On coastal trapped waves at low latitudes in a stratified ocean

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 δ R , which decreases as the Coriolis parameter f increases. The effect of the presence of a continental slope of width L s , 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 δ R > L s to mid-latitudes where δ R < L s . It is assumed that f varies slowly on the alongshore scale of the waves L , that L [Gt ] L s , 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 δ R / L s . For δ R / L s [Gt ] 1, the shelf waves are bottom trapped while for δ R / L s [Lt ] 1 they are barotropic. The wave speeds C n of the shelf waves vary linearly with f , whereas the wave speed c 0 of the internal Kelvin wave is independent of f . As f increases through critical values f Cn , where C n approaches C 0 , the phase speeds and the eigenfunctions vary so that the eigenfunctions represent a different type of wave on either side of f Cn . 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 < f C1 will transform into a shelf wave, at values of f near f C1 , 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.