Symmetry-breaking in periodic gravity waves with weak surface tension and gravity-capillary waves on deep water

Rabah Aider; Mohammed Debiane

doi:10.1016/j.crme.2004.03.003

Symmetry-breaking in periodic gravity waves with weak surface tension and gravity-capillary waves on deep water
[Brisure de symétrie dans les vagues de gravité avec une faible tension de surface et les vagues de gravité-capillarité périodiques en eau profonde]

Présenté par : Paul Clavin

Rabah Aider ¹ ; Mohammed Debiane ¹

¹ U.S.T.H.B, faculté de physique, BP 32, El Alia 16111, Bab Ezzouar, Alger, Algeria

Comptes Rendus. Mécanique, Volume 332 (2004) no. 7, pp. 565-570.

Résumé
Abstract

La méthode développée par Debiane et Kharif pour le calcul des ondes de gravité-capillarité symétriques en profondeur infinie a été étendue aux cas de vagues à profils non-symétriques. Nous avons calculé des ondes de gravité-capillarité non-symétriques périodiques et de formes permanentes. Elles apparaissent via des bifurcations à partir d'une solution symétrique. D'autre part, nous avons trouvé qu'en présence d'une très faible tension de surface, la brisure de symétrie d'une onde de gravité périodique de classe 1 en profondeur infinie est possible à l'approche de sa forme limite.

The method developed by Debiane and Kharif for the calculation of symmetric gravity-capillary waves on infinite depth is extended to the general case of non-symmetric solutions. We have calculated non-symmetric steady periodic gravity-capillary waves on deep water. It is found that they appear via bifurcations from a family of symmetric waves. On the other hand we found that the symmetry-breaking bifurcation of periodic steady class 1 gravity wave on deep water is possible when it approaches the limiting profile, if it is very weakly influenced by surface tension effects.

Reçu le : 2003-10-22
Accepté le : 2004-02-10
Publié le : 2004-04-30

DOI : 10.1016/j.crme.2004.03.003

Keywords: Fluid mechanics, Water waves, Bifurcation, Symmetry-breaking, Infinite depth
Mots-clés : Mécanique des fluides, Vagues, Bifurcation, Brisure de symétrie, Profondeur infinie

Affiliations des auteurs :

Rabah Aider ¹ ; Mohammed Debiane ¹

¹ U.S.T.H.B, faculté de physique, BP 32, El Alia 16111, Bab Ezzouar, Alger, Algeria

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     title = {Symmetry-breaking in periodic gravity waves with weak surface tension and gravity-capillary waves on deep water},
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     language = {en},
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Rabah Aider; Mohammed Debiane. Symmetry-breaking in periodic gravity waves with weak surface tension and gravity-capillary waves on deep water. Comptes Rendus. Mécanique, Volume 332 (2004) no. 7, pp. 565-570. doi : 10.1016/j.crme.2004.03.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.03.003/

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V. Kozlov; E. Lokharu Small-amplitude steady water waves with critical layers: non-symmetric waves, Journal of Differential Equations, Volume 267 (2019) no. 7, pp. 4170-4191 | DOI:10.1016/j.jde.2019.04.036 | Zbl:1420.35245
Hung-Chu Hsu; Meng-Syue Li; Li-Hung Tsai Lagrangian description of gravity-capillary waves propagating on a sloping bottom, Applied Mathematics and Computation, Volume 233 (2014), pp. 494-504 | DOI:10.1016/j.amc.2014.01.164 | Zbl:1334.76017
Rabah Aider; Mohammed Debiane A method for the calculation of nonsymmetric steady periodic capillary–gravity waves on water of arbitrary uniform depth, Comptes Rendus. Mécanique, Volume 334 (2006) no. 6, p. 387 | DOI:10.1016/j.crme.2006.04.002

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