Mathematically established chaos and forecast of statistics with recurrent patterns in Taylor-Couette flow
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866912218304479232 |
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| author | Wang, Baoying Ayats, Roger Deguchi, Kengo Meseguer, Alvaro Mellibovsky, Fernando |
| author_facet | Wang, Baoying Ayats, Roger Deguchi, Kengo Meseguer, Alvaro Mellibovsky, Fernando |
| contents | The transition to chaos in the subcritical regime of counter-rotating Taylor-Couette flow is investigated using a minimal periodic domain capable of sustaining coherent structures. Following a Feigenbaum cascade, the dynamics are found to be remarkably well approximated by a simple discrete map that admits rigorous proof of its chaotic nature. The chaotic set that arises for the map features densely distributed periodic points that are in one-to-one correspondence with unstable periodic orbits (UPOs) of the Navier-Stokes system. This supports the increasingly accepted view that UPOs may serve as the backbone of turbulence and, indeed, we demonstrate that it is possible to reconstruct every statistical property of chaotic fluid flow from UPOs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09234 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mathematically established chaos and forecast of statistics with recurrent patterns in Taylor-Couette flow Wang, Baoying Ayats, Roger Deguchi, Kengo Meseguer, Alvaro Mellibovsky, Fernando Chaotic Dynamics Mathematical Physics Fluid Dynamics The transition to chaos in the subcritical regime of counter-rotating Taylor-Couette flow is investigated using a minimal periodic domain capable of sustaining coherent structures. Following a Feigenbaum cascade, the dynamics are found to be remarkably well approximated by a simple discrete map that admits rigorous proof of its chaotic nature. The chaotic set that arises for the map features densely distributed periodic points that are in one-to-one correspondence with unstable periodic orbits (UPOs) of the Navier-Stokes system. This supports the increasingly accepted view that UPOs may serve as the backbone of turbulence and, indeed, we demonstrate that it is possible to reconstruct every statistical property of chaotic fluid flow from UPOs. |
| title | Mathematically established chaos and forecast of statistics with recurrent patterns in Taylor-Couette flow |
| topic | Chaotic Dynamics Mathematical Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2409.09234 |