Phase diagram for coherent vortex formation in the two-dimensional inviscid fluid in circular geometries

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Abstract
We calculate the equilibrium states of a two-dimensional inviscid fluid in disk and annular geometries using the mean field equations that respect all conservation laws of the Euler equations. Axisymmetric vorticity distributions and their bifurcations to asymmetric solutions are calculated for a wide range of system parameters. Approximate zero-temperature compact vortices are also constructed and compared to symmetric states. From these results, the parameter ranges leading to the formation of a coherent vortex by the long time evolution from given initial conditions can be predicted without knowledge of the intervening dynamics. Applications to models of Jupiter’s great red spot and experiments on one-component plasmas in a magnetic field are discussed.