Coastally trapped waves in a stratified ocean

Abstract

A new technique for determining coastally trapped wave modes in a stratified ocean is developed through the formulation of a vorticity equation in terms of the mass transport streamfunction. Density perturbations enter the equation through a term related to the generation of relative vorticity and for the weak stratification considered, are approximately related to the cross-isobath, depth-averaged flow: the equation obtained is valid provided that (l "SUB H" H *N "SUB o" /f) "SUP 2" 1, where N "SUB o" and f are the buoyancy and Coriolis frequencies, H * one-half the local depth and l "SUB H" the horizontal wavenumber. Analytical solutions for the wave modes are presented which simply show that phase speed increases with the degree of stratification and a physical explanation for this effect is given. The modal velocity eigenfunctions, are also determined and shown to compare favourably with more exact results obtained from extant numerical programmes for wave mode calculation. The formalism developed may also prove of use in extending previous barotropic studies, including the generation and scattering of coastally trapped waves in stratified seas. (A)