Abstract
We examine the stability of a quasi-geostrophic vortex in a two-layer ocean with a
thin upper layer on the f-plane. It is assumed that the vortex has a sign-definite swirl
velocity and is localized in the upper layer, whereas the disturbance is present in both
layers. The stability boundary-value problem admits three types of normal modes:
fast (upper-layer-dominated) modes, responsible for equivalent-barotropic instability,
and two slow baroclinic types (mixed- and lower-layer-dominated modes). Fast modes
exist only for unrealistically small vortices (with a radius smaller than half of the
deformation radius), and this paper is mainly focused on the slow modes. They
are examined by expanding the stability boundary-value problem in powers of the
ratio of the upper-layer depth to the lower-layer depth. It is demonstrated that the
instability of slow modes, if any, is associated with critical levels, which are located at
the periphery of the vortex. The complete (sufficient and necessary) stability criterion
with respect to slow modes is derived: the vortex is stable if and only if the potential-vorticity
gradient at the critical level and swirl velocity are of the same sign. Several
vortex profiles are examined, and it is shown that vortices with a slowly decaying
periphery are more unstable baroclinically and less barotropically than those with a
fast-decaying periphery, with the Gaussian profile being the most stable overall. The
asymptotic results are verified by numerical integration of the exact boundary-value
problem, and interpreted using oceanic observations.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
26 articles.
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