Stability of Multilayer Ocean Vortices: A Parameter Study Including Realistic Gulf Stream and Agulhas Rings

Abstract

Ocean rings, when isolated from major ocean currents, can have life spans on the order of years. This study focuses on the stability of such isolated ocean rings. Assuming axisymmetric basic-state profiles, the linear stability of a wide variety of rings is analyzed by examining the properties of the modes to which they become unstable and the associated energy conversions. Earlier studies have indicated that corotating rings, with a large barotropic component, are far less unstable than counterrotating ones. This sharp contrast between co- and counterrotating rings appears to be a consequence of the choice for a radial profile of the azimuthal velocity that decays only gradually on the ring's outer flank. For more realistic velocity profiles, co- and counterrotating rings have similar growth rates. Nearly compensated rings, that is, those with a weak flow in the deepest layer, are found to be the least unstable ones. In this paper, the problem for warm-core rings with a Gaussian profile is first revisited in a two-layer setup. A systematic survey of the sensitivity of the results for this standard case with respect to various ring parameters, such as the stratification, ring width, and, in particular, the radial profile of the azimuthal velocity, is presented. Besides exponential profiles, as used in earlier studies, the stability of rings with a core in solid-body rotation is also examined. Subsequently, more realistic cases are considered by discussing the stability of ocean rings designed as fits to an observed cold-core Gulf Stream ring and a warm-core Agulhas ring. Minimal growth rates for the latter rings are very large: the calculated e-folding timescales are about one week.