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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2023

Existence of orthogonal domain walls in Bénard-Rayleigh convection

Résumé

In Bénard-Rayleigh convection we consider the pattern defect in orthogonal domain walls connecting a set of convective rolls with another set of rolls orthogonal to the first set. This is understood as an heteroclinic orbit of a reversible system where the x-coordinate plays the role of time. This appears as a perturbation of the heteroclinic orbit proved to exist in a reduced 6-dimensional system studied by a variational method in [2], and analytically in [8]. We then prove the existence of a one parameter family of heteroclinic connections between orthogonal sets of rolls, which wave numbers (different in general) are linked with a shift of rolls parallel to the wall.
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Dates et versions

hal-04233484 , version 1 (09-10-2023)
hal-04233484 , version 2 (18-10-2023)
hal-04233484 , version 3 (20-12-2023)
hal-04233484 , version 4 (29-12-2023)
hal-04233484 , version 5 (02-01-2024)
hal-04233484 , version 6 (01-04-2024)
hal-04233484 , version 7 (22-04-2024)

Identifiants

  • HAL Id : hal-04233484 , version 7

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Gérard Iooss. Existence of orthogonal domain walls in Bénard-Rayleigh convection. 2024. ⟨hal-04233484v7⟩
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