A barotropic model of eddy saturation

Eddy saturation refers to a regime in which the total volume transport of an oceanic current is insensitive to the wind stress strength. Baroclinicity is currently believed to be the key to the development of an eddysaturated state. In this paper, it is shown that eddy saturation can also occur in a purely barotropic flow over topography, without baroclinicity. Thus, eddy saturation is a fundamental property of barotropic dynamics above topography. It is demonstrated that the main factor controlling the appearance or not of eddy-saturated states in the barotropic setting is the structure of geostrophic contours, that is, the contours of f/H(the ratio of the Coriolis parameter to the ocean's 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. This minimal requirement for eddy-saturated states is demonstrated using numerical integrations of a single-layer quasigeostrophic flow over two different topographies characterized by either open or closed geostrophic contours with parameter values loosely inspired by the Southern Ocean. In this setting, transient eddies are produced through a barotropic-topographic instability that occurs because of the interaction of the large-scale zonal flow with the topography. By studying this barotropic-topographic instability insight is gained on how eddysaturated states are established.