Local “Mean Field” Theory of Hydraulically Controlled Strait Flow

Abstract

The free discharge of a layer of bottom water in a wide strait (e.g., the Denmark Strait) differs from the classical control problem because of the strong geostrophic turbulence. As a consequence, the cross-stream (x) variation of the time-averaged downstream velocity ?(x) is ?underdetermined? and depends on more parameters than available conditions. To resolve this ?degeneracy? the classical control condition is generalized; the result requires the discharge Q to be extremized with respect to the degeneracy parameters and with respect to the constraints. One of these constraints is that a branch point or a local stationary wave can be supported at some section of the long channel. By either maximizing Q or by requiring a stationary wave, useful approximations are obtained. Future work should consider the joint variational problem. Specific calculations are made for nonuniform potential vorticity in a rectangular channel and also for variable cross-stream bottom topography. In the latter case, the current has a free streamline whose point of intersection with the bottom is computed. It is suggested that a necessary condition for hydraulic control at any section is that the flow does not separate from either side of the channel. The mean isopycnals in the Denmark Strait satisfy this condition, thereby suggesting that it does in fact (topographically) control the upstream state in the Greenland Sea.