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arXiv · 1209.3738

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

Vladimir Kozlov·Nikolay Kuznetsov
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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 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 quadric ones with arbitrary positive coefficients.

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Vladimir Kozlov, Nikolay Kuznetsov. 2012-09-17. No steady water waves of small amplitude are supported by a shear flow with still free surface. https://doi.org/10.1017/jfm.2012.593

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