Feigenbaum universality in subcritical Taylor-Couette flow
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912254130126848 |
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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 | Feigenbaum universality is shown to occur in subcritical shear flows. Our testing ground is the counter-rotation regime of the Taylor-Couette flow, where numerical calculations are performed within a small periodic domain. The accurate computation of up to the seventh period doubling bifurcation, assisted by a purposely defined Poincaré section, has enabled us to reproduce the two Feigenbaum universal constants with unprecedented accuracy in a fluid flow problem. We have further devised a method to predict the bifurcation diagram up to the accumulation point of the cascade based on the detailed inspection of just the first few period doubling bifurcations. Remarkably, the method is applicable beyond the accumulation point, with predictions remaining valid, in a statistical sense, for the chaotic dynamics that follows. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_16097 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Feigenbaum universality in subcritical Taylor-Couette flow Wang, Baoying Ayats, Roger Deguchi, Kengo Meseguer, Alvaro Mellibovsky, Fernando Fluid Dynamics Mathematical Physics Chaotic Dynamics Feigenbaum universality is shown to occur in subcritical shear flows. Our testing ground is the counter-rotation regime of the Taylor-Couette flow, where numerical calculations are performed within a small periodic domain. The accurate computation of up to the seventh period doubling bifurcation, assisted by a purposely defined Poincaré section, has enabled us to reproduce the two Feigenbaum universal constants with unprecedented accuracy in a fluid flow problem. We have further devised a method to predict the bifurcation diagram up to the accumulation point of the cascade based on the detailed inspection of just the first few period doubling bifurcations. Remarkably, the method is applicable beyond the accumulation point, with predictions remaining valid, in a statistical sense, for the chaotic dynamics that follows. |
| title | Feigenbaum universality in subcritical Taylor-Couette flow |
| topic | Fluid Dynamics Mathematical Physics Chaotic Dynamics |
| url | https://arxiv.org/abs/2407.16097 |