Steady water waves with vorticity : An analysis of the dispersion equation
(2014) In Journal of Fluid Mechanics 751. p.3-3- Abstract
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 & 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.
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https://lup.lub.lu.se/record/9d2a8ea9-f5ca-4eca-be49-21aa60b0a317
- author
- Kozlov, V. ; Kuznetsov, N. and Lokharu, E. LU
- publishing date
- 2014-07
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Surface gravity waves, waves/free-surface flows
- in
- Journal of Fluid Mechanics
- volume
- 751
- pages
- 3 - 3
- publisher
- Cambridge University Press
- external identifiers
-
- scopus:84902504578
- ISSN
- 0022-1120
- DOI
- 10.1017/jfm.2014.322
- language
- English
- LU publication?
- no
- id
- 9d2a8ea9-f5ca-4eca-be49-21aa60b0a317
- date added to LUP
- 2023-11-03 13:23:40
- date last changed
- 2024-01-04 07:24:26
@article{9d2a8ea9-f5ca-4eca-be49-21aa60b0a317, abstract = {{<p>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 & 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.</p>}}, author = {{Kozlov, V. and Kuznetsov, N. and Lokharu, E.}}, issn = {{0022-1120}}, keywords = {{Surface gravity waves; waves/free-surface flows}}, language = {{eng}}, pages = {{3--3}}, publisher = {{Cambridge University Press}}, series = {{Journal of Fluid Mechanics}}, title = {{Steady water waves with vorticity : An analysis of the dispersion equation}}, url = {{http://dx.doi.org/10.1017/jfm.2014.322}}, doi = {{10.1017/jfm.2014.322}}, volume = {{751}}, year = {{2014}}, }