Hostname: page-component-848d4c4894-sjtt6 Total loading time: 0 Render date: 2024-06-22T00:25:47.971Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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.