This article applied a general laminar flow model to simulate the cnoidal wave generation and its induced oscillatory flow over a wavy bed. The numerical model based on the stream function-vorticity (ψ −ω) formulation by the finite analytic (FA) discretization method is used. The time-evolving boundary-fitted grid system is adopted to conform with the transient free surface and the moving wave plate all the time, where the fully nonlinear conditions are treated. In this study, the cnoidal waves developed to its final permanent waveform on a flat bottom were generated by imposing the wave plate in motion. We thus investigated those unsteady near-bottom flow characteristics influenced by the roughness of wavy bottom. Numerical results are compared with analytical solutions presented by Tanaka et al. (1998) and experimental data conducted by Fredsøe et al. (1999). From the viscous flow near the wavy wall due to vortex shedding and flow separation, the interacting flow pattern, the oscillatory boundary-layer characteristics, and flow particle trajectories were investigated in detail herein.
Flat sea bed is rare in nature. The hydraulic roughness, or equivalent Nikuradse roughness, exhibits its scale to be the order of 100 to 200 grain diameters for a flat mobile sand bed in an oscillatory sheet flow from the available friction and energy dissipation data (Nielsen, 1992). This is surprisingly different from the corresponding roughness, which is generally one order of magnitude smaller, to a steady sheet flow. As covered by sedimentary material of a wide range of grain sizes, the sea bed possesses complicated geometrical structures of many different shapes. These structures, including for example, bars, dunes, ripples, etc., keep interacting with the flow field in several different ways. Wavy beds (or sea bed ripples) are present on sand beds in shallow water waves, and are formed by the to-and-fro flow induced by wave motion above the bed.
