Multi-layer hydraulic exchange flows

Flows between ocean basins are often controlled by narrow channels and shal low sills. A multi-layer hydraulic control theory is developed for exchange flow through such constrictions. The theory is based on the inviscid shall ow-water equations and extends the functional approach introduced by Gill(1 977) and developed by Dalziel (1991). The flows considered are those in rec tangular-cross-section channels connecting two large reservoirs, with a sin gle constriction (sill and/or narrows). The exchange flow depends on the st ratification in the two reservoirs, represented as a finite number of immis cible layers of(different) uniform density. For most cases the flow is 'con trolled' at the constriction and often at other points along the channel (v irtual controls) too. As with one- and two-layer hydraulics, controls are l ocations at which the flow passes from one solution branch to another, and at which (at least) one internal wave mode is stationary. The theory is app lied to three-layer flows, which have two internal wave modes, predicting i nterface heights and layer fluxes from the given reservoir conditions. The theoretical results for three-layer flows are compared to a comprehensive s et of laboratory experiments and found to give good agreement. The laborato ry experiments also show other features of the flow, such as the formation of waves on the interfaces. The implications of the results for oceanograph ic flows and ocean modelling are discussed.