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Detecting Lagrangian coherent structures from sparse and noisy trajectory data

Published online by Cambridge University Press:  06 September 2022

Saviz Mowlavi ,
Mattia Serra Open the ORCID record for Mattia Serra [Opens in a new window] ,
Enrico Maiorino  and
L. Mahadevan Open the ORCID record for L. Mahadevan [Opens in a new window]
Saviz Mowlavi
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Mattia Serra*
Affiliation:
School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA Department of Physics, University of California, San Diego, CA 92093, USA
Enrico Maiorino
Affiliation:
Channing Division of Network Medicine, Brigham and Women's Hospital and Harvard Medical School, Boston, MA 02115, USA
L. Mahadevan*
Affiliation:
School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA Department of Physics, Harvard University, Cambridge, MA 02138, USA
*
†Email addresses for correspondence: mserra@ucsd.edu, lmahadev@g.harvard.edu
†Email addresses for correspondence: mserra@ucsd.edu, lmahadev@g.harvard.edu
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Abstract

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.

JFM classification

Mathematical Foundations: Computational methods Nonlinear Dynamical Systems: Chaos Nonlinear Dynamical Systems: Pattern formation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 948 , 10 October 2022 , A4
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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Mowlavi et al. Supplementary Movie 1

Temporal evolution of particle positions in the Bickley jet, colored according to the coherent groups identified in Figure 5(e). Top: instantaneous positions of all particles. Bottom: trajectories up to current time of one particle in each coherent group, and one particle classified as noise.
Download Mowlavi et al. Supplementary Movie 1(Video)
Video 22.5 MB

Mowlavi et al. Supplementary Movie 2

Temporal evolution of particle positions in the ABC flow, colored according to the coherent groups identified in Figure 7(c). Left: instantaneous positions of all particles. Right: trajectories up to current time of one particle in the coherent red, orange and brown groups, and one particle classified as noise.
Download Mowlavi et al. Supplementary Movie 2(Video)
Video 10.2 MB