Mean field theory and coherent structures for vortex dynamics on the plane

We present a new derivation of the Onsager-Joyce-Montgomery (OJM) equilibri um statistical theory for point vortices on the plane, using the Bogoliubov -Feynman inequality for the free energy, Gibbs entropy function and Landau' s approximation. This formulation links the heuristic OJM theory to the mod ern variational mean field theories. Landau's approximation is the physical counterpart of a large deviation result, which states that the maximum ent ropy state does not only have maximal probability measure but overwhelmingl y large measure relative to other macrostates. (C) 1999 American Institute of Physics. [S1070-6631(99)01404-X].