Three-dimensional numerical simulation of laminar water wave boundary layer

Abstract

A 3-D numerical model with sigma-coordinate transformation is applied to simulate water waves and wave-induced laminar boundary layer. Unlike the previous investigations, which solved the simplified one-dimensional boundary layer equation of motion and neglected the interaction between boundary layer and outside flow, the present model solves the full Navier-stokes equations from the bottom to the free surface. The numerical results are compared to the analytical solutions and experimental data. It is found that good agreement exists for linear wave and Stokes finite amplitude wave. For cnoidal wave and solitary wave, the discrepancy is due to the deficiency of the analytical solutions, in which the first-order approximation is adopted as the free stream velocity that overestimates the near bottom velocity.