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Axisymmetric capillary water waves with vorticity and swirl connecting to static unduloid configurations

Otsetova, Anna Mariya ; Wahlén, Erik LU orcid and Weber, Jörg LU (2024) In Journal of Differential Equations 411. p.604-618
Abstract

We study steady axisymmetric water waves with general vorticity and swirl, subject to the influence of surface tension. Explicit solutions to such a water wave problem are static configurations where the surface is an unduloid, that is, a periodic surface of revolution with constant mean curvature. We prove that to any such configuration there connects a global continuum of non-static solutions by means of a global implicit function theorem. To prove this, the key is strict monotonicity of a certain function describing the mean curvature of an unduloid and involving complete elliptic integrals. From this point of view, this paper is an interesting interplay between water waves, geometry, and properties of elliptic integrals.

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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Axisymmetric flows, Constant mean curvature, Elliptic integrals, Steady water waves, Vorticity
in
Journal of Differential Equations
volume
411
pages
15 pages
publisher
Academic Press
external identifiers
  • scopus:85201238053
ISSN
0022-0396
DOI
10.1016/j.jde.2024.08.005
language
English
LU publication?
yes
id
0c748dc0-8db2-45bb-b689-a5788d977cb0
date added to LUP
2025-01-09 10:56:49
date last changed
2025-04-04 14:24:57
@article{0c748dc0-8db2-45bb-b689-a5788d977cb0,
  abstract     = {{<p>We study steady axisymmetric water waves with general vorticity and swirl, subject to the influence of surface tension. Explicit solutions to such a water wave problem are static configurations where the surface is an unduloid, that is, a periodic surface of revolution with constant mean curvature. We prove that to any such configuration there connects a global continuum of non-static solutions by means of a global implicit function theorem. To prove this, the key is strict monotonicity of a certain function describing the mean curvature of an unduloid and involving complete elliptic integrals. From this point of view, this paper is an interesting interplay between water waves, geometry, and properties of elliptic integrals.</p>}},
  author       = {{Otsetova, Anna Mariya and Wahlén, Erik and Weber, Jörg}},
  issn         = {{0022-0396}},
  keywords     = {{Axisymmetric flows; Constant mean curvature; Elliptic integrals; Steady water waves; Vorticity}},
  language     = {{eng}},
  pages        = {{604--618}},
  publisher    = {{Academic Press}},
  series       = {{Journal of Differential Equations}},
  title        = {{Axisymmetric capillary water waves with vorticity and swirl connecting to static unduloid configurations}},
  url          = {{http://dx.doi.org/10.1016/j.jde.2024.08.005}},
  doi          = {{10.1016/j.jde.2024.08.005}},
  volume       = {{411}},
  year         = {{2024}},
}