Existence of orthogonal domain walls in Bénard-Rayleigh convection - Archive ouverte HAL
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 [3], and studied analytically in [10]. We then prove for a given amplitude, and an imposed symmetry in coordinate y, the existence of a one parameter family of heteroclinic connections between orthogonal sets of rolls, with wave numbers (different in general) which are linked to an adapted "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)
hal-04233484 , version 8 (25-06-2024)
hal-04233484 , version 9 (05-07-2024)
hal-04233484 , version 10 (03-10-2024)
hal-04233484 , version 11 (10-10-2024)
hal-04233484 , version 12 (15-11-2024)

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Gérard Iooss. Existence of orthogonal domain walls in Bénard-Rayleigh convection. 2024. ⟨hal-04233484v12⟩
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