Numerical Modeling of 2D Wave Refraction and Shoaling

摘要

As waves propagate into shallow water area they undergo shoaling and refraction. Refraction is a bending wave phenomenon that leads the wave crest arriving at beach directed parallel to the shoreline. Shoaling is a phenomenon of increasing wave height with decreasing water depth. Shoaling and refraction are both direct consequence of energy conservation. In this paper we solve the 2D shallow water equations using the conservative finite volume method. This scheme is non dissipative, therefore it can produce shoaling coefficient correctly. Simulation of 2D plane wave above a parallel bottom contours shows that numerical wave refraction confirms the analytical wave refraction. In this way we are convinced that our scheme can produce shoaling and refraction correctly. When a wave travels over a continental shelf and further to the beach, before breaking, the wave will experience shoaling and refraction which is not homogeneous along the beach. Numerical simulation shows that a bottom sill may induce wave focusing. This wave focusing governed by offshore topography may explain the striking differences from the adjacent coastal damage.