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Supercritical withdrawal from a two-layer fluid through a line sink

Published online by Cambridge University Press:  26 April 2006

G. C. Hocking
G. C. Hocking
Affiliation:
School of Mathematics and Physical Science, Murdoch University, Murdoch, Western Australia, 6150, Australia
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Abstract

Accurate numerical solutions to the problem of finding the location of the interface between two unconfined regions of fluid of different density during the withdrawal process are presented. Supercritical flows are considered, in which the interface is drawn directly into the sink. As the flow rate is reduced, the interface enters the sink more steeply, until the solution method breaks down just before the interface enters the sink vertically from above, and becomes flow from the lower layer only. This lower bound on supercritical flow is compared with the upper bound on single-layer (free surface) flow with good agreement.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 297 , 25 August 1995 , pp. 37 - 47
Copyright
© 1995 Cambridge University Press

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References

Craya, A. 1949 Theoretical research on the flow of nonhomogeneous fluids. La Houille Blanche 4, 44–55.Google Scholar
Forbes, L. K. 1985 On the effects of non-linearity in free-surface flow about a submerged point vortex. J. Engng Maths 19, 139–155.Google Scholar
Gariel, P. 1949 Experimental research on the flow of nonhomogeneous fluids. La Houille Blanche 4, 56–65.Google Scholar
Harleman, D. R. F. & Elder, R. E. 1965 Withdrawal from two-layer stratified flow. Proc. ASCE 91 (HY4).Google Scholar
Hocking, G. C. 1985 Cusp-like free-surface flows due to a submerged source or sink in the presence of a flat or sloping bottom. J. Austral. Math Soc. B 26, 470–486.Google Scholar
Hocking, G. C. 1988 Infinite Froude number solutions to the problem of a submerged source or sink. J. Austral. Math Soc. B 29, 401–409.Google Scholar
Hocking, G. C. 1991a Critical withdrawal from a two-layer fluid through a line sink. J. Engng Maths 25, 1–11.Google Scholar
Hocking, G. C. 1991b Withdrawal from two-layer fluid through line sink. J. Hydraul. Engng ASCE 117, 800–805.Google Scholar
Hocking, G. C. & Forbes, L. K. 1991 A note on the flow induced by a line sink beneath a free surface. J. Austral. Math Soc. B 32, 251–260.Google Scholar
Huber, D. G. 1960 Irrotational motion of two fluid strata towards a line sink. J. Engng Mech. Div. ASCE 86, EM4, 71-85.Google Scholar
Imberger, J. & Hamblin, P. F. 1982 Dynamics of lakes, reservoirs and cooling ponds. Ann. Rev. Fluid Mech. 14, 153–187.Google Scholar
Jirka, G. H. 1979 Supercritical withdrawal from two-layered fluid systems, Part 1-Two-dimensional skimmer wall. J. Hydraul. Res. 17, 43–51.Google Scholar
Jirka, G. H. & Katavola, D. S. 1979 Supercritical withdrawal from two-layered fluid systems, Part 2 - Three-dimensional flow into a round intake. J. Hydraul. Res. 17, 53–62.Google Scholar
Lawrence, G. A. & Imberger, J. 1979 Selective withdrawal through a point sink in a continuously stratified fluid with a pycnocline. Tech. Rep. ED-79-002. Dept. of Civil Engng, University of Western Australia.
Sautreaux, C. 1901 Mouvement d'un liquide parfait soumis à la pesanteur. Dé termination des lignes de courant. J. Math. Pures Appl. (5) 7, 125-159.Google Scholar
Tuck, E. O. & Vanden-Broeck, J.-M. 1984 A cusp-like free-surface flow due to a submerged source or sink. J. Austral. Math Soc. B 25, 443–450.Google Scholar
Vanden-Broeck, J.-M. & Keller, J. B. 1987 Free surface flow due to a sink. J. Fluid Mech. 175, 109–117.Google Scholar
Wood, I. R. & Lai, K. K. 1972 Selective withdrawal from a two-layered fluid. J. Hydraul. Res. 10, 475–496.Google Scholar
Yih, C. S. 1980 Stratified Flows. Academic Press.