Propagation of bottom-trapped waves over variable topography

Abstract

The behavior of bottom-trapped waves on a topographic slope, as they propagate towards a deeper region of constant depth, is examined using a quasi-geostrophic model. It is seen that there can be no free transmitted wave to the region of constant depth. The bottom-trapped energy is thus segregated in the region of the slope and its vicinity. The details of how this occurs are worked out for a slope shoaling towards the west. For a given frequency and meridional wavenumber, two free bottom-trapped waves can exist on the slope, with the shorter (longer) of the two having an eastward (westward) group velocity. When the short wave propagates to the region of constant depth, a reflected wave is generated. There is no transmitted wave, but a 'fringe' which decays away from the interface between the slope and the region of flat topography is produced. Over the flat topography the fringe consists of baroclinic and barotropic motions which lead to bottom-intensification in the immediate vicinity of the slope and to increasingly barotropic currents farther away.