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

Vladimir Kozlov; Nikolay Kuznetsov; Evgeniy Lokharu

doi:10.1017/jfm.2014.747

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

Mathematical Physics 2015-06-23 v1 math.MP

Authors: Vladimir Kozlov , Nikolay Kuznetsov , Evgeniy Lokharu

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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 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.

Keywords

steady gravity waves vorticity free-surface profile bernoulli's constant shear flow non-existence results

Cite

@article{arxiv.1410.3665,
  title  = {On bounds and non-existence in the problem of steady waves with vorticity},
  author = {Vladimir Kozlov and Nikolay Kuznetsov and Evgeniy Lokharu},
  journal= {arXiv preprint arXiv:1410.3665},
  year   = {2015}
}