Constraints on the hydrography and geostrophic velocity shear of the Southern Ocean implicit in its potential vorticity field are discussed and illustrated by diagnostic study of observed and modeled potential vorticity fields. An analytical model of the zonally averaged ACC based on the uniform PV model is presented, which predicts a transport relative to the bottom of ~130 Sv (1 Sv ≡ 106 m3 s-1), close to the observed value, and a meridional eddy heat flux of 0.25 PW independent of any ad hoc eddy closure assumptions. The model is then applied in a more realistic setting and results compare favourably with observations. -from Authors