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On bounds and non-existence in the problem of steady waves with vorticity

Published online by Cambridge University Press:  15 January 2015

V. Kozlov ,
N. Kuznetsov  and
E. Lokharu
V. Kozlov
Affiliation:
Department of Mathematics, Linköping University, S-581 83 Linköping, Sweden
N. Kuznetsov*
Affiliation:
Laboratory for Mathematical Modelling of Wave Phenomena, Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, VO, Bol’shoy pr. 61, St Petersburg 199178, Russian Federation
E. Lokharu
Affiliation:
Department of Mathematics, Linköping University, S-581 83 Linköping, Sweden
*
†Email address for correspondence: [email protected]
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Abstract

For the problem describing steady gravity waves with vorticity on a two-dimensional unidirectional flow of finite depth the following results are obtained. (i) Bounds are found for the free-surface profile and for Bernoulli’s constant. (ii) If only one parallel shear flow exists for a given value of Bernoulli’s constant, then there are no wave solutions provided the vorticity distribution is subject to a certain condition.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 765 , 25 February 2015 , R1
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Copyright
© 2015 Cambridge University Press 

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