A Comparative Analysis of Logarithmic Law, Reynolds Stress, and Turbulence Kinetic Energy Methods for Bed Shear Stress Estimation in Complex Open-Channel Flow

Numerous indirect methods for estimating the bed shear stress using velocity or turbulent stress profiles have been suggested in previous research. Although these methods have proven effective for simple boundary-layer-type flows, their efficacy in complex flow scenarios remains largely unexplored. This study aimed to evaluate the predictive capabilities of three popular indirect bed-shear-stress estimation methods-the logarithmic law, Reynolds shear stress (RSS), and turbulence kinetic energy (TKE) techniques-in a complex flow environment involving an obstacle in an open channel, producing massive flow separation and unsteady vortex shedding. To circumvent the difficulties of direct bed shear-stress measurements, the reference bed shear stress was obtained from a high-resolution wall-resolving large-eddy simulation (LES) data set. The key findings of this study are as follows: First, the logarithmic law and TKE methods were effective only in regions where the streamlines were almost parallel to the primary flow direction. Second, the ratio of the bed shear stress to TKE varied significantly in space in complex-flow regions, rendering TKE methods virtually ineffective in these areas. Third, the RSS methods successfully reproduced the LES-computed bed shear stress distributions, both qualitatively and quantitatively. Fourth, the accuracy of the RSS methods was influenced by two critical factors: (a) the incorporation of the transverse RSS component in the RSS extrapolation and (b) the selection of extrapolation techniques. Finally, this study recommends the use of RSS methods employing two-point extrapolation for bed shear-stress estimation in complex flows. Indirect methods were tested to estimate bed shear stress in a complex flow setting using high-resolution large-eddy simulation data Log-law and turbulence kinetic energy methods were effective for straight flow regions but unsuitable for regions with complex flows The Reynolds shear stress method using two-point extrapolation with a lower point close to the bed was the most effective