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On the Benjamin-Lighthill conjecture for water waves with vorticity
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
Russian Academic Science, Russia.
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
2017 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 825, 961-1001 p.Article in journal (Refereed) Published
Abstract [en]

We consider the nonlinear problem of steady gravity-driven waves on the free surface of a two-dimensional flow of an inviscid, incompressible fluid (say, water). The water motion is supposed to be rotational with a Lipschitz continuous vorticity distribution, whereas the flow of finite depth is assumed to be unidirectional. We verify the Benjamin-Lighthill conjecture for flows with values of Bernoullis constant close to the critical one. For this purpose it is shown that a set of near-critical waves consists only of Stokes and solitary waves provided their slopes are bounded by a constant. Moreover, the subset of waves with crests located on a fixed vertical is uniquely parametrised by the flow force, which varies between its values for the supercritical and subcritical shear flows of constant depth. There exists another parametrisation for this set; it involves wave heights varying between the constant depth of the subcritical shear flow and the height of a solitary wave.

Place, publisher, year, edition, pages
CAMBRIDGE UNIV PRESS , 2017. Vol. 825, 961-1001 p.
Keyword [en]
surface gravity waves; waves/free-surface flows
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:liu:diva-139806DOI: 10.1017/jfm.2017.361ISI: 000406367300008OAI: oai:DiVA.org:liu-139806DiVA: diva2:1133922
Note

Funding Agencies|Swedish Research Council; G.S. Magnusons Foundation of Royal Swedish Academy of Sciences; Linkoping University

Available from: 2017-08-17 Created: 2017-08-17 Last updated: 2017-08-17

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CiteExportLink to record
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Citation style
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