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THE EFFECT OF SURFACE TENSION ON FREE-SURFACE FLOW INDUCED BY A POINT SINK

Published online by Cambridge University Press:  18 March 2016

G. C. HOCKING
Affiliation:
Mathematics & Statistics, Murdoch University, Perth, WA, Australia email G.Hocking@murdoch.edu.au, Ha.Nguyen@murdoch.edu.au
H. H. N. NGUYEN
Affiliation:
Mathematics & Statistics, Murdoch University, Perth, WA, Australia email G.Hocking@murdoch.edu.au, Ha.Nguyen@murdoch.edu.au
L. K. FORBES
Affiliation:
School of Mathematics & Physics, University of Tasmania, Hobart, Australia email Larry.Forbes@utas.edu.au
T. E. STOKES
Affiliation:
Department of Mathematics, University of Waikato, Hamilton, New Zealand email stokes@waikato.ac.nz
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Abstract

The steady, axisymmetric flow induced by a point sink (or source) submerged in an inviscid fluid of infinite depth is computed and the resulting deformation of the free surface is obtained. The effect of surface tension on the free surface is determined and is the new component of this work. The maximum Froude numbers at which steady solutions exist are computed. It is found that the determining factor in reaching the critical flow changes as more surface tension is included. If there is zero or a very small amount of surface tension, the limiting factor appears to be the formation of small wavelets on the free surface; but, as the surface tension increases, this is replaced by a tendency for the lowest point on the free surface to descend sharply as the Froude number is increased.

Type
Research Article
Copyright
© 2016 Australian Mathematical Society 

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