Bulletin of the American Physical Society
76th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2023; Washington, DC
Session T31: NLD Coherent Structures II
4:25 PM–6:09 PM,
Monday, November 20, 2023
Room: 156
Chair: Sutanu Sarkar, University of California, San Diego
Abstract: T31.00001 : Time delay embeddings to uncover unstable periodic orbits and exact coherent structures in chaotic fluid systems
4:25 PM–4:38 PM
Presenter:
Prerna M Patil
(University of Washington)
Authors:
Prerna M Patil
(University of Washington)
Eurika Kaiser
(University of Washington)
Nathan Kutz
(University of Washington)
Steven L Brunton
(University of Washington, Department of Mechanical Engineering)
In this talk, we evaluate numerical techniques for finding these UPOs for chaotic systems based on delay embedded data. The time delay embeddings obtained for these UPOs can be further used to predict the global characterizations of the dynamics of the attractor including natural measure, fractal dimensions, and Lyapunov exponents. Our results show that, for long time delay embeddings, UPOs disentangle and converge to a discrete Fourier decomposition. We present the analysis for the Lorenz attractor, Rössler attractor, Kuramoto-Shivashinsky equations, and plane Couette flow.
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