Coastal-Trapped Waves in a Continuously Stratified Ocean

Abstract

The theory of coastal-trapped waves is extended to include the general features of continuous density stratification, variable bottom topography, and a finite coastal wall. In the limit of a vanishing coastal wall, topographic Rossby waves are the only class of sub-inertial frequency, trapped wave motion. The stratification effect on topographic Rossby waves depends on both the local baroclinic radius of deformation and the characteristic offshore length scale of the wave motion. For intermediate density stratification, long waves are nearly depth-independent in the shelf region, and are bottom-trapped in the slope region. The topographic Rossby waves reduce to the barotropic shelf waves and the bottom-trapped waves in the limits of small and large density stratification, respectively. In the general case of comparable influences from the coastal wall and bottom slope effects, baroclinic Kelvin waves and topographic Rossby waves are eigenmodes of the system. The eigenfunctions are modified from the elementary cases, which can be discerned by their structures along the coastal and bottom bound-aries. In particular, a resonance condition is suggested, i.e., the properties of a wavemode vary with the wavenumber and stratification. For example, mode 1 is a topographic Rossby wave for small wavenumbers and it is a baroclinic Kelvin wave for large wavenumbers. Also, the high-frequency cutoff found in the barotropic theories is lost.