Detecting Lagrangian coherent structures from sparse and noisy trajectory data

Abstract

Many complex flows such as those arising from ocean plastics in geophysics or moving 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 approach to choose parameters. 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.

26 pages, 12 figures

References in corpus (5)

• On the Lagrangian Dynamics of Atmospheric Zonal Jets and the Permeability of the Stratospheric Polar Vortex
• Flow networks: A characterization of geophysical fluid transport
• Geometry of the ergodic quotient reveals coherent structures in flows
• Coherent structure coloring: identification of coherent structures from sparse data using graph theory
• Identification of individual coherent sets associated with flow trajectories using Coherent Structure Coloring

Cited by in corpus (3)

• Quasi-Objective Eddy Visualization from Sparse Drifter Data
• Lagrangian studies of coherent sets and heat transport in constant heat flux-driven turbulent Rayleigh-Bénard convection
• Relative Fluid Stretching and Rotation for Sparse Trajectory Observations