Bed shear stress and turbulence characteristics under unsteady flows

Abstract

A series of laboratory experiments were conducted to investigate the turbulence and bed shear stress characteristics under solitary waves and dam break flows. The Laser Doppler velocimetry (LDV) systems were used to measure the velocity profile very near the bottom. A method was developed to find the wave-induced bed shear stress over a smooth bed from the measured velocities within or near the viscous sub-layer. A unified 2D numerical model was developed to simulate the entire flow field from bottom to free surface. The model solves the Reynolds Averaged Navier-Stokes (RANS) equations, with the BSL k-ω turbulence closure model that can capture the turbulence inside and outside of boundary layer. The numerical results were compared to the experimental data and available theories in terms of free surface displacement, mean velocity, turbulence intensity, and bed shear stress. Discussions were made on the effects of the turbulence characteristics on changing the patterns of mean velocity profile and bed shear stress. Further efforts were made to revisit the existing boundary layer theories, trying to quantifying the role of free stream velocity and acceleration as well as eddy viscosity in modifying the response properties of the bed shear stress under unsteady flows. A formula was proposed to calculate the instantaneous bed shear using the free stream velocity and acceleration. The results using the present formula are compared to those from the earlier works for solitary wave, dam break wave, and saw-tooth wave.