Open-flow mixing and transfer operators

TL;DR

This paper investigates finite-time mixing in open flow systems using transfer operators and Markov chains, identifying chaotic structures and quantifying mixing efficiency through eigenvector analysis.

Contribution

It introduces a method to analyze open flow mixing by linking transfer operators with Markov chain representations and extracting chaotic structures from eigenvectors.

Findings

Chaotic saddle structures identified via eigenvectors.

Consistent mixing measures across different models.

Quantitative analysis of mixing efficiency.

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.