Vortex dynamics and zonal flows

Two-dimensional vortex dynamics have been studied in plasmas by exploiting the analogy between fluid velocity and the $E×B$ drift velocity. The analogy extends to geophysical flows by including physics that mimic zonal flows, dissipation and the β-effect due to the variation in the Coriolis parameter. Vortices with the same sign as the ambient zonal shear are stable, while opposite-signed vortices fragment. Rules for vortex merger derived by maximizing entropy or minimizing enstrophy do not work for vortices embedded in zonal flows. New rules based on the minimization of energy hold. When zonal flows are not imposed, and the flow is forced at small scales, large, coherent jet streams or eddies form that co-exist with turbulence. Their sizes are determined by an energy balance, not the length scales of the forcing or boundaries. The motivation for this work is to understand atmospheric and ocean vortices: Gulf stream meanders and eddies, the Antarctic ozone hole, the jet streams of Earth and Jupiter, and the Jovian Great Red Spot and White Ovals.