Hydraulic control and maximal flow in rotating stratified hydraulics

A general condition for the hydraulic control of rotating stratified fluid passing through a sill of arbitrary bottom topography is given, first for a one-layer reduced gravity model, and then extended to a continuously stratified fluid. As with non-rotating channel flow, control involves a pair of conditions. The first relates to the flow itself (and plays the equivalent role to unit Froude number in non-rotating hydraulics). The second relates to the local geometry of the sill (and is equivalent to the requirement of maximal constriction or topography in non-rotating hydraulics). Virtual controls are possible, and there may be an infinite number of these. These results are linked to conditions for maximal flow, and it is shown that this occurs if and only if the flow is controlled (again just as in the non-rotating case).