On the Stability of Oceanic Rings

Abstract

Oceanic rings tend to have length scales larger than the deformation radius and also to be long-lived. This latter characteristic, in view of the former, is particularly curious as many quasigeostrophic and primitive equation simulations suggest such eddies are quite unstable. Large eddies eventually break into smaller deformation scale vortices, with the attendant production of considerable variability.Here it is argued that the stability characteristics of oceanic eddies and rings are sensitive to the presence of deep flows. In particular, eddies in which the deep flow is counter to the sense of the shallow flows are often more unstable than eddies with no deep flow, while eddies with circulations in the same sense as the shallow circulation can experience an enhanced stability. For a given vertical shear, oceanic eddy stability can vary dramatically. (This is in contrast to quasigeostrophic theory, where stability properties are largely determined by vertical shear.) The onset of these mechanics is quite pronounced for Gaussian oceanic eddies. Linear ''f''-plane stability calculations reveal a marked suppression of unstable growth rates for warm corotating eddies with relatively weak deep flows. Cold eddies also experience a suppression of instability in the corotating state, although relatively weak unstable modes have been found. Comparisons of f- and beta-plane numerical primitive equation experiments support these results, as well as demonstrate some relevant limitations. Finally, studies of dipolar eddies and non-Gaussian circular eddies are used to examine the generality of the results, We suggest such stability considerations may be partially responsible for the observed long lives of oceanic rings.An examination of the unstable normal modes from the f-plane model demonstrates an intimate coupling between the suppression of instability and the appearance of multiple critical layers. The normal-mode energetics are used to demonstrate the role of upgradient momentum fluxes at the points of stabilization, and a heuristic argument involving critical layers is given.