Comptes Rendus
no. 11
Mathematical Problems in Mechanics
Equivariant cosymmetry and front solutions of the Dubreil–Jacotin–Long equation. Part 1: Boussinesq limit
[Cosymétrie équivariante et solutions « fronts » de l'équation de Dubreil–Jacotin–Long. 1ère partie : la limite Boussinesq]

Présenté par : Gérard Iooss

Nikolai Makarenko1
1 Lavrentyev Institute of Hydrodynamics, Lavrentyev av., 15, 630090 Novosibirsk, Russia
Comptes Rendus. Mathématique, Volume 337 (2003) no. 11, pp. 753-756.

On considère le problème d'écoulement bidimensionnel en ondes internes progressives dans un fluide parfait, à densité régulière voisine d'une stratification linéaire. On construit des solutions approchées de type « fronts » connectant un écoulement uniforme à un écoulement de cisaillement conjugué du premier mode. On montre que le nombre de branches de type « fronts » dépend essentiellement de l'échelle fine de la stratification de base.

The problem of two-dimensional internal travelling waves in a perfect fluid with smooth density being close to linear stratification is considered. Approximate front solutions connecting uniform flow with a conjugate shear flow of the first mode are constructed. It is demonstrated that the number of the front branches essentially depends on the fine-scale stratification for linear density background.

Reçu le :
Accepté le :
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DOI : 10.1016/j.crma.2003.09.035
Nikolai Makarenko 1

1 Lavrentyev Institute of Hydrodynamics, Lavrentyev av., 15, 630090 Novosibirsk, Russia 
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Nikolai Makarenko. Equivariant cosymmetry and front solutions of the Dubreil–Jacotin–Long equation. Part 1: Boussinesq limit. Comptes Rendus. Mathématique, Volume 337 (2003) no. 11, pp. 753-756. doi : 10.1016/j.crma.2003.09.035. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.09.035/

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