Joint Reduced Model for the Laminar and Chaotic Attractors in Plane Couette Flow
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918014742429696 |
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| author | Kaszás, Bálint Haller, George |
| author_facet | Kaszás, Bálint Haller, George |
| contents | We use the theory of spectral submanifolds (SSMs) to develop a low-dimensional reduced-order model for plane Couette flow in the permanently chaotic regime studied by Kreilos & Eckhardt (2012). Our three-dimensional model is obtained by restricting the dynamics to the slowest mixed-mode SSM of the edge state. We show that this results in a nonlinear model that accurately reconstructs individual trajectories, representing the entire chaotic attractor and the laminar dynamics simultaneously. In addition, we derive a two-dimensional Poincaré map that enables the rapid computation of the periodic orbits embedded in the chaotic attractor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05881 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Joint Reduced Model for the Laminar and Chaotic Attractors in Plane Couette Flow Kaszás, Bálint Haller, George Chaotic Dynamics Fluid Dynamics We use the theory of spectral submanifolds (SSMs) to develop a low-dimensional reduced-order model for plane Couette flow in the permanently chaotic regime studied by Kreilos & Eckhardt (2012). Our three-dimensional model is obtained by restricting the dynamics to the slowest mixed-mode SSM of the edge state. We show that this results in a nonlinear model that accurately reconstructs individual trajectories, representing the entire chaotic attractor and the laminar dynamics simultaneously. In addition, we derive a two-dimensional Poincaré map that enables the rapid computation of the periodic orbits embedded in the chaotic attractor. |
| title | Joint Reduced Model for the Laminar and Chaotic Attractors in Plane Couette Flow |
| topic | Chaotic Dynamics Fluid Dynamics |
| url | https://arxiv.org/abs/2505.05881 |