A simple scaling for the total transport and the vertical shear of the Antarctic Circumpolar Current

Over the last twenty years, it has become clear that the Antarctic Circumpolar Current (ACC) is in an eddy saturated state, for which the zonal transport is only weakly dependent on the applied wind stress. Eddy saturation has been observed and discussed in a variety of different contexts (e.g. with and without topography or stratification). Here we use simulations of a quasi-geostrophic two-layer model over a wide range of parameters in order to better understand the regime of eddy saturation pertinent for the ACC. For a given stratification, there exists essentially two regimes describing the vertically integrated transport: (i) a saturated regime from weak to intermediate wind stress and (ii) a strong wind regime where the transport increases linearly with wind stress. We demonstrate that the present day Southern Ocean is in the saturated regime. We show that the vertically integrated transport in the saturated regime depends on the stratification, the bottom friction, the gradient of the Coriolis parameter and the width and depth of the channel. Surprisingly the transport does not vanish for weak wind stress, no matter how weak as long as it is larger than zero. We conclude by providing a theoretical interpretation of the results.