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Steady water waves with vorticity: an analysis of the dispersion equation
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
Russian Academy of Sciences, St Petersburg, Russia.
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
2014 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 751Article in journal (Refereed) Published
Abstract [en]

Two-dimensional steady gravity waves with vorticity are considered on water of finite depth. The dispersion equation is analysed for general vorticity distributions, but under assumptions valid only for unidirectional shear flows. It is shown that for these flows (i) the general dispersion equation is equivalent to the Sturm-Liouville problem considered by Constantin and Strauss (Commun. Pure Appl. Math., vol. 57, 2004, pp. 481-527; Arch. Rat. Mech. Anal., vol. 202, 2011, pp. 133-175), (ii) the condition guaranteeing bifurcation of Stokes waves with constant wavelength is fulfilled. Moreover, a necessary and sufficient condition that the Sturm-Liouville problem mentioned in (i) has an eigenvalue is obtained.

Place, publisher, year, edition, pages
Cambridge University Press, 2014. Vol. 751
Keyword [en]
surface gravity waves; waves/free-surface flows
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-109176DOI: 10.1017/jfm.2014.322ISI: 000337925000003OAI: oai:DiVA.org:liu-109176DiVA: diva2:737372
Available from: 2014-08-12 Created: 2014-08-11 Last updated: 2017-12-05Bibliographically approved

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Kozlov, VladimirLokharu, Evgeniy

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