Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-25T11:59:47.806Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on withdrawal through a point sink in fluid of finite depth

Published online by Cambridge University Press:  17 February 2009

Lawrence K. Forbes ,
Graeme C. Hocking  and
Graeme A. Chandler
Lawrence K. Forbes
Affiliation:
Dept. of Math., The University of Queensland, QLD 4072, Australia.
Graeme C. Hocking
Affiliation:
Dept. of Math., The University of Western Australia, Nedlands, Western Australia 6009, Australia.
Graeme A. Chandler
Affiliation:
Dept. of Math., The University of Queensland, QLD 4072, Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Withdrawal flow through a point sink on the bottom of a fluid of finite depth is considered. The fluid is at rest at infinity, and a stagnation point is present at the free surface, directly above the point sink. Numerical solutions are computed by means of the method of fundamental solutions, and it is observed that flows of this type are apparently possible for Froude number less than about 1.5. Relationships to previous work are discussed.

Type
Research Article
Information
The ANZIAM Journal , Volume 37 , Issue 3 , January 1996 , pp. 406 - 416
Copyright
Copyright © Australian Mathematical Society 1996

References

[1] Bogomolny, A., “Fundamental solutions method for elliptic boundary value problems”, SIAM J. Numer. Anal. 22 (1985) 644–669.CrossRefGoogle Scholar
[2] Chandler, G. A. and Forbes, L. K., “The fundamental solutions method for a free boundary problem”, in Proc. 6th CTAC, Canberra, Australia (1994) 122–130.Google Scholar
[3] Forbes, L. K. and Hocking, G. C., “Flow caused by a point sink in a fluid having a free surface”,J. Austral. Math. Soc. Ser. B 32 (1990) 231–249.CrossRefGoogle Scholar
[4] Forbes, L. K. and Hocking, G. C., “Flow induced by a line sink in a quiescent fluid with surface-tension effects”, J. Austral. Math. Soc. Ser. B 34 (1993) 377–391.CrossRefGoogle Scholar
[5] 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. Ser. B 26 (1985) 470–486.CrossRefGoogle Scholar
[6] Hocking, G. C., “Infinite Froude number solutions to the problem of a submerged source or sink”, J. Austral. Math. Soc. Ser. B 29 (1988) 401–409.CrossRefGoogle Scholar
[7] Hocking, G. C., “Critical withdrawal from a two-layer fluid through a line sink”, J. Engin. Math. 25 (1991) 1–11.CrossRefGoogle Scholar
[8] 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. Ser. B 32 (1991) 251–260.CrossRefGoogle Scholar
[9] Hocking, G. C. and Forbes, L. K., “Subcritical free-surface flow caused by a line source in a fluid of finite depth”, J. Engin. Math. 26 (1992) 455–466.CrossRefGoogle Scholar
[10] Imberger, J., “Selective withdrawal: a review”, in 2nd Intnl Symp. on Stratified Flows, Trondheim, Norway (1980).Google Scholar
[11] Lawrence, G. A. and Imberger, J., “Selective withdrawal through a point sink in a continuously stratified fluid with a pycnocline”, Univ. of Western Australia, Centre for Water Research, Environmental Dynamics Report ED-79–002 (1979).Google Scholar
[12] Mathon, R. and Johnston, R. L., “The approximate solution of elliptic boundary-value problems by fundamental solutions”, SIAM J. Numer. Anal. 14 (1977) 638–650.CrossRefGoogle Scholar
[13] Mekias, H. and Vanden-Broeck, J.-M., “Subcritical flow with a stagnation point due to a source beneath a free surface”, Phys. Fluids, Ser. A 3 (1991) 2652–2658.CrossRefGoogle Scholar
[14] Mekias, H. and Vanden-Broeck, J.-M., “Free-surface flow due to a source submerged in a fluid of infinite depth with two stagnant regions”, J. Austral. Math. Soc., Ser. B 34 (1993) 368–376.CrossRefGoogle Scholar
[15] Milne-Thomson, L. M., Theoretical hydrodynamics, 5th edition (Macmillan Press Ltd., London, 1979).Google Scholar
[16] Miloh, T. and Tyvand, P. A., “Nonlinear transient free-surface flow and dip formation due to a point sink”, Phys. Fluids, Ser. A 5 (1993) 1368–1375.CrossRefGoogle Scholar
[17] Peregrine, D. H., “A line source beneath a free surface”, Univ. Wisconsin Math. Res. Center Tech. Summ. Report 1248 (1972).Google Scholar
[18] Reichel, L., “Solving a model interface problem for the Laplacian operator by boundary collocation and applications”, in Proc. of the 3rd European Conf. on Mathematics in Industry (ed. Manley, J.et. al), (Kluwer Academic Publishers, Stuttgart, 1990), 119–130.Google Scholar
[19] Singler, T. J. and Geer, J. F., “A hybrid perturbation-Galerkin solution to a problem in selective withdrawal”, Phys. Fluids, Ser. A 5 (1993) 1156–1166.CrossRefGoogle Scholar
[20] 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. Ser. B 25 (1984) 443–450.CrossRefGoogle Scholar