Open-flow mixing and transfer operators

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We study finite-time mixing in time-periodic open flow systems. We describe the transport of densities in terms of a transfer operator, which is represented by the transition matrix of a finite-state Markov chain. The transport processes in the open system are organized by the chaotic saddle and its stable and unstable manifolds. We extract these structures directly from leading eigenvectors of the transition matrix. We use different measures to quantify the degree of mixing and show that they give consistent results in parameter studies of two model systems. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 1)'.

Original languageEnglish
Article number20210028
JournalPhilosophical transactions. Series A, Mathematical, physical, and engineering sciences
Issue number2225
Number of pages22
Publication statusPublished - 13.06.2022

Bibliographical note

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© 2022 The Author(s).

    Research areas

  • Mathematics
  • chaotic mixing, chaotic saddle, open dynamical system, Perron–Frobenius operator