Braids of entangled particle trajectories
In many applications, the two-dimensional trajectories of fluid particles are available, but little is known about the underlying flow. Oceanic floats are a clear example. To extract quantitative information from such data, one can measure single-particle dispersion coefficients, but this only uses...
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craippubl:10.1063/1.3262494 2024-06-23T07:54:26+00:00 Braids of entangled particle trajectories Thiffeault, Jean-Luc 2010 http://dx.doi.org/10.1063/1.3262494 https://pubs.aip.org/aip/cha/article-pdf/doi/10.1063/1.3262494/14604297/017516_1_online.pdf en eng AIP Publishing Chaos: An Interdisciplinary Journal of Nonlinear Science volume 20, issue 1 ISSN 1054-1500 1089-7682 journal-article 2010 craippubl https://doi.org/10.1063/1.3262494 2024-06-13T04:03:54Z In many applications, the two-dimensional trajectories of fluid particles are available, but little is known about the underlying flow. Oceanic floats are a clear example. To extract quantitative information from such data, one can measure single-particle dispersion coefficients, but this only uses one trajectory at a time, so much of the information on relative motion is lost. In some circumstances the trajectories happen to remain close long enough to measure finite-time Lyapunov exponents, but this is rare. We propose to use tools from braid theory and the topology of surface mappings to approximate the topological entropy of the underlying flow. The procedure uses all the trajectory data and is inherently global. The topological entropy is a measure of the entanglement of the trajectories, and converges to zero if they are not entangled in a complex manner (for instance, if the trajectories are all in a large vortex). We illustrate the techniques on some simple dynamical systems and on float data from the Labrador Sea. The method could eventually be used to identify Lagrangian coherent structures present in the flow. Article in Journal/Newspaper Labrador Sea AIP Publishing Chaos: An Interdisciplinary Journal of Nonlinear Science 20 1 |
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English |
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In many applications, the two-dimensional trajectories of fluid particles are available, but little is known about the underlying flow. Oceanic floats are a clear example. To extract quantitative information from such data, one can measure single-particle dispersion coefficients, but this only uses one trajectory at a time, so much of the information on relative motion is lost. In some circumstances the trajectories happen to remain close long enough to measure finite-time Lyapunov exponents, but this is rare. We propose to use tools from braid theory and the topology of surface mappings to approximate the topological entropy of the underlying flow. The procedure uses all the trajectory data and is inherently global. The topological entropy is a measure of the entanglement of the trajectories, and converges to zero if they are not entangled in a complex manner (for instance, if the trajectories are all in a large vortex). We illustrate the techniques on some simple dynamical systems and on float data from the Labrador Sea. The method could eventually be used to identify Lagrangian coherent structures present in the flow. |
format |
Article in Journal/Newspaper |
author |
Thiffeault, Jean-Luc |
spellingShingle |
Thiffeault, Jean-Luc Braids of entangled particle trajectories |
author_facet |
Thiffeault, Jean-Luc |
author_sort |
Thiffeault, Jean-Luc |
title |
Braids of entangled particle trajectories |
title_short |
Braids of entangled particle trajectories |
title_full |
Braids of entangled particle trajectories |
title_fullStr |
Braids of entangled particle trajectories |
title_full_unstemmed |
Braids of entangled particle trajectories |
title_sort |
braids of entangled particle trajectories |
publisher |
AIP Publishing |
publishDate |
2010 |
url |
http://dx.doi.org/10.1063/1.3262494 https://pubs.aip.org/aip/cha/article-pdf/doi/10.1063/1.3262494/14604297/017516_1_online.pdf |
genre |
Labrador Sea |
genre_facet |
Labrador Sea |
op_source |
Chaos: An Interdisciplinary Journal of Nonlinear Science volume 20, issue 1 ISSN 1054-1500 1089-7682 |
op_doi |
https://doi.org/10.1063/1.3262494 |
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Chaos: An Interdisciplinary Journal of Nonlinear Science |
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20 |
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1 |
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1802646587964391424 |