A fifth-order approximation to gravity-capillary interfacial waves of infinite depth

Nabil Allalou; Imane Trea; Dalila Boughazi; Mohammed Debiane; Christian Kharif

doi:10.1016/j.crme.2015.12.001

A fifth-order approximation to gravity-capillary interfacial waves of infinite depth

Nabil Allalou ^1,² ; Imane Trea ² ; Dalila Boughazi ² ; Mohammed Debiane ² ; Christian Kharif ³

¹ Université M'Hamed Bougara de Boumerdes, Faculté des sciences, Département de physique, Siège (ex-INIL), Boumerdes 35000, Algeria
² Faculté de physique, Université des sciences et de la technologie Houari-Boumedienne, B.P. 32, El Alia, Algiers 16111, Algeria
³ Institut de recherche sur les phénomènes hors équilibre, Technopole de Chateau-Gombert, 49, rue Frédéric-Joliot-Curie, B.P. 146, 13384 Marseille cedex 13, France

Comptes Rendus. Mécanique, Volume 344 (2016) no. 3, pp. 137-150.

Résumé

Two-dimensional periodic gravity-capillary waves at the interface between two unbounded fluids with different density are analyzed. The lighter fluid is above the interface. The perturbation method is used to obtain solutions to the fifth order for interface profile, velocity potential and oscillation frequency. The solutions have been carefully controlled by other solutions (third-order surface gravity-capillary solutions, third-order interface gravity waves and fifth-order surface gravity waves). These solutions can be used to describe the qualitative nature of small-amplitude traveling waves and provide initial guesses for numerical solutions to the full Euler system. The results highlight the significant influence on wave profile and wave frequency. In addition, this study extends the Wilton singularity to interfacial waves.

Reçu le : 2015-06-28
Accepté le : 2015-12-02
Publié le : 2016-01-28

DOI : 10.1016/j.crme.2015.12.001

Mots clés : Gravity-capillary interfacial wave, Perturbation method, Harmonic resonance

Affiliations des auteurs :

Nabil Allalou ^{1, 2} ; Imane Trea ² ; Dalila Boughazi ² ; Mohammed Debiane ² ; Christian Kharif ³

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     author = {Nabil Allalou and Imane Trea and Dalila Boughazi and Mohammed Debiane and Christian Kharif},
     title = {A fifth-order approximation to gravity-capillary interfacial waves of infinite depth},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {137--150},
     publisher = {Elsevier},
     volume = {344},
     number = {3},
     year = {2016},
     doi = {10.1016/j.crme.2015.12.001},
     language = {en},
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Nabil Allalou; Imane Trea; Dalila Boughazi; Mohammed Debiane; Christian Kharif. A fifth-order approximation to gravity-capillary interfacial waves of infinite depth. Comptes Rendus. Mécanique, Volume 344 (2016) no. 3, pp. 137-150. doi : 10.1016/j.crme.2015.12.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2015.12.001/

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