Abstract
This paper presents a model which yields examples of stable vortices in a continuously stratified rotating fluid, thus providing a possible explanation of the observed longevity of oceanic eddies. The model is based on two assumptions. Firstly, the ocean comprises a thin upper (active) layer and a thick lower (passive) one, with large and small vertical gradients of density, respectively. Secondly, the Rossby number is small, justifying the use of the geostrophic and quasi-geostrophic approximations for the active and passive layers (the two are treated differently because the vortex-induced displacement of the isopycnal surfaces is comparable to the depth of the active layer, but is much smaller than that of the passive one). Using the asymptotic equations derived on the basis of the above assumptions, we prove a stability criterion and thus identify a class of stable vortex profiles. This class is much wider than the one following from the standard requirement that the potential vorticity be monotonic in the whole bulk of the fluid.
Highlights
It has been known since the 1977 paper by Lai and Richardson [1] that oceanic eddies can exist for years, but most of the subsequent theoretical work [2,3,4,5,6,7,8,9,10,11] seems to suggest that vortices with "real"
The first step toward resolving the paradox was made in 1995 by Dewar and Killworth [12]. They examined a Gaussian vortex in the upper layer of a two-layer ocean and a co-rotating flow in the lower layer: it turned out that a relatively weak “deep flow” could stabilize the vortex
It generalizes the class discovered in [14,15] and has the potential to explain the observed longevity of oceanic eddies
Summary
It has been known since the 1977 paper by Lai and Richardson [1] that oceanic eddies can exist for years, but most of the subsequent theoretical work [2,3,4,5,6,7,8,9,10,11] seems to suggest that vortices with "real". A different approach was used in [14,15]: these papers examined the deep flow that makes the lower-layer potential vorticity (PV) uniform and showed that it stabilizes all vortices, not just the Gaussian one It was argued in [14,15] that “deep flow with uniform PV arises naturally below oceanic eddies, as suggested by the fact that most of them are shed by unstable frontal currents. In order to model real oceanic eddies, one should instead use a continuous approximation This problem was first addressed in [16], where it was shown that a vortex with a constant PV value, surrounded by fluid with a different (and constant) PV value, is stable.
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