Abstract
We consider the problem of a low-frequency, two-layer, coastal Kelvin wave which impinges on a topographic ridge or valley at some angle to the coastline, with the aim of bounding the transmission of the Kelvin wave beyond the topography (or, put alternatively, of bounding the scattering of energy into topographic waves along the ridge). The width of the topographic feature is assumed to be of order the internal deformation radius. It is not necessary to solve the very complicated interaction problem near the junction of the ridge and the coastline. Instead, a simple series of eigenvalue o.d.e.'s must be solved.
The main contribution to loss of energy by the Kelvin wave comes from long waves along the ridge. Whether this loss is significant depends crucially on whether the topography is high enough to intersect a density surface (in this case, the interface between the two layers). If the topography remains solely in the lower layer, then the Kelvin wave continues with negligible loss of energy in the limit of very small frequency.
In a continuously stratified fluid, topography of any height would cut through an infinite number of density strata, so that a more realistic model would permit the topography to intersect the interface. This case is also considered, and results in a finite loss of energy from the Kelvin wave to topographic waves along the ridge (as in the one-layer reduced gravity case considered in an earlier paper). As a rough guide, the amplitude of the transmitted wave is reduced by an amount approximately equal to the fractional depth of the fluid blocked by the topography. Thus, models that do not permit topography to break through a density interface give qualitatively different answers from those which do—which should be considered when second-generation ocean models are being consructed.
It is found that, even using a supercomputer, available numerical resolution cannot adequately represent the topographically trapped waves, so topographical scattering processes will inevitably be badly misrepresented in numerical models. The case of a continuously stratified fluid is also briefly considered, although solutions would be considerably more complicated to produce.
