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The hydraulics of two flowing layers with different densities

Published online by Cambridge University Press:  21 April 2006

Laurence Armi
Laurence Armi
Affiliation:
Scripps Institution of Oceanography, La Jolla, California 92093
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Abstract

This is a theoretical and experimental study of the basic hydraulics of two flowing layers. Unlike single-layer flows, two-layer flows respond quite differently to bottom depth as opposed to width variations. Bottom-depth changes affect the lower layer directly and the upper layer only indirectly. Changes in width can affect both layers. In fact for flows through a contraction control two distinct flow configurations are possible; which one actually occurs depends on the requirements of matching a downstream flow. Two-layer flows can pass through internally critical conditions at other than the narrowest section. When the two layers are flowing in the same direction, the result is a strong coupling between the two layers in the neighbourhood of the control. For contractions a particularly simple flow then exists upstream in which there is no longer any significant interfacial dynamics; downstream in the divergent section the flow remains internally supercritical, causing one of the layers to be rapidly accelerated with a resulting instability at the interface. A brief discussion of internal hydraulic jumps based upon the energy equations as opposed to the more traditional momentum equations is included. Previous uniqueness problems are thereby avoided.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 163 , February 1986 , pp. 27 - 58
Copyright
© 1986 Cambridge University Press

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References

Aemi, L. 1975 The internal hydraulics of two flowing layers of different densities. Ph.D. thesis, University of California Berkeley.
Benton, G. S. 1954 The occurrence of critical flow and hydraulic jumps in a multi-layered fluid system. J. Met. 11, 139–150.Google Scholar
Baines, P. G. 1984 A unified description of two-layer flow over topography. J. Fluid Mech. 146, 127–167.Google Scholar
Chow, V. T. 1959 Open-Channel Hydraulics. McGraw-Hill.
Chu, V. H. & Baddour, R. E. 1984 Turbulent gravity-stratified shear flows. J. Fluid Mech. 138, 353–378.Google Scholar
Hayakawa, N. 1970 Internal hydraulic jump in co-current stratified flow. J. Engng Mech. Div. ASCE 96 (EMS), 797–800.Google Scholar
Houghton, D. D. & Isaacson, E. 1970 Mountain winds. Stud. Numer. Anal. 2, 21–52.Google Scholar
Lai, K. K. & Wood, I. R. 1975 A two-layer flow through a contraction. J. Hyd. Res. IAHR 13, 19–34.Google Scholar
Lawrence, G. A. 1985 Mixing in steady two-layer flow over topography. Ph.D. thesis, University of California, Berkeley.
Liepmann, H. W. & Roshko, A. 1957 Elements of Gasdynamics. John Wiley and Sons.
Long, R. R. 1954 Some aspects of the flow of stratified fluids. II. Experiments with a two-fluid system. Tellus 6, 97–115.Google Scholar
Long, R. R. 1956 Long waves in a two-fluid system. J. Met. 13, 70–74.Google Scholar
Long, R. R. 1970 Blocking effects in flow over obstacles. Tellus 22, 471–480.Google Scholar
Long, R. R. 1974 Some experimental observations of upstream disturbances in a two-fluid system. Tellus 26, 313–317.Google Scholar
Mehrotra, S. C. 1973a Limitations on the existence of shock solutions in a two-fluid system. Tellus 25, 169–173.
Mehrotra, S. C. 1973b Boundary contractions as controls in two-layer flows. J. Hydr. Div. ASCE 99, HY11,2003–2012.Google Scholar
Mehrotra, S. C. & Kelly, R. E. 1973 On the question of non-uniqueness of internal hydraulic jumps and drops in a two-fluid system. Tellus 25, 560–566.Google Scholar
Prandtl, L. 1952 Essentials of Fluid Dynamics. Blackie and Son.
Schijf, J. B. & SchoUnfeld, J. C. 1953 Theoretical considerations on the motion of salt and fresh water. In Proc. of the Minn. Int. Hydraulics Conv., Joint meeting IAHR and Hyd. Div ASCE., Sept. 1953, pp. 321–333.
Stommel, H. & Farmer, H. G. 1953 Control of salinity in an estuary by a transition. J. Mar. Res. 12, 13–20.Google Scholar
Turner, J. S. 1973 Bouyancy Effects in Fluids. Cambridge University Press.
Wilkinson, D. L. & Wood, I. R. 1971 A rapidly varied flow phenomenon in a two-layer flow. J. Fluid Mech. 47, 241–256.Google Scholar
Wood, I. R. 1968 Selective withdrawal from a stably stratified fluid. J. Fluid Mech. 32, 209–223.Google Scholar
Wood, I. R. 1970 A lock exchange flow. J. Fluid Mech. 42, 671–687.Google Scholar
Wood, I. R & Lai, K. K. 1972 Flow of layered fluid over broad crested weir. J. Hyd. Div. ASCE 98, 87–104.Google Scholar
Wood, I. R. & Simpson, J. E. 1984 Jumps in layered miscible fluids. J. Fluid Mech. 140, 329–342.Google Scholar
Yih, C. S. 1969 A class of solutions for steady stratified flows. J. Fluid Mech. 36, 75–85.Google Scholar
Yih, C. S. & Guha, C. R. 1955 Hydraulic jump in a fluid system of two layers. Tellua 7, 358–366.Google Scholar