Small-amplitude Stokes and solitary gravity water waves with an arbitrary distribution of vorticity
(2008) In Physica D: Nonlinear Phenomena 237(10-12). p.1530-1538- Abstract
- This paper presents an existence theory for small-amplitude Stokes and solitary-wave solutions to the classical water-wave problem in the absence of surface tension and with an arbitrary distribution of vorticity. The hydrodynamic problem is formulated as an infinite-dimensional Hamiltonian system in which the horizontal spatial coordinate is the time-like variable. A centre-manifold technique is used to reduce the system to a locally equivalent Hamiltonian system with one degree of freedom for values of a dimensionless parameter a near its critical value alpha*. The phase portrait of the reduced system contains a homoclinic orbit for alpha < alpha* and a family of periodic orbits for alpha > alpha*; the corresponding solutions of... (More)
- This paper presents an existence theory for small-amplitude Stokes and solitary-wave solutions to the classical water-wave problem in the absence of surface tension and with an arbitrary distribution of vorticity. The hydrodynamic problem is formulated as an infinite-dimensional Hamiltonian system in which the horizontal spatial coordinate is the time-like variable. A centre-manifold technique is used to reduce the system to a locally equivalent Hamiltonian system with one degree of freedom for values of a dimensionless parameter a near its critical value alpha*. The phase portrait of the reduced system contains a homoclinic orbit for alpha < alpha* and a family of periodic orbits for alpha > alpha*; the corresponding solutions of the water-wave problem are respectively a solitary wave of elevation and a family of Stokes waves. (c) 2008 Elsevier B.V. All rights reserved. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1254596
- author
- Groves, M. D. and Wahlén, Erik LU
- organization
- publishing date
- 2008
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- bifurcation theory, water waves, vorticity
- in
- Physica D: Nonlinear Phenomena
- volume
- 237
- issue
- 10-12
- pages
- 1530 - 1538
- publisher
- Elsevier
- external identifiers
-
- wos:000257529200017
- scopus:44649184941
- ISSN
- 0167-2789
- DOI
- 10.1016/j.physd.2008.03.015
- language
- English
- LU publication?
- yes
- id
- 096193ec-1f5c-4921-be9a-6bea63e58788 (old id 1254596)
- date added to LUP
- 2016-04-01 13:48:46
- date last changed
- 2022-01-27 21:10:41
@article{096193ec-1f5c-4921-be9a-6bea63e58788,
abstract = {{This paper presents an existence theory for small-amplitude Stokes and solitary-wave solutions to the classical water-wave problem in the absence of surface tension and with an arbitrary distribution of vorticity. The hydrodynamic problem is formulated as an infinite-dimensional Hamiltonian system in which the horizontal spatial coordinate is the time-like variable. A centre-manifold technique is used to reduce the system to a locally equivalent Hamiltonian system with one degree of freedom for values of a dimensionless parameter a near its critical value alpha*. The phase portrait of the reduced system contains a homoclinic orbit for alpha < alpha* and a family of periodic orbits for alpha > alpha*; the corresponding solutions of the water-wave problem are respectively a solitary wave of elevation and a family of Stokes waves. (c) 2008 Elsevier B.V. All rights reserved.}},
author = {{Groves, M. D. and Wahlén, Erik}},
issn = {{0167-2789}},
keywords = {{bifurcation theory; water waves; vorticity}},
language = {{eng}},
number = {{10-12}},
pages = {{1530--1538}},
publisher = {{Elsevier}},
series = {{Physica D: Nonlinear Phenomena}},
title = {{Small-amplitude Stokes and solitary gravity water waves with an arbitrary distribution of vorticity}},
url = {{http://dx.doi.org/10.1016/j.physd.2008.03.015}},
doi = {{10.1016/j.physd.2008.03.015}},
volume = {{237}},
year = {{2008}},
}