Bifurcation analysis for axisymmetric capillary water waves with vorticity and swirl
(2022) In Studies in Applied Mathematics 149(4). p.904-942- Abstract
We study steady axisymmetric water waves with general vorticity and swirl, subject to the influence of surface tension. This can be formulated as an elliptic free boundary problem in terms of Stokes' stream function. A change of variables allows us to overcome the generic coordinate-induced singularities and to cast the problem in the form “identity plus compact,” which is amenable to Rabinowitz's global bifurcation theorem, whereas no restrictions 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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/5c933f9f-c5d2-4894-9dcd-0727d8de1114
- author
- Erhardt, André H. LU ; Wahlén, Erik LU and Weber, Jörg LU
- organization
- publishing date
- 2022
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- axisymmetric flows, bifurcation, steady water waves, vorticity
- in
- Studies in Applied Mathematics
- volume
- 149
- issue
- 4
- pages
- 904 - 942
- publisher
- Wiley-Blackwell
- external identifiers
-
- pmid:36605702
- scopus:85135898055
- ISSN
- 0022-2526
- DOI
- 10.1111/sapm.12525
- language
- English
- LU publication?
- yes
- id
- 5c933f9f-c5d2-4894-9dcd-0727d8de1114
- date added to LUP
- 2022-09-12 14:33:44
- date last changed
- 2024-04-18 15:38:05
@article{5c933f9f-c5d2-4894-9dcd-0727d8de1114,
abstract = {{<p>We study steady axisymmetric water waves with general vorticity and swirl, subject to the influence of surface tension. This can be formulated as an elliptic free boundary problem in terms of Stokes' stream function. A change of variables allows us to overcome the generic coordinate-induced singularities and to cast the problem in the form “identity plus compact,” which is amenable to Rabinowitz's global bifurcation theorem, whereas no restrictions 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 = {{Erhardt, André H. and Wahlén, Erik and Weber, Jörg}},
issn = {{0022-2526}},
keywords = {{axisymmetric flows; bifurcation; steady water waves; vorticity}},
language = {{eng}},
number = {{4}},
pages = {{904--942}},
publisher = {{Wiley-Blackwell}},
series = {{Studies in Applied Mathematics}},
title = {{Bifurcation analysis for axisymmetric capillary water waves with vorticity and swirl}},
url = {{http://dx.doi.org/10.1111/sapm.12525}},
doi = {{10.1111/sapm.12525}},
volume = {{149}},
year = {{2022}},
}