Open-flow mixing and transfer operators

Anna Klünker; Kathrin Padberg-Gehle; Jean-Luc Thiffeault

doi:10.1098/rsta.2021.0028

Open-flow mixing and transfer operators

Anna Klünker
, Kathrin Padberg-Gehle
, Jean-Luc Thiffeault^*

^*Corresponding author for this work

Professorship of Applied Mathematics

University of Wisconsin - Madison

Research output: Journal contributions › Journal articles › Research › peer-review

3 Citations (Scopus)

Abstract

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 language	English
Article number	20210028
Journal	Philosophical transactions. Series A, Mathematical, physical, and engineering sciences
Volume	380
Issue number	2225
Number of pages	22
ISSN	1364-503X
DOIs	https://doi.org/10.1098/rsta.2021.0028
Publication status	Published - 13.06.2022

Bibliographical note

Publisher Copyright:
© 2022 The Author(s).

Research areas and keywords

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

ASJC Scopus Subject Areas

Physics and Astronomy(all)
Engineering(all)
Mathematics(all)

Access to Document

10.1098/rsta.2021.0028

Lagrangian aspects of turbulent superstructures: numerical analysis of long-term dynamics and transport properties
Padberg-Gehle, K. (Project manager, academic) & Schneide, C. (Project staff)
German Research Foundation
09.12.19 → 30.06.23
Project: Research

Cite this

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AU - Klünker, Anna

AU - Padberg-Gehle, Kathrin

AU - Thiffeault, Jean-Luc

PY - 2022/6/13

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N2 - 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)'.

AB - 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)'.

KW - Mathematics

KW - chaotic mixing

KW - chaotic saddle

KW - open dynamical system

KW - Perron–Frobenius operator

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DO - 10.1098/rsta.2021.0028

M3 - Journal articles

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SN - 1364-503X

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JO - Philosophical transactions. Series A, Mathematical, physical, and engineering sciences

JF - Philosophical transactions. Series A, Mathematical, physical, and engineering sciences

IS - 2225

M1 - 20210028

ER -

Open-flow mixing and transfer operators

Abstract

Bibliographical note

Research areas and keywords

ASJC Scopus Subject Areas

Access to Document

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Projects

Lagrangian aspects of turbulent superstructures: numerical analysis of long-term dynamics and transport properties

Cite this