On existence of Sadovskii vortex patch: A touching pair of symmetric counter-rotating uniform vortex
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| Format: | Preprint |
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2024
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| _version_ | 1866916779583864832 |
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| author | Choi, Kyudong Jeong, In-Jee Sim, Young-Jin |
| author_facet | Choi, Kyudong Jeong, In-Jee Sim, Young-Jin |
| contents | The Sadovskii vortex patch is a traveling wave for the two-dimensional incompressible Euler equations consisting of an odd symmetric pair of vortex patches touching the symmetry axis. Its existence was first suggested by numerical computations of Sadovskii in [J. Appl. Math. Mech., 1971], and has gained significant interest due to its relevance in inviscid limit of planar flows via Prandtl--Batchelor theory and as the asymptotic state for vortex ring dynamics. In this work, we prove the existence of a Sadovskii vortex patch, by solving the energy maximization problem under the exact impulse condition and an upper bound on the circulation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_11379 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On existence of Sadovskii vortex patch: A touching pair of symmetric counter-rotating uniform vortex Choi, Kyudong Jeong, In-Jee Sim, Young-Jin Analysis of PDEs Mathematical Physics The Sadovskii vortex patch is a traveling wave for the two-dimensional incompressible Euler equations consisting of an odd symmetric pair of vortex patches touching the symmetry axis. Its existence was first suggested by numerical computations of Sadovskii in [J. Appl. Math. Mech., 1971], and has gained significant interest due to its relevance in inviscid limit of planar flows via Prandtl--Batchelor theory and as the asymptotic state for vortex ring dynamics. In this work, we prove the existence of a Sadovskii vortex patch, by solving the energy maximization problem under the exact impulse condition and an upper bound on the circulation. |
| title | On existence of Sadovskii vortex patch: A touching pair of symmetric counter-rotating uniform vortex |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2406.11379 |