Eddy Saturation in a Barotropic Model

"Eddy saturation" refers to a regime in which the total zonal volume transport of an ocean current is insensitive to the wind stress strength; the Antarctic Circumpolar Current (ACC) is the most prominent example. Baroclinicity is currently believed to be key to the development of an eddy-saturated state. Here, we show that eddy saturation occurs in a barotropic flow over topography, without baroclinicity. We show that eddy saturation is a fundamental property of barotropic dynamics above topography. We demonstrate that the main factor controlling the appearance or not of eddy saturated states is the structure of geostrophic contours, that is the contours of f/H, with f the Coriolis parameter and H the depth. Eddy saturated states occur when the geostrophic contours are open, that is when the geostrophic contours span the whole zonal extent of the domain. We demonstrate this minimal requirement for eddy saturated states in a scenario relevant to the ACC using numerical integrations of a single-layer quasi-geostrophic flow over two different topographies characterized by either open or closed geostrophic contours.

Starting from the work of Charney & DeVore [J. Atmos. Sci., 36, 1205-1216, (1979)] a series of low-dimensional truncated models were advanced for the study of zonal flow-topography interactions. Our barotropic model recapitulates many of the features identified by these low-dimensional models. With open geostrophic contours, we find both a lower and an upper branch consisting of stationary solutions, multiple stable equilibria as well as a sudden transitions between the two branches as wind stress strength varies. However, in addition our model also predicts a fully turbulent regime with strong transients that is not captured by the low-dimensional models. This turbulent regime shows impressive eddy saturation: only 4-fold transport increase over 60-fold wind stress increase. Furthermore, in the eddy saturation regime the eddy kinetic energy increases linearly with wind stress and also the mean transport increases with increasing Ekman drag. Both these feature are symptomatic of eddy saturation in comprehensive models of the ACC. We explain the various flow transitions that occur in the case with open geostrophic contours by studying the stability of the flow, extending the stability method initially presented by Hart [J. Atmos. Sci., 36, 1736–1746, (1979)].