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Free-surface flow due to a source submerged in a fluid of infinite depth with two stagnant regions

Published online by Cambridge University Press:  17 February 2009

Hocine Mekias  and
Jean-Marc Vanden-Broeck
Hocine Mekias
Affiliation:
Dept. of Math, and Center for Math. Sciences, University of Wisconsin-Madison, WI 53705.
Jean-Marc Vanden-Broeck
Affiliation:
Dept. of Math, and Center for Math. Sciences, University of Wisconsin-Madison, WI 53705.
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Abstract

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Two-dimensional free-surface flows produced by a submerged source in a fluid of infinite depth are considered. It is assumed that the point on the free surface just above the source is a stagnation point and that the fluid outside two shear layers is at rest. The free-surface profile and the shape of the shear layers are determined numerically by using a series-truncation method. It is shown that there is a solution for each value of the Froude number F > 0. When F tends to infinity, the flow also describes a thin jet impinging in a fluid at rest.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 34 , Issue 3 , January 1993 , pp. 368 - 376
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Craya, A., “Theoretical research on the flow of non-homogeneous fluids”, La Houille Blanche 4 (1949) 44–55.CrossRefGoogle Scholar
[2]Hocking, G. C., “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 (1985) 470–486.CrossRefGoogle Scholar
[3]Hocking, G. C. and Forbes, L. K., “A note on the flow induced by a line sink beneath a free surface”, J. Austral. Math. Soc. B 32 (1991) 251–260.CrossRefGoogle Scholar
[4]Mekias, H. and Vanden-Broeck, J.-M., “Supercritical free-surface flow with a stagnation point due to a submerged source”, Phys. Fluids A 1 (1989) 1694–.CrossRefGoogle Scholar
[5]Mekias, H. and Vanden-Broeck, J.-M., “Subcritical flow with a stagnation point due to a source beneath a free surface”, Phys. Fluids A 3 (1991) 2652.CrossRefGoogle Scholar
[6]Peregrine, D. H., “A line source beneath a ffee surface”, Univ. Wisconsin Math. Res. Center Tech. Summ. Report 1248 (1972).Google Scholar
[7]Tuck, E. O. and Vanden-Broeck, J.-M., “A cusp-like free-surface flow due to a submerged source or sink”, J. Austral. Math. Soc. B 25 (1984) 443–450.CrossRefGoogle Scholar
[8]Vanden-Broeck, J.-M. and Keller, J. B., “Free surface flow due to a sink”, J. Fluid Mech. 175 (1987) 109–117.CrossRefGoogle Scholar