Abstract

The nonlinear influence of isolated topography on an equivalent barotropic, quasigeostrophic jet is considered. The flow depends on several dimensional parameters including the mass flux Q, the mean layer thickness H, the planetary potential vorticity gradient β the inertial boundary layer thickness (u0/β)½ and a parameter a – c measuring the north-south potential vorticity difference across the jet. Eastward jets can achieve one of two steady forms, the first supercritical and the second subcritical with respect to upstream propagation of a long potential vorticity wave. An isolated topographic feature such as a ridge can cause the jet to undergo transition from subcritical to supercritical flow and thereby achieve a steady state analogous to hydraulically controlled open channel flow. In a critically-controlled state the values of Q, a-c, H, and (u0/β)½ cannot be specified independently of the topographic parameters and the topography thereby exerts an 'upstream influence' which is felt by the general circulation of the ocean as a whole. Critically-controlled states also experience topographic form drag, whereas noncontrolled states experience none. The form drag is determined by the upstream potential vorticity distribution of the flow and the critical jet width, suggesting that this type of drag might be estimated in practice by a combination of hydrographic data and satellite imagery. The Antarctic Circumpolar Current is discussed as a possible example.

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