Two-dimensional turbulence above topography

Abstract

In a turbulent two-dimensional flow enstrophy systematically cascades to very small scales, at which it is dissipated. The kinetic energy, on the other hand, remains at large scales and the total kinetic energy is constant. Above random topography an initially turbulent flow tends to a steady state with streamlines parallel to contours of constant depth, anticyclonic around a bump. A numerical experiment verifies this prediction. In a closed basin on a beta-plane the solution with minimum enstrophy implies a westward flow in the interior, returning in narrow boundary layers to the north and south. This result is interpreted using a parameterization of the effects of the eddies on the large-scale flow. The numerical solution is in qualitative agreement, but corresponds to a minimum of a more complex measure of the total enstrophy than the usual quadratic integral.