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Global Bifurcation of Capillary-Gravity Water Waves With Overhanging Profiles and Arbitrary Vorticity

Wahlen, Erik LU and Weber, Jörg LU (2023) In International Mathematics Research Notices 2023(20). p.17377-17410
Abstract

We study two-dimensional periodic capillary-gravity water waves propagating at the free surface of water in a flow with arbitrary, prescribed vorticity over a flat bed. Using conformal mappings and a new reformulation of Bernoulli's equation, the problem is equivalently cast into the form "identity plus compact", which is amenable to Rabinowitz's global bifurcation theorem, while no restrictions on the geometry of the surface profile and no assumptions regarding the absence of stagnation points in the flow have to be made. Within the scope of this new formulation, local curves and global families of solutions, bifurcating from laminar flows with a flat surface, are constructed.

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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
International Mathematics Research Notices
volume
2023
issue
20
pages
34 pages
publisher
Oxford University Press
external identifiers
  • scopus:85176934027
ISSN
1073-7928
DOI
10.1093/imrn/rnac280
language
English
LU publication?
yes
id
8269b3a9-8fd6-4cad-aea0-2bd78c47e102
date added to LUP
2024-01-02 15:13:18
date last changed
2024-01-02 15:16:48
@article{8269b3a9-8fd6-4cad-aea0-2bd78c47e102,
  abstract     = {{<p>We study two-dimensional periodic capillary-gravity water waves propagating at the free surface of water in a flow with arbitrary, prescribed vorticity over a flat bed. Using conformal mappings and a new reformulation of Bernoulli's equation, the problem is equivalently cast into the form "identity plus compact", which is amenable to Rabinowitz's global bifurcation theorem, while no restrictions on the geometry of the surface profile and no assumptions regarding the absence of stagnation points in the flow have to be made. Within the scope of this new formulation, local curves and global families of solutions, bifurcating from laminar flows with a flat surface, are constructed.</p>}},
  author       = {{Wahlen, Erik and Weber, Jörg}},
  issn         = {{1073-7928}},
  language     = {{eng}},
  month        = {{10}},
  number       = {{20}},
  pages        = {{17377--17410}},
  publisher    = {{Oxford University Press}},
  series       = {{International Mathematics Research Notices}},
  title        = {{Global Bifurcation of Capillary-Gravity Water Waves With Overhanging Profiles and Arbitrary Vorticity}},
  url          = {{http://dx.doi.org/10.1093/imrn/rnac280}},
  doi          = {{10.1093/imrn/rnac280}},
  volume       = {{2023}},
  year         = {{2023}},
}