Ergodicity and spectral cascades in point vortex flows on the sphere.

We present results for the equilibrium statistics and dynamic evolution of moderately large [n=O(10(2)-10(3))] numbers of interacting point vortices on the sphere under the constraint of zero mean angular momentum. For systems with equal numbers of positive and negative identical circulations, the density of rescaled energies, p(E), converges rapidly with n to a function with a single maximum with maximum entropy. Ensemble-averaged wave-number spectra of the nonsingular velocity field induced by the vortices exhibit the expected k(-1) behavior at small scales for all energies.