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Steady water waves with vorticity : An analysis of the dispersion equation

Kozlov, V. ; Kuznetsov, N. and Lokharu, E. LU (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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author
; and
publishing date
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 &amp; 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}},
}