Direct Calculation of Low-Frequency Coastally Trapped Waves and Their Scattering

Abstract

A new, direct numerical method is proposed for finding the phase speeds and pressure fields of low-frequency nondispersive coastally trapped waves in a continuously stratified flow. The usual two-dimensional problem is reduced to a one-dimensional integral equation across the shelf. The structure of the problem depends on the strength of the stratification measured by the parameter B = NoD/fL for typical buoyancy frequency No, depth D, Coriolis parameter f, and shelf width L. Asymptotic approximations are given for both strong (B?1) and weak (B ? 1) stratification, and attempts are made to provide analytical expressions for the phase speeds over the whole range of B using Padé approximations. These compare well with the numerical results. Examples are given using a number of different topographies and the conditions for which mode kissing between baroclinic and barotropic wave modes occur are discussed. The method is particularly suited to evaluating the scattering for waves moving from one topography to another.