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Unsteady flows induced by a point source or sink in a fluid of finite depth

Published online by Cambridge University Press:  22 July 2016

T. E. STOKES ,
G. C. HOCKING  and
L. K. FORBES
T. E. STOKES
Affiliation:
Department of Mathematics, University of Waikato, Hamilton, New Zealand email: stokes@waikato.ac.nz
G. C. HOCKING
Affiliation:
Mathematics and Statistics, Murdoch University, Murdoch, Western Australia, 6150, Australia email: G.Hocking@murdoch.edu.au
L. K. FORBES
Affiliation:
School of Mathematics and Physics, University of Tasmania, GPO Box 252-37, Hobart 7001, Australia email: Larry.Forbes@utas.edu.au
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Abstract

The time-varying flow in which fluid is withdrawn from or added to a reservoir of infinite or arbitrary finite depth through a point sink or source of variable strength beneath a free surface is considered. Backed up by some analytic work, a numerical method is used, and the results are compared with previous work on steady and unsteady flows. In the case of withdrawal for an impulsively started flow, it is found that the critical flow rate increases with reservoir depth, although it changes little as the depth increases beyond double the sink submergence depth. The largest flow rate at which steady solutions can evolve in source flows follows a similar pattern although at a considerably higher value. Simulations indicate that some of the previously calculated steady state solutions at higher flow rates may be unstable, if they exist at all.

Keywords

Free-surface potential flowsideal fluids
Type
Papers
Information
European Journal of Applied Mathematics , Volume 28 , Issue 3 , June 2017 , pp. 357 - 379
Copyright
Copyright © Cambridge University Press 2016 

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