Effect of Acceleration on Bottom Shear Stress in Tidal Estuaries

Abstract

A formulation specifying the bottom shear stress boundary condition for an unsteady, tidal flow model is derived through theoretical analysis. The unsteady boundary layer equation is solved for the velocity distribution adjacent to the boundary using a regular perturbation expansion. When applied to the bottom layer of the computation grid of a numerical model, the solution relates the bottom shear stress to the velocity and acceleration computed in that layer. Numerical experiments with a hypothetical homogeneous estuary indicate that the error in calculated bottom stress increases with vertical grid spacing if the logarithmic profile is used to relate bottom stress to velocity. The use of the formulation including the correction terms can significantly reduce this error and adequately specify the boundary condition in a numerical model of estuarine flow with a practical range of vertical grid spacing. The numerical experiments also show that, if the roughness height and bottom stress are estimated by fitting a logarithmic profile to the velocity distribution, they may be off by more than 100%.