Modal Analysis of Internal Wave Propagation and Scattering over Large-Amplitude Topography

Abstract

AbstractCoupled-mode equations describing the propagation and scattering of internal waves over large-amplitude arbitrary topography in a two-dimensional stratified fluid are derived. They consist of a simple set of ordinary differential equations describing the evolution of modal amplitudes, based on an orthogonality condition that allows one to distinguish leftward- and rightward-propagating modes. The coupling terms expressing exchange of energy between modes are given in an analytical form using perturbation theory. This allows the derivation of a weak-topography approximate solution, generalizing previous linear solutions for a barotropic forcing that were described in 2002 by Llewellyn Smith and Young . In addition, the orthogonality condition derived is valid for a different set of eigenmodes defined on a sloping bottom, which shows a better convergence rate when compared with the standard set of modes. The work presented here provides a useful and simple framework for the investigation of internal wave propagation in an inhomogeneous ocean, along with theoretical insight.