Gill's semigeostrophic equations of one-layer, rotating channel hydraulics are exactly solved at the critical section, for flows with a finite uniform potential vorticity (PV). A detailed characterization of the critical flow at the sill is consequently obtained, together with a simple, explicit expression for the associated mass transport, that provides a direct extension of the well-known transport formula of zero-PV theory. The dependence of the mass transport on the PV, for a given average flow energy, is found to be non-monotonic. In particular, the transport increases when the PV is raised from zero, attaining a maximum value that can be up to twice those predicted by the zero-PV theory. This suggests that, contrary to common belief, finite-PV effects may be important in determining the mass transport in real oceanic outflows. © 2006 Cambridge University Press.
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering