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Rigidity of symmetric doubly-periodic water waves near shear flows

Svensson Seth, Douglas ; Varholm, Kristoffer LU ; Wahlén, Erik LU orcid and Weber, Jörg LU (2026) In Nonlinearity 39(3).
Abstract

We prove that symmetric, doubly periodic, capillary-gravity water waves in finite depth bifurcating from non-uniform non-stagnant shear flows are necessarily two-dimensional to leading order. This is in stark contrast to the case of uniform background flows, where the existence of truly three-dimensional bifurcating waves is well known. While this paper focuses on capillary-gravity water waves, our proof also applies to other suitable types of dynamic boundary conditions, such as hydroelastic waves.

Please use this url to cite or link to this publication:
author
; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
bifurcation, doubly periodic, rigidity, shear flow, steady, vorticity, water waves
in
Nonlinearity
volume
39
issue
3
article number
035015
publisher
IOP Publishing
external identifiers
  • scopus:105034542495
ISSN
0951-7715
DOI
10.1088/1361-6544/ae49d8
language
English
LU publication?
yes
id
ad510a7b-e27c-4c9f-8709-c794eba7a6ce
date added to LUP
2026-04-30 12:27:13
date last changed
2026-04-30 12:28:16
@article{ad510a7b-e27c-4c9f-8709-c794eba7a6ce,
  abstract     = {{<p>We prove that symmetric, doubly periodic, capillary-gravity water waves in finite depth bifurcating from non-uniform non-stagnant shear flows are necessarily two-dimensional to leading order. This is in stark contrast to the case of uniform background flows, where the existence of truly three-dimensional bifurcating waves is well known. While this paper focuses on capillary-gravity water waves, our proof also applies to other suitable types of dynamic boundary conditions, such as hydroelastic waves.</p>}},
  author       = {{Svensson Seth, Douglas and Varholm, Kristoffer and Wahlén, Erik and Weber, Jörg}},
  issn         = {{0951-7715}},
  keywords     = {{bifurcation; doubly periodic; rigidity; shear flow; steady; vorticity; water waves}},
  language     = {{eng}},
  number       = {{3}},
  publisher    = {{IOP Publishing}},
  series       = {{Nonlinearity}},
  title        = {{Rigidity of symmetric doubly-periodic water waves near shear flows}},
  url          = {{http://dx.doi.org/10.1088/1361-6544/ae49d8}},
  doi          = {{10.1088/1361-6544/ae49d8}},
  volume       = {{39}},
  year         = {{2026}},
}