Steady water waves with vorticity: an analysis of the dispersion equation
2014 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 751Article in journal (Refereed) Published
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
surface gravity waves; waves/free-surface flows
IdentifiersURN: urn:nbn:se:liu:diva-109176DOI: 10.1017/jfm.2014.322ISI: 000337925000003OAI: oai:DiVA.org:liu-109176DiVA: diva2:737372