Statistical mechanics of two-dimensional Euler equations and Jupiter's great red spot

Abstract

For the first time, we construct a statistical mechanics for the two-dimensional Euler fluid which respects all conservation laws. We derive mean-field equations for the equilibrium, and show that they are exact. Our methods ought to apply to a wide variety of Hamiltonian systems possessing an infinite family of Casimirs. We illustrate our theory by a comparison to numerical simulations of Jupiter's Great Red Spot.