Finite-amplitude evolution of two-layer geostrophic vortices

Abstract

The finite-amplitude evolution of circular two-layer quasi-geostrophic vortices with piecewise uniform potential vorticity in each layer (also termed ‘heton’ clouds by Hogg & Stommel 1985a and Pedlosky 1985) is studied using the contour dynamics method. The numerical investigations are preceded by a linear stability analysis which shows the stabilizing influence of deepening the lower layer. Net barotropic flow may be either stabilizing or destabilizing. The contour dynamics calculations for baroclinic vortices show that supercritical (i.e. linearly unstable) conditions may lead to explosive break up of the vortex via the generation of continuous hetons at the cloud boundary. The number of vortex pairs is equal to the azimuthal mode number of the initial disturbance. An additional weakly supercritical regime in which amplitude vacillation occurs, but not explosive growth, is identified. Vortices with net barotropic circulation behave similarly except that the layer with vorticity opposite to the barotropic circulation will break up first. Strong barotropic circulation can inhibit the development of hetons. The stronger layer may eject thin filaments, but remain mostly intact. Calculations for initial conditions composed of several unstable modes show that the linearly most unstable mode dominates at finite amplitude.