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Flow induced by a line sink in a quiescent fluid with surface-tension effects

Published online by Cambridge University Press:  17 February 2009

Lawrence K. Forbes  and
Graeme C. Hocking
Lawrence K. Forbes
Affiliation:
Dept. of Math., The University of Queensland, St. Lucia, Qld. 4072, Australia.
Graeme C. Hocking
Affiliation:
Dept. of Math., The University of Western Australia, Nedlands, W. A. 6009, Australia.
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Abstract

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When a line sink is placed beneath the free surface of an otherwise quiescent fluid of infinite depth, two different flow types are now known to be possible. One type of flow involves the fluid being drawn down toward the sink, and in the other type, a stagnation point forms at the surface immediately above the position of the sink.

This paper investigates the second of these two flow types, which involves a free-surface stagnation point. The effects of surface tension are included, and even when small, these are shown to have a very significant effect on the overall solution behaviour. We demonstrate by direct numerical calculation that there are regions of genuine non-uniqueness in the nonlinear solution, when the surface-tension parameter does not vanish. In addition, an asymptotic solution valid for small Froude number is derived.

Type
Research Article
Information
The ANZIAM Journal , Volume 34 , Issue 3 , January 1993 , pp. 377 - 391
Copyright
Copyright © Australian Mathematical Society 1993

References

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