Abstract
The equilibrium statistics of a large number of two-dimensional point vortices of arbitrary sign, evolving in an arbitrary domain closed by a bounded curve, are investigated in the microcanonical formulation. The resulting differential equations for the spatial distribution function of the vortices are numerically integrated in various cases and the associated thermodynamic functions are computed. The case of a globally neutral, spatially uniform distribution is particularly studied for its connections with two-dimensional turbulence and the use of the random phase approximation. Some numerical simulations of vortex motion in a circular domain support the theoretical development.
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