PHASE-DIAGRAM FOR COHERENT VORTEX FORMATION IN THE 2-DIMENSIONAL INVISCID FLUID IN CIRCULAR GEOMETRIES

We calculate the equilibrium states of a two-dimensional inviscid flui d in disk and annular geometries using the mean field equations that r espect all conservation laws of the Euler equations. Axisymmetric vort icity distributions and their bifurcations to asymmetric solutions are calculated for a wide range of system parameters. Approximate zero-te mperature compact vortices are also constructed and compared to symmet ric states. From these results, the parameter ranges leading to the fo rmation of a coherent vortex by the long time evolution from given ini tial conditions can be predicted without knowledge of the intervening dynamics. Applications to models of Jupiter's great red spot and exper iments on one-component plasmas in a magnetic field are discussed.