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Maximal two-layer exchange through a contraction with barotropic net flow. (English) Zbl 0587.76168

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 narrowest 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 H. Stommel and H. G. Farmer [J. Mar. Res. 12, 13- 20 (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.

MSC:

76T99 Multiphase and multicomponent flows
76M99 Basic methods in fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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[1] DOI: 10.1017/S0022112068000133 · Zbl 0169.28503 · doi:10.1017/S0022112068000133
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[5] DOI: 10.1017/S0022112070001544 · doi:10.1017/S0022112070001544
[6] Stommel, J. Mar. Res. 12 pp 13– (1953)
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