Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-18T18:37:07.899Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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