The Scattering at Low Frequencies of Coastally Trapped Waves

Abstract

The scattering of coastally trapped waves is described in a particular low frequency limit where the fundamental results are independent of the relative importance of stratification and rotation in the dynamics. Progress is made possible by restricting attention to frequencies small compared to a “profile” frequency, N0H/L that estimates the combined effect of the density and shelf profiles through the product of a typical buoyancy frequency N0 and the average shelf slope (for ocean depth H and shelf width L. Combined with results on the scattering of barotropic shelf waves, the present results describe scattering irrespective of the strength of any stratification provided solely that the frequency of the motion is small compared to either the inertial frequency or the profile frequency. In all cases the transmitted wavefield follows directly by tracing an incident pressure field along coastal isobaths. Strong notification is shown to suppress scattering at all subinertial frequencies, leading to particularly simple flow fields. At moderate stratification all energy is scattered forwards. An example is given where isobath tracing determines explicitly the amount of internal wave energy that passes over a ridge abutting a coastal wall. Various flows are possible if stratification is weak. In each flow the transmitted field is given by the barotropic connection formula. If the scatterer is conservative, this is the whole field. If the scatterer is nonconservative and the incident frequency is small compared to the profile frequency, so stratification dominates locally, then energy is carried forward in a narrow, intense boundary current. Over larger distances the current disperses into an internal Kelvin wave field. If the scatterer is nonconservative but the incident frequency is large compared to the profile frequency, then energy is dissipated or reflected as short barotropic waves. It is noted briefly that the results describe how coastal energy can split at the mouths of bays and straits and may be relevant to observations of long period motions near the Gulf of California and energy propagation through Bass Strait.