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Free streamline flows with singularities

Published online by Cambridge University Press:  18 March 2010

J. EGGERS  and
A. F. SMITH
J. EGGERS*
Affiliation:
School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK
A. F. SMITH
Affiliation:
School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK
*
†Email address for correspondence: [email protected]
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Abstract

We rederive and expand upon a method for finding solutions to the two-dimensional irrotational (inviscid) flow equations in the presence of a free surface, found by Hopkinson. This method allows the flow to be driven by placing singularities, like sources or vortices, in the interior of the flow domain. We then apply the method to find a number of novel solutions: separated flow driven by a source, vortices behind a plate and free-surface flow stirred by a double vortex. Free surfaces generically exhibit cusp singularities with a 2/3 power index, similar to those found in very viscous flow.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 647: Dedicated to Professor S. H. Davis on his 70th birthday , 25 March 2010 , pp. 187 - 200
Copyright
Copyright © Cambridge University Press 2010

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