Balanced motion of a stratified, rotating fluid induced by bottom topography

Abstract

The topographically bound, balanced motion of an incompressible, inviscid, and stratified fluid on the f-plane is studied. The potential vorticity of the fluid is specified as a positive function of its density.

For an infinite, straight bottom ridge, it is shown that a solution with constant density along the entire bottom surface is possible only when the crest height is less than a critical value, which depends on the shape of the ridge profile and on its width in comparison with the deformation radius. If the crest height exceeds the critical value, the upper part of the ridge must protrude into less dense layers above, disrupting the lowest isopycnic surfaces. The critical crest height is calculated for certain simple ridge profiles.

The situation seems to be qualitatively similar for a circular bottom topography. In this case, the critical summit height must be determined from the non-linear gradient wind equation, since the geostrophic approximation fails when the critical height is approached. Although no explicit expression for the critical height is offered, it seems plausible that its value will be smaller than for a ridge of similar profile.