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.
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.
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Mots-clés : Mécanique des fluides, Vagues, Bifurcation, Brisure de symétrie, Profondeur infinie
Rabah Aider 1; Mohammed Debiane 1
@article{CRMECA_2004__332_7_565_0,
author = {Rabah Aider and Mohammed Debiane},
title = {Symmetry-breaking in periodic gravity waves with weak surface tension and gravity-capillary waves on deep water},
journal = {Comptes Rendus. M\'ecanique},
pages = {565--570},
publisher = {Elsevier},
volume = {332},
number = {7},
year = {2004},
doi = {10.1016/j.crme.2004.03.003},
language = {en},
}
TY - JOUR AU - Rabah Aider AU - Mohammed Debiane TI - Symmetry-breaking in periodic gravity waves with weak surface tension and gravity-capillary waves on deep water JO - Comptes Rendus. Mécanique PY - 2004 SP - 565 EP - 570 VL - 332 IS - 7 PB - Elsevier DO - 10.1016/j.crme.2004.03.003 LA - en ID - CRMECA_2004__332_7_565_0 ER -
%0 Journal Article %A Rabah Aider %A Mohammed Debiane %T Symmetry-breaking in periodic gravity waves with weak surface tension and gravity-capillary waves on deep water %J Comptes Rendus. Mécanique %D 2004 %P 565-570 %V 332 %N 7 %I Elsevier %R 10.1016/j.crme.2004.03.003 %G en %F CRMECA_2004__332_7_565_0
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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