Shear velocity estimates in rough‐bed open‐channel flow

Abstract

Shear velocity u * is an important parameter in geophysical flows, in particular with respect to sediment transport dynamics. In this study, we investigate the feasibility of applying five standard methods [the logarithmic mean velocity profile, the Reynolds stress profile, the turbulent kinetic energy (TKE) profile, the wall similarity and spectral methods] that were initially developed to estimate shear velocity in smooth bed flow to turbulent flow over a loose bed of coarse gravel (D 50 = 1Á5 cm) under sub-threshold conditions. The analysis is based on quasi-instantaneous three-dimensional (3D) full depth velocity profiles with high spatial and temporal resolution that were measured with an Acoustic Doppler Velocity Profiler (ADVP) in an open channel. The results of the analysis confirm the importance of detailed velocity profile measurements for the determination of shear velocity in rough-bed flows. Results from all methods fall into a range of AE 20% variability and no systematic trend between methods was observed. Local and temporal variation in the loose bed roughness may contribute to the variability of the logarithmic profile method results. Estimates obtained from the TKE and Reynolds stress methods reasonably agree. Most results from the wall similarity method are within 10% of those obtained by the TKE and Reynolds stress methods. The spectral method was difficult to use since the spectral energy of the vertical velocity component strongly increased with distance from the bed in the inner layer. This made the choice of the reference level problematic. Mean shear stress for all experiments follows a quadratic relationship with the mean velocity in the flow. The wall similarity method appears to be a promising tool for estimating shear velocity under rough-bed flow conditions and in field studies where other methods may be difficult to apply. This method allows for the determination of u * from a single point measurement at one level in the intermediate range (0Á3 < h < 0Á6).

Laboratory studies on bedload transport under unsteady flow conditions

“…Suitability of this method was demonstrated by Mrokowska et al (2016) in selected experimental datasets. This paper confirmed that the results of Savitzky-Golay filter were compatible with those obtained by approximating the data with a difference quotient and then by Fourier Transform filtering that is very popular in unsteady flow data smoothing (Bagherimiyab and Lemmin, 2013;Rowiński and Czernuszenko, 1998;Song and Graf, 1996). Nonetheless, in this case, Savitzky-Golay filter appeared to be superior to the other one thanks to its straightforward application; it also produced much fewer oscillations.…”

An experimental study of mean and turbulent flow in a 180 degree sharp open channel bend: Secondary flow and bed shear stress

“…In this table, represents the cross section at which the measurement is carried out, L the distance from the outer bank, R the radial distance from the bend center, and X and Y the coordination of the points in x-and y-directions in Cartesian system sequentially. It can be seen at some points in the field (e.g., B, D, F, I, S, U, W, Z, Bagherimeyab et al (2008), and Bagherimiyab and Lemmin (2013) have conducted studies on the difference in the Reynolds shear stress method at two different layers near the bed by investigating straight channels, and hence reported an increase in bed shear stress from water surface to bed; Whereas, it was observed that the deeper the depth from the bed, the greater the Reynolds stress. According to the data given in Table 2, in most of the presented points (note the stress values at H, K, M, N, O, Q, R, T, V, X, HA, KA, and QA Points), the bed shear stress distribution in the 180 degree sharp bend in depth has either become disorderly or experienced increased shear stress.…”

How does the bed surface impact low‐magnitude bedload transport rates over gravel‐bed rivers?

“…In some studies, is deduced from local values of bed shear stress , which are generally computed from the velocity or turbulent profiles obtained with ADV or PIV measurements (Biron et al. ; Bagherimiyad and Lemmin, ). These measurements are time consuming and not adapted for experiments in unsteady flows.…”