J Austral Math Soc Ser B 32 pp231--249, 1990.

Flow caused by a point sink in a fluid having a free surface

Lawrence K. Forbes and Graeme C. Hocking

Abstract

The flow caused by a point sink immersed in an otherwise stationary fluid is investigated. Low Froude number solutions are sought, in which the flow is radially symmetric and possesses a stagnation point at the surface, directly above the sink. A small-Froude-number expansion is derived and compared with the results of a numerical solution to the fully nonlinear problem. It is found that solutions of this type exist for all Froude numbers less than some maximum value, at which a secondary circular stagnation line is formed at the surface. The nonlinear solutions are reasonably well predicted by the small-Froude-number expansion, except for Froude numbers close to this maximum.

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Authors

Lawrence K. Forbes

Department of Mathematics, University of Queensland, St. Lucia, Queensland 4067, Australia.

Graeme C. Hocking

Centre for Water Research, University of Western Australia, Western Australia 6009, Australia.