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A NOTE ON STEADY FLOW INTO A SUBMERGED POINT SINK

Published online by Cambridge University Press:  14 October 2014

G. C. HOCKING ,
L. K. FORBES  and
T. E. STOKES
G. C. HOCKING*
Affiliation:
Mathematics & Statistics, Murdoch University, Perth, WA, Australia email [email protected]
L. K. FORBES
Affiliation:
School of Mathematics & Physics, University of Tasmania, Hobart, Australia email [email protected]
T. E. STOKES
Affiliation:
Department of Mathematics, University of Waikato, Hamilton, New Zealand email [email protected]
*
✉[email protected]
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Abstract

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The steady, axisymmetric flow induced by a point sink (or source) submerged in an unbounded inviscid fluid is computed. The resulting deformation of the free surface is obtained, and a limit of steady solutions is found that is quite different to those obtained in past work. More accurate solutions indicate that the old limiting flow rate was too high and, in fact, the breakdown of steady solutions at a lower flow rate is characterized by the appearance of spurious wavelets at the free surface.

Keywords

0102selective withdrawalpoint sinkaxisymmetric flowfree surface flow
Type
Research Article
Information
The ANZIAM Journal , Volume 56 , Issue 2 , October 2014 , pp. 150 - 159
Copyright
Copyright © 2014 Australian Mathematical Society 

References

Abramowitz, M. and Stegun, I. A., Handbook of mathematical functions (Dover, New York, 1972).Google Scholar
Craya, A., “Theoretical research on the flow of nonhomogeneous fluids”, La Houille Blanche 4 (1949) 44–55 ; doi:10.1051/lhb/1949017.Google Scholar
Forbes, L. K. and Hocking, G. C., “Flow caused by a point sink in a fluid having a free surface”, J. Aust. Math. Soc. B 32 (1990) 231–249 ; doi:10.1017/S0334270000008465.CrossRefGoogle Scholar
Forbes, L. K. and Hocking, G. C., “Withdrawal from a two-layer inviscid fluid in a duct”, J. Fluid Mech. 361 (1998) 275–296 ; doi:10.1017/S0334270000010742.CrossRefGoogle Scholar
Forbes, L. K. and Hocking, G. C., “Supercritical withdrawal from a two-layer fluid through a line sink if the lower layer is of finite depth”, J. Fluid Mech. 428 (2001) 333–348 ;doi:10.1017/S0022112000002780.Google Scholar
Forbes, L. K. and Hocking, G. C., “On the computation of steady axi-symmetric withdrawal from a two-layer fluid”, Comput. & Fluids 32 (2003) 385–401 ; doi:10.1017/S0022112098008805.Google Scholar
Forbes, L. K., Hocking, G. C. and Chandler, G. A., “A note on withdrawal through a point sink in fluid of finite depth”, J. Aust. Math. Soc. B 37 (1996) 406–416 ;doi:10.1017/S0334270000008961.CrossRefGoogle Scholar
Hocking, G. C., “Withdrawal from two-layer fluid through line sink”, J. Hydraul. Engrg. ASCE 117 (1991) 800–805 ; doi:10.1061/(ASCE)0733-9429(1991)117:6(800).CrossRefGoogle Scholar
Hocking, G. C., “Supercritical withdrawal from a two-layer fluid through a line sink”, J. Fluid Mech. 297 (1995) 37–47 ; doi:10.1017/S022112095002990.Google Scholar
Hocking, G. C., Vanden Broeck, J. M. and Forbes, L. K., “Withdrawal from a fluid of finite depth through a point sink”, ANZIAM J. 44 (2002) 181–191 ; doi:10.1017/S1446181100013882.Google Scholar
Huber, D. G., “Irrotational motion of two fluid strata towards a line sink”, J. Engrg. Mech. Div. Proc. ASCE 86 (1960) 71–85.Google Scholar
Imberger, J. and Patterson, J. C., “Physical limnology”, in: Advances in applied mechanics, Volume 27 (eds Hutchinson, J. W. and Wu, T.), (Academic Press, Boston, MA, 1989) 303–475. doi:10.1016/S0065-2156(08)70199-6.Google Scholar
Jirka, G. H., “Supercritical withdrawal from two-layered fluid systems, Part 1 – Two-dimensional skimmer wall”, J. Hydraul. Res. 17 (1979) 43–51 ; doi:10.1080/00221687909499599.Google Scholar
Jirka, G. H. and Katavola, D. S., “Supercritical withdrawal from two-layered fluid systems, Part 2 – Three-dimensional flow into a round intake”, J. Hydraul. Res. 17 (1979) 53–62 ;doi:10.1080/00221687909499600.CrossRefGoogle Scholar
Moore, D. W., “Spontaneous appearance of a singularity in the shape of an evolving vortex sheet”, Proc. R. Soc. Lond. Ser. A 365 (1979) 105–119 ; doi:10.1098/rspa.1979.0009.Google Scholar
Sautreaux, C., “Mouvement d’un liquide parfait soumis à lapesanteur. Détermination des lignes de courant”, J. Math. Pures Appl. 7 (1901) 125–159.Google Scholar
Stokes, T. E., Hocking, G. C. and Forbes, L. K., “Unsteady free surface flow induced by a line sink”, J. Engrg. Math. 47 (2003) 137–160 ; doi:10.1023/A:1025892915279.Google Scholar
Stokes, T. E., Hocking, G. C. and Forbes, L. K., “Unsteady flow induced by a withdrawal point beneath a free surface”, ANZIAM J. 47 (2005) 185–202 ; doi:10.1017/S1446181100009986.Google Scholar
Stokes, T. E., Hocking, G. C. and Forbes, L. K., “Steady free surface flow induced by a submerged ring source or sink”, J. Fluid Mech. 694 (2012) 352–370 ; doi:10.1017/jfm.2011.551.Google Scholar
Tuck, E. O., “On air flow over free surfaces of stationary water”, J. Aust. Math. Soc. B 19 (1975) 66–80 ; doi:10.1017/S0334270000000953.CrossRefGoogle Scholar
Tuck, E. O. and Vanden Broeck, J. M., “A cusp-like free surface flow due to a submerged source or sink”, J. Aust. Math. Soc. B 25 (1984) 443–450 ; doi:10.1017/S0334270000004197.Google Scholar
Tyvand, P. A., “Unsteady free-surface flow due to a line source”, Phys. Fluids A 4 (1992) 671–676 ; doi:10.1063/1.858285.Google Scholar
Wood, I. R. and Lai, K. K., “Selective withdrawal from a two-layered fluid”, J. Hydraul. Res. 10 (1972) 475–496 ; doi:10.1080/00221687209500036.CrossRefGoogle Scholar
Xue, X. and Yue, D. K. P., “Nonlinear free-surface flow due to an impulsively started submerged point sink”, J. Fluid Mech. 364 (1998) 325–347 ; doi:10.1017/S022112098001335.CrossRefGoogle Scholar