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

2025/05/09 by Bálint Kaszás, George Haller, Kaszás, Bálint +1
Computer Science · Physics and Astronomy · #Chaos control and synchronization #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2505.05881

openalex publication_date 2025/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Poincaré map that enables the rapid computation of the periodic orbits embedded in the chaotic attractor.

Citations

• Robust quantum reservoir computers for forecasting chaotic dynamics: generalized synchronization and stability
• Stability analysis of chaotic systems in latent spaces
• Mathematically established chaos and forecast of statistics with recurrent patterns in Taylor-Couette flow
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• Dynamics of a data-driven low-dimensional model of turbulent minimal Couette flow
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