LARGE-AMPLITUDE STEADY GRAVITY WATER WAVES WITH GENERAL VORTICITY AND CRITICAL LAYERS
(2024) In Duke Mathematical Journal 173(11). p.2197-2258- 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 reformulation of Bernoulli’s equation, we uncover an equivalent formulation as “identity plus compact,” which is amenable to Rabinowitz’s 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 certain spectral assumption involving the vorticity function. Lastly,... (More)
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 reformulation of Bernoulli’s equation, we uncover an equivalent formulation as “identity plus compact,” which is amenable to Rabinowitz’s 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 certain spectral assumption involving the vorticity function. Lastly, downstream waves are investigated in more detail.
(Less)
- author
- Wahlén, Erik LU and Weber, Jörg LU
- organization
- publishing date
- 2024
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Duke Mathematical Journal
- volume
- 173
- issue
- 11
- pages
- 62 pages
- publisher
- Duke University Press
- external identifiers
-
- scopus:85200454460
- ISSN
- 0012-7094
- DOI
- 10.1215/00127094-2023-0054
- language
- English
- LU publication?
- yes
- id
- 6bf2c2e7-cb07-4d4e-81a9-bbb3e21a15d3
- date added to LUP
- 2024-11-05 15:29:58
- date last changed
- 2024-11-05 15:39:40
@article{6bf2c2e7-cb07-4d4e-81a9-bbb3e21a15d3, abstract = {{<p>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 reformulation of Bernoulli’s equation, we uncover an equivalent formulation as “identity plus compact,” which is amenable to Rabinowitz’s 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 certain spectral assumption involving the vorticity function. Lastly, downstream waves are investigated in more detail.</p>}}, author = {{Wahlén, Erik and Weber, Jörg}}, issn = {{0012-7094}}, language = {{eng}}, number = {{11}}, pages = {{2197--2258}}, publisher = {{Duke University Press}}, series = {{Duke Mathematical Journal}}, title = {{LARGE-AMPLITUDE STEADY GRAVITY WATER WAVES WITH GENERAL VORTICITY AND CRITICAL LAYERS}}, url = {{http://dx.doi.org/10.1215/00127094-2023-0054}}, doi = {{10.1215/00127094-2023-0054}}, volume = {{173}}, year = {{2024}}, }