In the Southern Ocean, the use of relative wind stress is important because eddies are crucial in the Antarctic Circumpolar Circulation, and the damping of these eddies with relative wind stress will affect the overturning circulation. The Residual Meridional Overturning Circulation (RMOC), is a streamfunction that quantifies the transport of tracers across isopycnals. Wind stress is taken into account through the formulation of the RMOC, which is the sum of the Eulerian mean MOC   and eddy-induced bolus overturning . The Eulerian mean MOC is dependent on the meridional winds that drive Ekman transport in zonal direction. The eddy-induced bolus overturning acts to restore sloping isopycnals to the horizontal, which are induced by eddies. The formulation of the RMOC is given by: 
with  being the zonal mean wind stress,  the reference density,   the Coriolis parameter (negative in Southern Hemisphere),  the quasi-Stokes eddy diffusivity field, equal to  being the length and the velocity of the eddy, respectively, and  the slope of the isopycnals. 
Inserting a lower wind stress, by using relative wind stress instead of resting ocean wind stress, directly leads to lower residual overturning, by reducing the Eulerian mean MOC (). Furthermore, it affects the eddy-induced bolus overturning () by damping eddies which results in reduced length and velocity scale (  & ) of eddies. The sum of this thus leads to a lower .