Finite-Amplitude Long Waves on Coastal Currents

Abstract

Two models of coastal currents are described that allow fully nonlinear wavelike solutions for the limit of long waves. The first model is an adaptation of a model used by Yi and Warn for finite-amplitude ?plane Rossby waves in a channel. It utilizes a particular choice of continental shelf topography to obtain a nonlinear evolution equation for long waves of finite amplitude. The second model describes the waves that form at the vorticity interface between two regions of constant potential vorticity. Again a nonlinear evolution equation is obtained for long waves of finite amplitude. For both model equations, numerical results are presented and compared with the corresponding results for the BDA equation, which is the weakly nonlinear limit for both models.