Water wave overwash of a step

Water wave overwash of a step by small steepness, regular incident waves is analysed using a computational fluid dynamics (CFD) model and a mathematical model, in two spatial dimensions. The CFD model is based on the two-phase, incompressible Navier-Stokes equations, and the mathematical model is based on the coupled potential-flow and nonlinear shallow-water theories. The CFD model is shown to predict vortices, breaking and overturning in the region where overwash is generated, and that the overwash develops into fast-travelling bores. The mathematical model is shown to predict bore heights and velocities that agree with the CFD model, despite neglecting the complicated dynamics where the overwash is generated. Evidence is provided to explain the agreement in terms of the underlying agreement of mass and energy fluxes.