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The hydraulics of a stratified fluid flowing through a contraction

Published online by Cambridge University Press:  26 April 2006

Laurence Armi  and
Richard Williams
Laurence Armi
Affiliation:
Scripps Institution of Oceanography, University of California at San Diego, La Jolla, CA 92093–0230, USA
Richard Williams
Affiliation:
Scripps Institution of Oceanography, University of California at San Diego, La Jolla, CA 92093–0230, USA
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Abstract

The steady hydraulics of a continuously stratified fluid flowing from a stagnant reservoir through a horizontal contraction was studied experimentally and theoretically. As the channel narrows, the flow accelerates through a succession of virtual controls, at each of which the flow passes from sub-critical to supercritical with respect to a particular wave mode. When the narrowest section acts as a control, the flow is asymmetric about the narrowest section, supercritical in the divergent section and self- similar throughout the channel. With increased flow rate a new enclosed self-similar solution was found with level isopycnals and velocity uniform with depth. This flow is only symmetric in the immediate neighbourhood of the narrowest section, and in the divergent section remains supercritical with respect to higher internal modes, has separation isopycnals and splits into one or more jets separated by regions of stagnant, constant-density fluid. Flows which are subcritical with respect to lowest modes can also be asymmetric about the narrowest section for higher internal modes. The experiments are interpreted using steady, inviscid hydraulic theory. Solutions require separation isopycnals and regions of stationary, constant-density fluid in the divergent section.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 251 , June 1993 , pp. 355 - 375
Copyright
© 1993 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. M. 1986 Maximal two-layer exchange through a contraction with barotropic net flow. J. Fluid Mech. 164, 27–51.Google Scholar
Baines, P. G. & Guest, F. 1988 The nature of upstream blocking in uniformly stratified flow over long obstacles. J. Fluid Mech. 188, 23–45.Google Scholar
Benjamin, T. B. 1981 Steady flows drawn from a stably stratified reservoir. J. Fluid Mech. 106, 245–260.Google Scholar
Bernstein, A., Heiser, W. H. & Hevenor, C. 1967 Compound-compressible nozzle flow. Trans. ASMEE: J. Appl. Mech. 34, 548–554.Google Scholar
Long, R. R. 1953 Some aspects of the flow of stratified fluids. I. A theoretical investigation. Tellus 5, 42–58.Google Scholar
Long, R. R. 1953 Some aspects of the flow of stratified fluids. III. Continuous density gradients. Tellus 7, 341–357.Google Scholar
Smith, R. B. 1985 On severe downslope winds. J. Atmos. Sci. 42, 2597–2603.Google Scholar
Williams, R. & Armi, L. 1991 Two-layer hydraulics with comparable internal wave speeds. J. Fluid Mech. 230, 667–691.Google Scholar
Wood, I. R. 1968 Selective withdrawal from a stably stratified fluid. J. Fluid Mech. 32, 209–223.Google Scholar
Yih, C.-S. 1969 A class of solutions for steady stratified flows. J. Fluid Mech. 36, 75–85.Google Scholar