Journal
JOURNAL OF FLUID MECHANICS
Volume 948, Issue -, Pages -Publisher
CAMBRIDGE UNIV PRESS
DOI: 10.1017/jfm.2022.652
Keywords
computational methods; chaos; pattern formation
Categories
Funding
- Schmidt Science Fellowship
- Swiss National Foundation
- NSF-Simons Center for Mathematical and Statistical Analysis of Biology Award [1764269]
- Simons Foundation
- Henri Seydoux Fund
- NIH [1R01HD097068]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1764269] Funding Source: National Science Foundation
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This study introduces a method for identifying Lagrangian coherent structures in sparse and noisy trajectory datasets, computing hyperbolic and elliptic LCSs, and demonstrating their accuracy. By deploying these methods on various fluid and experimental datasets, their practicality is showcased.
Many complex flows such as those arising from the collective motion of ocean plastics in geophysics or motile cells in biology are characterized by sparse and noisy trajectory datasets. We introduce techniques for identifying Lagrangian coherent structures (LCSs) of hyperbolic and elliptic nature in such datasets. Hyperbolic LCSs, which represent surfaces with maximal attraction or repulsion over a finite amount of time, are computed through a regularized least-squares approximation of the flow map gradient. Elliptic LCSs, which identify regions of coherent motion such as vortices and jets, are extracted using DBSCAN - a popular data clustering algorithm - combined with a systematic parameter selection strategy. We deploy these methods on various benchmark analytical flows and real-life experimental datasets ranging from oceanography to biology and show that they yield accurate results, despite sparse and noisy data. We also provide a lightweight computational implementation of these techniques as a user-friendly and straightforward Python code.
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