Modal analysis of internal wave propagation and scattering over large-amplitude topography

Abstract

Coupled-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 mode are given in a analytical form using perturbation theory. This allows the derivation of a weak-topography approximate solution, generalizing previous linear solutions for a barotropic forcing (Llewellyn Smith and Young 2002). In addition, the orthogonality condition derived is valid for a different set of eigenmode defined on a sloping bottom, which shows a better convergence rate compared to the standard set of modes. The present work provides a useful and simple framework for the investigation of internal wave propagation in an inhomogeneous ocean, along with theoretical insight.