Interfacial capillary–gravity short-crested waves

Dalila Boughazi; Mohammed Debiane; Nabil Allalou

doi:10.5802/crmeca.221

Research article

Interfacial capillary–gravity short-crested waves

Dalila Boughazi ^1,²; Mohammed Debiane ² ; Nabil Allalou ³

¹ Université M’Hamed Bougara, Faculté des Sciences, Siège (Ex. INIL) Boumerdès 35000, Algérie
² USTHB, Faculté de physique, BP 32 El Alia Alger, Algérie
³ USTHB, Faculté de physique, BP 32 El Alia Alger Algérie

Comptes Rendus. Mécanique, Volume 351 (2023), pp. 315-334.

Abstract
Résumé

This paper presents a method derived from Whitham’s variational formulation of the problem of interfacial capillary–gravity short-crested waves. It is developed for the resolution of the problem of waves generated by obliquely reflecting interfacial waves from a vertical wall. In essence, Whitham’s method is not changed, but computations are performed and arranged to produce a method that has been applied to a number of cases demonstrating the effectiveness and the flexibility of the approach. The performance of the method is illustrated in several examples including the case of harmonic resonance.

Cet article présente une méthode dérivée de la formulation variationnelle de Whitham du problème des ondes interfaciales à courte crête de gravité–capillarité. Elle est développée pour la résolution du problème des ondes générées par la réflexion oblique des ondes interfaciales sur une paroi verticale. La méthode de Whitham n’est pas modifiée, mais des calculs sont effectués et organisés pour produire une méthode qui a été appliquée à un certain nombre de cas démontrant l’efficacité et la flexibilité de l’approche. La performance de la méthode est illustrée par plusieurs exemples, y compris le cas de la résonance harmonique.

Received: 2023-02-15
Accepted: 2023-07-13
Revised after acceptance: 2023-07-17
Published online: 2023-08-03

DOI: 10.5802/crmeca.221

Keywords: Short-crested interfacial waves, Gravity, Capillarity, Arbitrary depths, Resonance
Mots-clés : Ondes à courtes crêtes interfaciales, Gravité, Capillarité, Épaisseurs arbitraires, Résonance

Author's affiliations:

Dalila Boughazi ^{1, 2}; Mohammed Debiane ²; Nabil Allalou ³

¹ Université M’Hamed Bougara, Faculté des Sciences, Siège (Ex. INIL) Boumerdès 35000, Algérie
² USTHB, Faculté de physique, BP 32 El Alia Alger, Algérie
³ USTHB, Faculté de physique, BP 32 El Alia Alger Algérie

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     author = {Dalila Boughazi and Mohammed Debiane and Nabil Allalou},
     title = {Interfacial capillary{\textendash}gravity short-crested waves},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {315--334},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {351},
     year = {2023},
     doi = {10.5802/crmeca.221},
     language = {en},
}

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Dalila Boughazi; Mohammed Debiane; Nabil Allalou. Interfacial capillary–gravity short-crested waves. Comptes Rendus. Mécanique, Volume 351 (2023), pp. 315-334. doi : 10.5802/crmeca.221. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.221/

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