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IMA Journal of Applied Mathematics 2004 69(3):259-269; doi:10.1093/imamat/69.3.259
© 2004 by Institute of Mathematics and its Applications
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Capillary waves past a flat plate in water of finite depth

S. Tooley1 and J.-M. Vanden-Broeck1

1 School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK

Free-surface flow past a semi-infinite flat plate in a channel of finite depth is considered. The fluid is assumed to be inviscid and incompressible, and the flow to be two-dimensional and irrotational. Surface tension is included in the dynamic boundary condition but the effects of gravity are neglected. It is shown that there is a three-parameter family of solutions with waves in the far field and a discontinuity in slope at the separation point. This family includes as particular cases the solutions previously computed by Osborn & Stump (2001, Phys. Fluids, 13, 616–623) and by Andersson & Vanden-Broeck (1996, Proc. R. Soc., 452, 1985–1997).

Keywords: free surface flows; surface tension; water waves.

Received 29 May 2002. Revised 3 April 2003.


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