Bragg reflection of random waves with the Boussinesq equations

Abstract

The Bragg resonant reflection of water waves propagating over a sinusoidally varying topography is investigated numerically by using a couple of ordinary differential equations derived from the Boussinesq equations. Derived governing equations are integrated with a fourth-order Runge-Kutta method. Applied topographies are focused on the shallow-water environment and intermediate depth zone, where the Boussinesq equations are suitable for describing behaviors of waves. Incident waves are random waves, which can be frequently observed in shallow-water regions. Optional shapes of incident waves are approximated with the Fourier decomposition. The Bragg reflection of random waves is simulated by using the TEXEL storm, MARSEN, ARSLOE (TMA) shallow-water spectrum in this study. Evolution and reflection of random waves are largely influenced by nonlinearity.