Instability of Surface Quasigeostrophic Vortices

Abstract

The instability of circular vortices is studied numerically in the surface quasigeostrophic (SQG) model, and their evolutions are compared with those of barotropically unstable 2D vortices. The growth rates in the SQG model evidence similarity with their barotropic counterparts for moderate radial gradients of temperature (or of vorticity in the 2D model). For stronger gradients, SQG vortices are more unstable than 2D vortices. The nonlinear, finite-amplitude evolutions of perturbed vortices provide evidence that moderately unstable, elliptically perturbed vortices form tripoles. When they are more unstable, they break into two dipoles. Weakly unstable vortices with triangular perturbations form transient quadrupoles that break; they stabilize only for large gradients of mean temperature. Finally, with square perturbations, pentapoles degenerate into dipoles, at least for the range of mean temperature gradients explored here. The analysis of nonlinear stabilizations reveals that the deformation of the vortex core and the leak of its temperature anomaly to the periphery are essential ingredients to stabilize the perturbation at finite amplitude. In conclusion, SQG vortex instability exhibits considerable similarity to the barotropic instability of 2D vortices.