Study of dynamics in post-transient flows using Koopman mode decomposition

Hassan Arbabi and Igor Mezić
Phys. Rev. Fluids 2, 124402 – Published 29 December 2017

Abstract

The Koopman mode decomposition (KMD) is a data-analysis technique which is often used to extract the spatiotemporal patterns of complex flows. In this paper, we use KMD to study the dynamics of the lid-driven flow in a two-dimensional square cavity based on theorems related to the spectral theory of the Koopman operator. We adapt two algorithms, from the classical Fourier and power spectral analysis, to compute the discrete and continuous spectrum of the Koopman operator for the post-transient flows. Properties of the Koopman operator spectrum are linked to the sequence of flow regimes occurring between Re=10000 and Re=30000, and changing the flow nature from steady to aperiodic. The Koopman eigenfunctions for different flow regimes, including flows with mixed spectra, are constructed using the assumption of ergodicity in the state space. The associated Koopman modes show remarkable robustness even as the temporal nature of the flow is changing substantially. We observe that KMD outperforms the proper orthogonal decomposition in reconstruction of the flows with strong quasiperiodic components.

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  • Received 4 April 2017

DOI:https://doi.org/10.1103/PhysRevFluids.2.124402

©2017 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
  1. Physical Systems
Nonlinear DynamicsFluid Dynamics

Authors & Affiliations

Hassan Arbabi* and Igor Mezić

  • University of California, Santa Barbara, Santa Barbara, California 93106, USA

  • *harbabi@engineering.ucsb.edu
  • mezic@engineering.ucsb.edu

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Issue

Vol. 2, Iss. 12 — December 2017

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