Existence of orthogonal domain walls in B{é}nard-Rayleigh convection
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866918224941023232 |
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| author | Iooss, Gérard |
| author_facet | Iooss, Gérard |
| contents | In B{é}nard-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08594 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence of orthogonal domain walls in B{é}nard-Rayleigh convection Iooss, Gérard Mathematical Physics In B{é}nard-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. |
| title | Existence of orthogonal domain walls in B{é}nard-Rayleigh convection |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2410.08594 |