Dispersion Equation for Water Waves with Vorticity and Stokes Waves on Flows with Counter-Currents
2014 (English)In: Archive for Rational Mechanics and Analysis, ISSN 0003-9527, E-ISSN 1432-0673, Vol. 214, no 3, 971-1018 p.Article in journal (Refereed) Published
The two-dimensional free-boundary problem of steady periodic waves with vorticity is considered for water of finite depth. We investigate how flows with small-amplitude Stokes waves on the free surface bifurcate from a horizontal parallel shear flow in which counter-currents may be present. Two bifurcation mechanisms are described: one for waves with fixed Bernoullis constant, and the other for waves with fixed wavelength. In both cases the corresponding dispersion equations serve for defining wavelengths from which Stokes waves bifurcate. Necessary and sufficient conditions for the existence of roots of these equations are obtained. Two particular vorticity distributions are considered in order to illustrate the general results.
Place, publisher, year, edition, pages
Springer Verlag (Germany) , 2014. Vol. 214, no 3, 971-1018 p.
IdentifiersURN: urn:nbn:se:liu:diva-112460DOI: 10.1007/s00205-014-0787-0ISI: 000343912400006OAI: oai:DiVA.org:liu-112460DiVA: diva2:766860
Funding Agencies|Swedish Research Council (VR); Linkoping University2014-11-282014-11-282014-11-28