On the optimal rate of vortex stretching for axisymmetric Euler flows without swirl
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909541591941120 |
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| author | Lim, Deokwoo Jeong, In-Jee |
| author_facet | Lim, Deokwoo Jeong, In-Jee |
| contents | For axisymmetric flows without swirl and compactly supported initial vorticity, we prove the upper bound of $t^{4/3}$ for the growth of the vorticity maximum, which was conjectured by Childress [Phys. D, 2008] and supported by numerical computations from Childress--Gilbert--Valiant [J. Fluid Mech. 2016]. The key is to estimate the velocity maximum by the kinetic energy together with conserved quantities involving the vorticity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_19497 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the optimal rate of vortex stretching for axisymmetric Euler flows without swirl Lim, Deokwoo Jeong, In-Jee Analysis of PDEs Mathematical Physics For axisymmetric flows without swirl and compactly supported initial vorticity, we prove the upper bound of $t^{4/3}$ for the growth of the vorticity maximum, which was conjectured by Childress [Phys. D, 2008] and supported by numerical computations from Childress--Gilbert--Valiant [J. Fluid Mech. 2016]. The key is to estimate the velocity maximum by the kinetic energy together with conserved quantities involving the vorticity. |
| title | On the optimal rate of vortex stretching for axisymmetric Euler flows without swirl |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2409.19497 |