On the stability of stratified quasi-geostrophic currents with vertical shear above isolated topographic features

Abstract

The nonlinear stability of stratified quasi-geostrophic background currents streaming isolated seamount on f- and β-plane is investigated. Arnol'd theory (1966) and it's implications for quasi-geostrophic flows by McIntyre and Shepherd (1987) are used. The realistic situation in the ocean when the background flow is not homogeneous and has a vertical shift in velocity, whereas the Brunt-Väisälä frequency is not constant, is considered. The hyperbolic law is used for the approximation of the Brunt-Väisälä frequency. Sufficient conditions of the stability are proved. In particularly the stability of the important type of stratified shear currents represented by two-layer flow with differently directed flow in different layers is considered. The topographic eddy in this current has the form of a vortex lens. As it was shown some of two-layer background currents are stable and hence the new type of topographic eddies in the form of a vortex lens is a stable formation. © 2008 Springer.