Computation and optimal perturbation of finite-time coherent sets for aperiodic flows without trajectory integration
- Understanding the macroscopic behavior of dynamical systems is an important tool to unravel transport mechanisms in complex flows. A decomposition of the state space into coherent sets is a popular way to reveal this essential macroscopic evolution. To compute coherent sets from an aperiodic time-dependent dynamical system we consider the relevant transfer operators and their infinitesimal generators on an augmented space-time manifold. This space-time generator approach avoids trajectory integration and creates a convenient linearization of the aperiodic evolution. This linearization can be further exploited to create a simple and effective spectral optimization methodology for diminishing or enhancing coherence. We obtain explicit solutions for these optimization problems using Lagrange multipliers and illustrate this technique by increasing and decreasing mixing of spatial regions through small velocity field perturbations.
Author details: | Gary Froyland, Peter Koltai, Martin StahnORCiD |
---|---|
DOI: | https://doi.org/10.1137/19M1261791 |
ISSN: | 1536-0040 |
Title of parent work (English): | SIAM journal on applied dynamical systems |
Publisher: | Society for Industrial and Applied Mathematics |
Place of publishing: | Philadelphia |
Publication type: | Article |
Language: | English |
Date of first publication: | 2020/07/22 |
Publication year: | 2020 |
Release date: | 2022/10/05 |
Tag: | coherent set; infinitesimal generator; mixing; mixing optimization; transfer operator; unsteady flow |
Volume: | 19 |
Issue: | 3 |
Number of pages: | 42 |
First page: | 1659 |
Last Page: | 1700 |
Funding institution: | ARCAustralian Research Council [DP180101223]; Deutsche; Forschungsgemeinschaft (DFG)German Research Foundation (DFG) [CRC 1114]; DFG through the Priority Programme 1881; [SFB 1294] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
DDC classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
Peer review: | Referiert |
Publishing method: | Open Access / Hybrid Open-Access |
License (German): | CC-BY - Namensnennung 4.0 International |