Skip to main content

Lund University Publications

LUND UNIVERSITY LIBRARIES

Large-amplitude steady gravity water waves with general vorticity and critical layers

Weber, Jörg LU and Wahlén, Erik LU orcid (2022)
Abstract
We consider two-dimensional steady periodic gravity waves on water of finite depth with a prescribed but arbitrary vorticity distribution. The water surface is allowed to be overhanging and no assumptions regarding the absence of stagnation points and critical layers are made. Using conformal mappings and a new Babenko-type reformulation of Bernoulli's equation, we uncover an equivalent formulation as "identity plus compact", which is amenable to Rabinowitz' global bifurcation theorem. This allows us to construct a global connected set of solutions, bifurcating from laminar flows with a flat surface. Moreover, a nodal analysis is carried out for these solutions under a monotonicity assumption on the vorticity function.
Please use this url to cite or link to this publication:
author
and
organization
publishing date
type
Working paper/Preprint
publication status
published
subject
publisher
arXiv.org
DOI
10.48550/arXiv.2204.10071
language
English
LU publication?
yes
id
05d704e9-909c-4b44-9547-f203fc9959f9
date added to LUP
2023-03-25 18:57:52
date last changed
2023-04-27 10:53:13
@misc{05d704e9-909c-4b44-9547-f203fc9959f9,
  abstract     = {{We consider two-dimensional steady periodic gravity waves on water of finite depth with a prescribed but arbitrary vorticity distribution. The water surface is allowed to be overhanging and no assumptions regarding the absence of stagnation points and critical layers are made. Using conformal mappings and a new Babenko-type reformulation of Bernoulli's equation, we uncover an equivalent formulation as "identity plus compact", which is amenable to Rabinowitz' global bifurcation theorem. This allows us to construct a global connected set of solutions, bifurcating from laminar flows with a flat surface. Moreover, a nodal analysis is carried out for these solutions under a monotonicity assumption on the vorticity function.}},
  author       = {{Weber, Jörg and Wahlén, Erik}},
  language     = {{eng}},
  note         = {{Preprint}},
  publisher    = {{arXiv.org}},
  title        = {{Large-amplitude steady gravity water waves with general vorticity and critical layers}},
  url          = {{http://dx.doi.org/10.48550/arXiv.2204.10071}},
  doi          = {{10.48550/arXiv.2204.10071}},
  year         = {{2022}},
}