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Non-existence of three-dimensional travelling water waves with constant non-zero vorticity

Published online by Cambridge University Press:  01 April 2014

E. Wahlén
E. Wahlén*
Affiliation:
Centre for Mathematical Sciences, Lund University, PO Box 118, 22100 Lund, Sweden
*
†Email address for correspondence: [email protected]
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Abstract

We prove that there are no three-dimensional bounded travelling gravity waves with constant non-zero vorticity on water of finite depth. The result also holds for gravity–capillary waves under a certain condition on the pressure at the surface, which is satisfied by sufficiently small waves. The proof relies on unique continuation arguments and Liouville-type results for elliptic equations.

JFM classification

Mathematical Foundations: Mathematical Foundations Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 746 , 10 May 2014 , R2
Copyright
© 2014 Cambridge University Press 

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