Southern Ocean eddy-induced overturning and circumpolartransport inferred from eddy energy and its residence time

A simple theoretical model of the Antarctic Circumpolar Current is used to derive expressions for the eddy-induced overturning streamfunction and circumpolar volume transport in terms of the eddy energy and its residence time, respectively. Specifically, our prediction for the circumpolar volume transport, neglecting any contribution from bottom flow, is

\[

T_{\rm ACC} \sim \frac{1}{t_{\rm eddy}} \frac{\pi L_D L_y H}{ \alpha},

\]

where $L_D$ is the Rossby deformation radius, $L_y$ is the width of the circumpolar current, $H$ is the e-folding depth scale for the stratification and circulation, $\alpha$ is a non-dimensional eddy efficiency parameter, and $t_{eddy}$ is the residence time for eddy energy in the Southern Ocean. Altimetric data, profiling float data, climatological hydrography and climatological wind stresses are used to estimate the eddy energy, its residence time, and hence the eddy-induced overturning streamfunction and the circumpolar volume transport. The eddy energy residence time is found to be relatively short, just a few months within the Southern Ocean. The inferred eddy-induced overturning streamfunction is found to have a realistic vertical structure and the inferred circumpolar volume transport is of order 130 Sv, in accord with independent estimates from hydrographic data.