Rotating hydraulics of strait and sill flows†

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Abstract
Theoretical and laboratory models of certain types of strait and sill flows are discussed. Specifically, we consider a two‐layer rotating fluid; the upper layer is at rest and the lower layer flows from one large basin to another via a connecting channel. The flow is assumed to be principally in a down‐channel direction. The cross‐channel balance is therefore geostrophic and the Bernoulli and potential vorticity equations are simplified. We further invoke the usual non‐rotating hydraulic principle of maximum transport in flow over a weir—here the end of the channel—and thereby calculate relations between transport, rotation rate, and upstream interface height. One of these relations is tested experimentally with favorable results. A nonsteady decaying flow in the same system is analyzed similarly and also compares well with experiment, as does a flow in both layers driven by an initial density imbalance. Some connections with oceanic strait and sill flows are discussed.

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