Theory of Two-Layer Hydraulic Exchange Flows with Rotation

By Ulrike Riemenschneider

School of Ocean and Earth Science, Southampton Oceanography Centre, European Way, Southampton, SO14 3ZH, UK

Peter D. Killworth and David A. Smeed

James Rennell Division, Southampton Oceanography Centre, European Way, Southampton, SO14 3ZH, UK

Two-layer rotating exchange flows through channels of rectangular cross-section are modelled using semi-geostrophic, zero potential vorticity theory. For a given channel cross-section the full range of possible flow states is considered. The interface always has a uniform slope across the channel, but may separate from one or both of the side walls to attach to the upper or lower boundary. The flow may be subcritical, critical or supercritical. These different states are identified in a pseudoFroude number plane analogous to that developed by Armi (1986) for non-rotating flows. If the ratio of the channel width to the Rossby radius is constant along the length of the channel, then the solution may be traced along the entire channel using a single diagram. Several examples of maximal and sub-maximal exchanges are considered. This graphical method of solution is contrasted with the functional approach of Dalziel (1988, 1990). The exchange flux is determined as a function of the channel geometry, the strength of rotation and the difference in Bernoulli potential between the two layers.