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No steady water waves of small amplitude are supported by a shear flow with a still free surface

Published online by Cambridge University Press:  01 February 2013

Vladimir Kozlov  and
Nikolay Kuznetsov
Vladimir Kozlov
Affiliation:
Department of Mathematics, Linköping University, S-581 83 Linköping, Sweden
Nikolay Kuznetsov*
Affiliation:
Laboratory for Mathematical Modelling of Wave Phenomena, Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, V.O., Bol’shoy pr. 61, St. Petersburg 199178, Russian Federation
*
†Email address for correspondence: nikolay.g.kuznetsov@gmail.com
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Abstract

The two-dimensional free-boundary problem describing steady gravity waves with vorticity on water of finite depth is considered. It is proved that no small-amplitude waves are supported by a horizontal shear flow whose free surface is still, that is, it is stagnant in a coordinate frame such that the flow is time-independent in it. The class of vorticity distributions for which such flows exist includes all positive constant distributions, as well as linear and quadratic ones with arbitrary positive coefficients.

JFM classification

Waves/Free-surface Flows: Channel flow Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 717 , 25 February 2013 , pp. 523 - 534
Copyright
©2013 Cambridge University Press

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