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By calculating the two-dimensional solutions and the second-order bifurcation analysis of the mean field equations of a two-dimensional ideal fluid, we are able to complete the phase diagram of coherent vortex formation in an annulus, which we have partially calculated in a previous paper [Phys. Rev. E 50, 2022 (1994)]. The complete phase diagram demonstrates the advantage of the statistical mechanics approach to determine the final equilibrium directly from the initial condition.

Complete phase diagram for coherent vortex formation in a two-dimensional inviscid fluid in an annulus