Coastal-trapped Wave Scattering into and out of Straits and Bays

Abstract

A theory for the generation of coastal-trapped waves (CTWs) by an oscillatory coastal flux through a strait is extended so as to make velocity, pressure and energy flux everywhere continuous. This development is achieved through the inclusion of Kelvin and Poinearé wave modes in a match for pressure leading to a system of linear equations for the unknown amplitudes. A Kelvin wave incident on the eastern mouth of Bass Strait for example is shown to preferentially scatter energy into CTW modes 2 and 1 on the shelf, as well as driving a Poincaré wave field that results in a velocity jet trapped to the Victorian coast. Such coastal velocity jets are also a feature of the scattering of CTWs incident on a strait. For a mode n incident CTW, the fraction of net energy flux that enters the strait is also shown to be well approximated by h0bn2 where h0 is the strait depth and bn coupling coefficient. The scattering of the remaining energy among other CTW modes is detailed and shown to become larger as the incident mode number or frequency is increased. Similar results are also found for the scattering by a bay and while the net energy flux into a bay will in general be near zero, the coastal jets on each side of the bay may significantly effect the local circulation.