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Free surface flow due to a sink

Published online by Cambridge University Press:  21 April 2006

Jean-Marc Vanden-Broeck  and
Joseph B. Keller
Jean-Marc Vanden-Broeck
Affiliation:
Department of Mathematics and Mathematics Research Center, University of Wisconsin-Madison, Madison, WI 53706, USA
Joseph B. Keller
Affiliation:
Departments of Mathematics and Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
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Abstract

Two-dimensional free surface flows without waves, produced by a submerged sink in a reservoir, are computed numerically for various configurations. For a sink above the horizontal bottom of a layer of fluid, there are solutions for all values of the Froude number F greater than some particular value. However, when the fluid is sufficiently deep, there is an additional solution for one special value of F < 1. The results for a sink at the vertex of a sloping bottom, treated by Craya and by Hocking, and for a sink in fluid of infinite depth, treated by Tuck & Vanden-Broeck, are confirmed and extended. In particular it is shown that as the bottom tends to the horizontal, the solution for a sink at the vertex of a sloping bottom approaches a solution for a horizontal bottom with F = 1. However solutions are found for all values of the Froude number F [ges ] 1 for a sink on a horizontal bottom.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 175 , February 1987 , pp. 109 - 117
Copyright
© 1987 Cambridge University Press

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References

Collings, I. L. 1986 J. Austral. Math. Soc. B28, 260.
Craya, A. 1949 Houille Blanche 4, 44.
Hocking, G. C. 1985 J. Austral. Math. Soc. B:26, 470.
Tuck, E. O. & Vanden-Broeck, J.-M. 1984 J. Austral. Math. Soc. B:25, 443.
Vanden-Broeck, J.-M. 1986 Phys. Fluids 29, 3148.
Vanden-Broeck, J.-M. & Keller, J. B. 1987 J. Fluid Mech. 176, 283.
Yih, C. S. 1965 Dynamics of Nonhomogeneous Fluids. Macmillan.