On coastal trapped waves at low latitudes in a stratified ocean

Abstract

Results from idealized ocean models indicate that equatorially trapped baroclinic waves incident on an eastern boundary may be partially transmitted north and south along the coast as boundary-trapped internal Kelvin waves. The offshore scale of the coastal internal Kelvin waves is the internal Rossby radius of deformation δR, which decreases as the Coriolis parameter f increases. The effect of the presence of a continental slope of width Ls, along a north–south oriented coastline, on the poleward propagation of coastal trapped internal Kelvin waves is studied in a two-layer β-plane model. The waves propagate from regions near the equator where δR > Ls to mid-latitudes where δR < Ls. It is assumed that f varies slowly on the alongshore scale of the waves L, that L [Gt ] Ls, and that either the topographic slope is weak or that the upper-layer depth is small compared to the lower-layer depth. All of the coastal trapped waves present in the model are non-dispersive. For most values of f, the cross-shelf eigen-functions consist of the internal Kelvin wave and an infinite set of continental shelf waves whose vertical structure depends on δR/Ls. For δR/Ls [Gt ] 1, the shelf waves are bottom trapped while for δR/Ls [Lt ] 1 they are barotropic. The wave speeds Cn of the shelf waves vary linearly with f, whereas the wave speed c0 of the internal Kelvin wave is independent of f. As f increases through critical values fCn, where Cn approaches C0, the phase speeds and the eigenfunctions vary so that the eigenfunctions represent a different type of wave on either side of fCn. In the slowly-varying approximation, the alongshore energy flux in each eigenfunction is a constant. It follows that an internal Kelvin wave which has a wavelength short enough that the slowly-varying approximation remains valid and which propagates poleward from the equatorial region where f < fC1 will transform into a shelf wave, at values of f near fC1, and will continue propagation poleward in that form. As a result, coastal trapped baroclinic disturbances may be able to propagate efficiently from the equatorial region to mid-latitudes where they may take the form of barotropic shelf waves.