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Maximal two-layer exchange through a contraction with barotropic net flow

Published online by Cambridge University Press:  21 April 2006

L. Armi  and
D. M. Farmer
L. Armi
Affiliation:
Scripps Institution of Oceanography, La Jolla, California 92093
D. M. Farmer
Affiliation:
Institute of Ocean Sciences, Sidney, BC, Canada, V8L 4B2
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Abstract

The gravitational exchange of two fluids with different densities between reservoirs connected by a channel of constant depth and slowly varying breadth is analysed as a problem of internal hydraulics. It is shown that maximal two-way exchange with a net barotropic flow requires the presence of two controls, one at the narrrowest section and a second or ‘virtual’ control lying to one side of the narrowest section. The two controls are connected by a subcritical region, but are separated from subcritical conditions in the reservoirs by supercritical flow and stationary internal bores. Solutions are found for maximal exchange without a net barotropic component, in which case the problem is similar to that first examined by Stommel & Farmer (1953). The Stommel & Farmer analysis is shown to be a rather special limiting example of submaximal exchange, not generally applicable to natural flows. The addition of a net barotropic flow yields a range of different flow types, including maximal exchange, one-layer baroclinic flow, one-layer barotropic flow, submaximal flow governed by a reservoir condition and two-layer unidirectional flow. The maximal-exchange solution is integrated for periodic barotropic flow.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 164 , March 1986 , pp. 27 - 51
Copyright
© 1986 Cambridge University Press

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