Statistical mechanics of axisymmetric vortex rings

We construct maximum entropy states of a collection of interacting uniform (omega/R = const) axisymmetric vortex rings in a semiperiodic bounded volume. Following Miller [Phys. Rev. Lett, 65, 2137 (1990)] and Robert and Sommeria [J. Fluid Mech. 229, 291 (1991)], we obtain an equilibrium measure that preserves all the ideal invariants such as the total energy, total impulse, circulation, and an infinity of Casimirs. The numerical solution for a wide range of total flow energy and for given values of total circulation and total impulse is presented.