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No steady water waves of small amplitude are supported by a shear flow with a still free surface
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
Russian Academic Science, St. Petersburg, Russia .
2013 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 717, 523-534 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Cambridge University Press, 2013. Vol. 717, 523-534 p.
Keyword [en]
channel flow, surface gravity waves, waves/free-surface flows
National Category
Natural Sciences
URN: urn:nbn:se:liu:diva-89745DOI: 10.1017/jfm.2012.593ISI: 000314423900023OAI: diva2:609364

Funding Agencies|Swedish Research Council (VR)||G. S. Magnusons Foundation of the Royal Swedish Academy of Sciences||Linkoping University||

Available from: 2013-03-05 Created: 2013-03-05 Last updated: 2013-03-14

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Kozlov, Vladimir
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