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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.

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

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References

Armi, L. 1986 The hydraulics of two flowing layers with different densities. J. Fluid Mech. 163, 27–58.Google Scholar
Armi, L. & Farmer, D. 1985 The internal hydraulics of the Strait of Gibraltar and associated sills and narrows. Oceanologica Acta 8, 37–46.Google Scholar
Assaf, G. & Hecht, A. 1974 Sea straits: a dynamical model. Deep-Sea Res. 21, 947–958.Google Scholar
Benjamin, T. B. 1968 Gravity currents and related phenomena. J. Fluid Mech. 31, 209–248.Google Scholar
Bryden, H. L. & Stommel, H. M. 1984 Limiting processes that determine basic features of the circulation in the Mediterranean Sea. Oceanologica Acta 7, 289–296.Google Scholar
Chow, V. T. 1959 Open-Channel Hydraulics. McGraw-Hill. 680 pp.
Dyer, K. R. 1973 Estuaries: A Physical Introduction. John Wiley & Sons. 140 pp.
Farmer, D. & Armi, L. 1986 Maximal two-layer exchange over a sill and through the combination of a sill and contraction with barotropic flow. J. Fluid Mech. 164, 53–76.Google Scholar
Long, R. R. 1956 Long wave in a two-fluid system. J. Met. 13, 70–74.Google Scholar
Murray, S. P., Hecht, A. & Babcock, A. 1984 On the mean flow in the Tiran Strait in winter. J. Mar. Res. 42, 265–287.Google Scholar
Stommel, H. & Farmer, H. G. 1952 Abrupt change in width in two-layer open channel flow. J. Mar. Res. 11, 205–214.Google Scholar
Stommel, H. & Farmer, H. G. 1953 Control of salinity in an estuary by a transition. J. Mar. Res. 12, 13–20.Google Scholar
Wood, I. R. 1970 A lock exchange flow. J. Fluid Mech. 42, 671–687.Google Scholar