Can Large Oceanic Vortices Be Stable?

Abstract

Observations show that radii of oceanic eddies often exceed the Rossby radius of deformation, whereas theoretical studies suggest that such vortices should be unstable. The present paper resolves this paradox by presenting a wide class of large geostrophic vortices with a sign‐definite gradient of potential vorticity (which makes them stable), in an ocean where the density gradient is mostly confined to a thin near‐surface layer (which is indeed the case in the real ocean). The condition of a thin “active” layer is what makes the present work different from the previous theoretical studies and is of utmost importance. It turns out that without it, the joint requirement that a vortex be large and have a sign‐definite potential vorticity gradient trivializes the problem by eliminating all vortices except nearly barotropic ones.

Topographic Stabilization of Ocean Rings

“…To develop fully baroclinic solutions for large‐scale vortices, Benilov (2018) proposed an asymptotic model in which the strongly stratified active surface layer was placed above a deep, nearly motionless, and more homogeneous abyssal layer. This configuration allowed for vortices with radii exceeding the radius of deformation to remain stable and thereby helped to resolve the stability conundrum.…”

Three-dimensional quasi-geostrophic vortices with vanishing amount of potential vorticity anomaly

“…Though this paradox has been considered previously in several theoretical and numerical ways, 5,[8][9][10] the possible reasons that might explain the stability of these ocean vortices are still under discussion. 4,9,11,12 In particular, some piecewise-constant neutral vorticity monopoles were found to be stable when the outer ring was sufficiently thick relative to the vortex core, 9 while Benilov 11 found stable baroclinic solutions dividing the ocean into a thin surface and a thick deep layer. Gulliver and Radko 12 discovered that, independent of the sign-reversal potential vorticity gradients, the bottom topography stabilizes the vortices.…”