A simple model of eddy saturation

A simple model is developed for eddy saturation of the Antarctic Circumpolar Current (ACC): the relative insensitivity of its volume transport to the magnitude of the surface wind stress in ocean models with explicit eddies. The simple model solves prognostic equations for the ACC volume transport and the eddy energy, forming a 2-dimensional nonlinear dynamical system. In equilibrium, the volume transport is independent of the surface wind stress but scales with the bottom drag, whereas the eddy energy scales with the wind stress but is independent of bottom drag. The magnitude of the eddy energy is controlled by the zonal momentum balance between the surface wind stress and eddy form stress, whereas the baroclinic volume transport is controlled by the eddy energy balance between the mean-to-eddy energy conversion and bottom dissipation. The theoretical predictions are confirmed in eddy-resolving numerical calculations for an idealised reentrant channel. The results suggest that the rate of eddy energy dissipation has a strong impact not only the volume transport of the ACC, but also on global ocean stratification and heat content through the thermal wind relation. Moreover, a vital ingredient in this model is a relation between the eddy form stress and eddy energy derived in the eddy parameterisation framework of Marshall et al. (2012, J. Phys. Oceanogr.), offering the prospect of obtaining eddy saturation in ocean models with parameterised eddies.