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A line sink in a flowing stream with surface tension effects

Published online by Cambridge University Press:  30 October 2015

R. J. HOLMES  and
G. C. HOCKING
R. J. HOLMES
Affiliation:
Mathematics and Statistics, Murdoch University, Perth, Western Australia email: rachel.holmes.22@gmail.com, G.Hocking@murdoch.edu.au
G. C. HOCKING
Affiliation:
Mathematics and Statistics, Murdoch University, Perth, Western Australia email: rachel.holmes.22@gmail.com, G.Hocking@murdoch.edu.au
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Abstract

We examine a problem in which a line sink causes a disturbance to an otherwise uniform flowing stream of infinite depth. We consider the fully non-linear problem with the inclusion of surface tension and find the maximum sink strength at which steady solutions exist for a given stream flow, before examining non-unique solutions. The addition of surface tension allows for a more thorough investigation into the characteristics of the solutions. The breakdown of steady solutions with surface tension appears to be caused by a curvature singularity as the flow rate approaches the maximum. The non-uniqueness in solutions is shown to occur for a range of parameter values in all cases with non-zero surface tension.

Keywords

free surface flowsubmerged sinksurface tensionselective withdrawal
Type
Papers
Information
European Journal of Applied Mathematics , Volume 27 , Issue 2 , April 2016 , pp. 248 - 263
Copyright
Copyright © Cambridge University Press 2015 

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