An amplitude equation for surface gravity wave-topography interactions

Abstract

We derive an amplitude equation that captures the effect of small but arbitrary topography on small-amplitude surface gravity waves. The robustness of this reduced model is demonstrated by numerical simulations that compare it with the fully nonlinear water wave equations. The amplitude equation is seen to accurately capture intricate and complex wave dynamics, compared with the fully nonlinear equations, while being much faster than the latter. Consequently, the model offers great potential for various surface wave-topography interaction investigations, especially when a large number of simulations are needed to obtain wave statistics, a process that is much slower if attempted using the full set of equations.