Equilibrium statistical mechanics of barotropic flow over finite topography

Inviscid equilibria of barotropic flows over finite-amplitude topography are determined by means of statistical mechanics, extending previous quasigeostrophic theory. Imposing constraints of energy and enstrophy conservation leads to a linear relation between equilibrium mean potential vorticity and mean transport streamfunction. This relation is tested numerically and is found to hold over a wide range of topographic amplitudes. Implications for improving parameterizations of entropy generation by eddies are discussed.