  "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 key to the development of an eddy-saturated 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 $f/H$ of 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 quasi-geostrophic 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 due tot the interaction of the large-scale zonal flow
with the topography. Through the study of this barotropic-topographic
instability insight is gained on how eddy-saturated states are established.
