The effect of ageostrophy on the stability of thin oceanic vortices

This paper examines the stability of vortices in a two-layer ocean on the f -plane. The mean depth h̄1 of the upper layer is assumed to be much smaller than the depth h̄2 of the lower layer. Using the primitive equations, we derive an asymptotic criterion for baroclinic instability of compensated (i.e. confined to the upper layer) vortices. Surprisingly, it coincides exactly with a similar criterion derived from the quasigeostrophic equations [Benilov, E.S., 2003. Instability of quasigeostrophic vortices in a two-layer ocean with thin upper layer. J. Fluid Mech. 475, 303–331]. Thus, to leading order in h̄1/h̄2, ageostrophy does not affect the stability properties of thin compensated vortices. As a result, whether a vortex is stable or not, depends on its shape, not amplitude (although the growth rate of an unstable vortex does depend on its amplitude). © 2005 Elsevier B.V. All rights reserved.