Numerical hybrid grid for cnoidal wave generation and induced separated flow over a wavy bed

A simple but effective hybrid grid method is proposed to solve a two-dimensional, multiscale, moving-boundary flow problem. Two unsteady flows of different length scales and degrees of boundary movability are involved in the numerical simulation: (1) the generation and propagation of cnoidal waves, and (2) the induced oscillatory boundary-layer flow over a ripple bottom. For wave generation by a given motion pattern of waveplate, the fully nonlinear, free-surface conditions are applied to get the flow solution in a moving boundary-fitted grid. The generated cnoidal wave is developed to its permanent form after five periods without introduction of a wave theory. On the other hand, under nonlinear wave motion, the thin oscillatory boundary layer with intermittent separation around the wavy solid boundary is resolved by a very fine and stationary grid. The unified hybrid grid enables the authors to carry out the detailed flow analysis and track particle trajectories in this study.