condition for initial sediment motion could be overestimated if the Shields diagram is applied for the condition of flows with high turbulence intensities.

Bed shear stress is a fundamental variable in river studies to link flow conditions to sediment transport. It is, however, difficult to estimate this variable accurately, particularly in complex flow fields. This study compares shear stress estimated from the log profile, drag, Reynolds and turbulent kinetic energy (TKE) approaches in a laboratory flume in a simple boundary layer, over plexiglas and over sand, and in a complex flow field around deflectors. Results show that in a simple boundary layer, the log profile estimate is always the highest. Over plexiglas, the TKE estimate was the second largest with a value 30 per cent less than the log estimate. However, over sand, the TKE estimate did not show the expected increase in shear stress. In a simple boundary layer, the Reynolds shear stress seems the most appropriate method, particularly the extrapolated value at the bed obtained from a turbulent profile. In a complex flow field around deflectors, the TKE method provided the best estimate of shear stress as it is not affected by local streamline variations and it takes into account the increased streamwise turbulent fluctuations close to the deflectors. It is suggested that when single-point measurements are used to estimate shear stress, the instrument should be positioned close to 0•1 of the flow depth, which corresponds to the peak value height in profiles of Reynolds and TKE shear stress.

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 b R e b~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.

New experimental measurements of bed shear under solitary waves and solitary bores that
represent tsunamis are presented. The total bed shear stress was measured directly using a
shear cell apparatus. The solitary wave characteristics were measured using ultrasonic
wave gauges and free stream velocities were measured using an Acoustic Doppler
Velocimeter. The measurements were carried out in laminar and transitional flow regimes
(¡«104 < Re < ¡«105). This sort of data is sparsely available in literature. In the absence of
direct measurements, shear stress is indirectly estimated using velocity profiles or is
inferred using standard friction factors. However, this indirect method has its limitations,
e.g., under unsteady hydrodynamic conditions and relatively large roughness the
assumptions of both approaches are no longer valid. More than 168 experimental runs
comprising solitary waves and bores were carried out over a smooth flat bed with wave
height to water depth ratio varying between 0.12 and 0.69. Analytical modeling was
carried out to predict shear stresses using Fourier and convolution integration methods.
This paper presents comparison of the measured and predicted bed shear stress or skin
friction stress, together with estimates of traditional wave friction factors. Overall, the
models can predict the bed shear stress with a satisfactory degree of accuracy.

Bed shear stress is a fundamental variable in river studies to link flow conditions to sediment transport. It is, however, difficult to estimate this variable accurately, particularly in complex flow fields. This study compares shear stress estimated from the log profile, drag, Reynolds and turbulent kinetic energy (TKE) approaches in a laboratory flume in a simple boundary layer, over plexiglas and over sand, and in a complex flow field around deflectors. Results show that in a simple boundary layer, the log profile estimate is always the highest. Over plexiglas, the TKE estimate was the second largest with a value 30 per cent less than the log estimate. However, over sand, the TKE estimate did not show the expected increase in shear stress. In a simple boundary layer, the Reynolds shear stress seems the most appropriate method, particularly the extrapolated value at the bed obtained from a turbulent profile. In a complex flow field around deflectors, the TKE method provided the best estimate of shear stress as it is not affected by local streamline variations and it takes into account the increased streamwise turbulent fluctuations close to the deflectors. It is suggested that when single-point measurements are used to estimate shear stress, the instrument should be positioned close to 0•1 of the flow depth, which corresponds to the peak value height in profiles of Reynolds and TKE shear stress.