Fast relaxation of a viscous vortex in an external flow
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914413898891264 |
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| author | Donati, Martin Gallay, Thierry |
| author_facet | Donati, Martin Gallay, Thierry |
| contents | We study the evolution of a concentrated vortex advected by a smooth, divergence-free velocity field in two space dimensions. In the idealized situation where the initial vorticity is a Dirac mass, we compute an approximation of the solution which accurately describes, in the regime of high Reynolds numbers, the motion of the vortex center and the deformation of the streamlines under the shear stress of the external flow. For ill-prepared initial data, corresponding to a sharply peaked Gaussian vortex, we prove relaxation to the previous solution on a time scale that is much shorter than the diffusive time, due to enhanced dissipation inside the vortex core. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_20643 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fast relaxation of a viscous vortex in an external flow Donati, Martin Gallay, Thierry Analysis of PDEs Fluid Dynamics 35Q30, 35B35, 76D17 We study the evolution of a concentrated vortex advected by a smooth, divergence-free velocity field in two space dimensions. In the idealized situation where the initial vorticity is a Dirac mass, we compute an approximation of the solution which accurately describes, in the regime of high Reynolds numbers, the motion of the vortex center and the deformation of the streamlines under the shear stress of the external flow. For ill-prepared initial data, corresponding to a sharply peaked Gaussian vortex, we prove relaxation to the previous solution on a time scale that is much shorter than the diffusive time, due to enhanced dissipation inside the vortex core. |
| title | Fast relaxation of a viscous vortex in an external flow |
| topic | Analysis of PDEs Fluid Dynamics 35Q30, 35B35, 76D17 |
| url | https://arxiv.org/abs/2503.20643 |