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arXiv · 2505.05881

Joint Reduced Model for the Laminar and Chaotic Attractors in Plane Couette Flow

Bálint Kaszás·George Haller
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Abstract

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 Poincar\'e map that enables the rapid computation of the periodic orbits embedded in the chaotic attractor.

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Bálint Kaszás, George Haller. 2025-05-09. Joint Reduced Model for the Laminar and Chaotic Attractors in Plane Couette Flow. https://arxiv.org/abs/2505.05881

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