On the stability and instability of Kelvin-Stuart cat's-eye flows
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914527825625088 |
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| author | Liao, Shasha Lin, Zhiwu Zhu, Hao |
| author_facet | Liao, Shasha Lin, Zhiwu Zhu, Hao |
| contents | Kelvin-Stuart vortices are classical mixing layer flows with many applications in fluid mechanics, plasma physics and astrophysics. We prove that the whole family of Kelvin-Stuart vortices is nonlinearly orbitally stable for co-periodic perturbations, and linearly unstable for multi-periodic and modulational perturbations. This verifies a long-standing conjecture since the discovery of the Kelvin-Stuart cat's-eye flows in the 1960s. Kelvin-Stuart cat's eyes also appear as magnetic islands which are magnetostatic equilibria for the planar ideal MHD equations in plasmas. We prove nonlinear orbital stability of Kelvin-Stuart magnetic islands for co-periodic perturbations, and give the first rigorous proof of coalescence instability for the whole family, which is important for magnetic reconnection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_00264 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the stability and instability of Kelvin-Stuart cat's-eye flows Liao, Shasha Lin, Zhiwu Zhu, Hao Analysis of PDEs Kelvin-Stuart vortices are classical mixing layer flows with many applications in fluid mechanics, plasma physics and astrophysics. We prove that the whole family of Kelvin-Stuart vortices is nonlinearly orbitally stable for co-periodic perturbations, and linearly unstable for multi-periodic and modulational perturbations. This verifies a long-standing conjecture since the discovery of the Kelvin-Stuart cat's-eye flows in the 1960s. Kelvin-Stuart cat's eyes also appear as magnetic islands which are magnetostatic equilibria for the planar ideal MHD equations in plasmas. We prove nonlinear orbital stability of Kelvin-Stuart magnetic islands for co-periodic perturbations, and give the first rigorous proof of coalescence instability for the whole family, which is important for magnetic reconnection. |
| title | On the stability and instability of Kelvin-Stuart cat's-eye flows |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2304.00264 |