Interactions between geostrophic eddies and the mean circulation over large-scale bottom topography

The presence of intense recirculations in the abyssal oceans has been revealed by both observations and modeling studies. A suggested mechanism is the interactions between geostrophic eddies and the mean circulation in the presence of variable bottom topography. Here such interactions are studied using an idealized numerical model, consisting of a single active abyssal layer overlying variable bottom topography. An initial ensemble of eddies quickly organize themselves to generate a mean anticyclonic circulation around seamounts. During this rearrangement energy is approximately conserved while potential enstrophy is dissipated, consistent with previous studies of geostrophic turbulence. A parameterization of geostrophic eddies is formulated in terms of an eddy-induced transport, U*. Based on results from the eddy-resolving experiments it is hypothesized that U* should dissipate potential enstrophy while conserving energy. Using variational methods, a solution for U* is found that dissipates potential enstrophy most efficiently, subject to energy being conserved. For a shallow water layer, it is shown that U* 5 k[del (Q(2)/2) + lambda delB], where Q is the potential vorticity, B is the Bernoulli potential, kappa (x, y) is an arbitrary function that describes the efficiency with which eddies can rearrange fluid within a layer, and lambda is a Lagrange multiplier that is determined through the energetic constraint. Results from a coarse resolution version of the model using the parameterization compare favorably with those obtained using the eddy-resolving model.