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The hydraulics of steady two-layer flow over a fixed obstacle

Published online by Cambridge University Press:  26 April 2006

Gregory A. Lawrence
Affiliation:
Department of Civil Engineering, University of British Columbia, Vancouver, BC, Canada, V6T 1Z4

Abstract

This paper reports the results of a theoretical and experimental study of steady two-layer flow over a fixed two-dimensional obstacle. A classification scheme to predict the regime of flow given the maximum height of the obstacle, the total depth of flow, and the density and flow rate of each layer, is presented with experimental confirmation. There are differences between this classification scheme and that derived for flow over a towed obstacle by Baines (1984, 1987). These differences are due to the motion of upstream disturbances in towed obstacle flows. Approach-controlled flows, i.e. flows with an internal hydraulic control in the flow just upstream of the obstacle are studied in detail for the first time. This study reveals that non-hydrostatic forces, rather than a shock solution (called an internal hydraulic drop by previous investigators), need to be considered to explain the behaviour of Approach-controlled flows.

Type
Research Article
Copyright
© 1993 Cambridge University Press

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References

Armi, L. 1986 The hydraulics of two flowing layers of different densities. J. Fluid Mech. 163, 27.Google Scholar
Baines, P. G. 1984 A unified description of two-layer flow over topography. J. Fluid Mech. 146, 127.Google Scholar
Baines, P. G. 1987 Upstream blocking and airflow over mountains. Ann. Rev. Fluid Mech. 19, 75.Google Scholar
Dalziel, S. B. 1990 Two-layer hydraulics: a functional approach. J. Fluid Mech. 223, 135.Google Scholar
Denton, R. A. 1987 Locating and identifying hydraulic controls for layered flow through an obstruction. J. Hydraul. Res. 25, 281.Google Scholar
Farmer, D. M. & Denton, R. A. 1985 Hydraulic control of flow over the sill in Observatory Inlet. J. Geophys. Res. 90(C5), 9051.Google Scholar
Farmer, D. M. & Freeland, H. J. 1983 The physical oceanography of fjords. Prog. Oceanogr. 12, 147.Google Scholar
Farmer, D. M. & Smith, J. D. 1980 Tidal interaction of stratified flow with a sill in Knight Inlet. Deep-Sea Res. 17, 239.Google Scholar
Harlow, F. H. & Welch, J. E. 1965 Calculation of time-dependent viscous incompressible flow of fluid with a free surface. Phys. Fluids 8, 2182.Google Scholar
Henderson, F. M. 1966 Open Channel Flow. MacMillan.
Houghton, D. D. & Isaacson, E. 1970 Mountain winds. Stud. Numer. Anal. 2, 21.Google Scholar
Huppert, H. E. & Britter, R. E. 1982 Separation of hydraulic flow over topography. J. Hydraul. Engng 108, 1532.Google Scholar
Jameel, M. I. 1991 Modelling of two-layer flow over an obstacle. PhD thesis, Department of Mechanical Engineering, University of Calgary.
Jirka, G. H. 1984 Discussion of ‘Separation of hydraulic flow over topography’ by Huppert & Britter (1982). J. Hydraul. Engng 110, 357.Google Scholar
Lawrence, G. A. 1984 Discussion of ‘Separation of hydraulic flow over topography' by Huppert & Britter (1982). J. Hydraul. Engng 110, 359.Google Scholar
Lawrence, G. A. 1985 The hydraulics and mixing of two-layer flow over an obstacle. PhD thesis, Department of Civil Engineering, University of California, Berkeley.
Lawrence, G. A. 1987 Steady flow over an obstacle. J. Hydraul. Engng 113, 981.Google Scholar
Lawrence, G. A. 1990 On the hydraulics of Boussinesq and non-Boussinesq two-layer flows. J. Fluid Mech. 215, 457.Google Scholar
Long, R. R. 1954 Some aspects of the flow of stratified fluids. II. Experiments with a two-fluid system. Tellus 6, 97.Google Scholar
Marchant, T. R. & Smyth, N. F. 1990 The extended Korteweg–de Vries equation and the resonant flow of a fluid over topography. J. Fluid Mech. 221, 263.Google Scholar
Melville, W. K. & Helfrich, K. R. 1987 Transcritical two-layer flow over topography. J. Fluid Mech. 178, 31.Google Scholar
Murray, S. P., Hecht, A. & Babcock, A. 1983 On the mean flow in the Tiran Strait in winter. J. Mar. Res. 42, 265.Google Scholar
Pite, H. D., Topham, D. R. & Hardenberg, B. J. van 1992 Laboratory measurements of the drag force on two-dimensional topographic features in a two-layer flow. J. Fluid Mech. (submitted.)Google Scholar
US Army Corps OF Engineers 1980 Hydraulic Model Study for the John F. Baldwin Ship Channel – Incremental Improvements with/without Fluid Submerged Barriers. Department of the Army, San Francisco, CA, July 1980.
Wood, I. R. 1968 Selective withdrawal from a stably stratified fluid. J. Fluid Mech. 32 209.Google Scholar
Wood, I. R. & Simpson, J. E. 1984 Jumps in layered miscible fluids. J. Fluid Mech. 140, 329.Google Scholar