Barotropic and Baroclinic Instabilities of Axisymmetric Vortices in a Quasigeostrophic Model

Abstract We investigate here the finite-amplitude evolution of isolated, axisymmetric barotropic and baroclinic vortices perturbed by an unstable normal mode, with an azimuthal wavenumber ranging between 1 and 5, in one- and two-layer quasi-geostrophic models. For the barotropic instability, the nonlinear evolution is very much dependent on the horizontal mean vorticity profile, while the baroclinic instability is less sensitive to it. Many numerical examples show that, at modest supercriticahty, perturbations with a moderate amplitude lead to a finite-amplitude stabilization. For azimuthal wavenumber 2, the stabilization behavior is oscillatory about a tripolar steady state in both the one- and two-layer models. In both models an analysis of energy transfers among azimuthal modes demonstrates the similarity of the equilibration processes. Semi-analytical techniques are under development to allow a fuller interpretation of the numerical solutions.