Constant Potential Vorticity Hydraulically Controlled Flow—Complexities from Passage Shape*

Abstract

Velocity, surface height profiles, and volume flux are calculated for critically controlled flow of a layer of rotating fluid from a channel to an exit passage. The upstream fluid possesses constant potential vorticity. These are models of an internal layer of ocean water flowing out of a basin through a passage. An analysis is used that allows general passage bottom shapes. A number of features differ from those of nonrotating critically controlled flow. First, sizeable gyres appear for a range of upstream conditions. Second, more than one critical flow (maximum flux) is possible at the control point for the same upstream condition, but only one of these is allowed with continuous laminar flow from the channel to the passage. Third, a bottom that slopes away from the right-hand side (Northern Hemisphere rotation) and that is at right angles to flow direction produces small volume flux at high rotation rates. Fourth, although there is a rigorous bound for flux out of a passage, this is exceeded for some cases with multiple exits.