Quasi-Objective Coherent Structure Diagnostics from Single Trajectories

TL;DR

This paper introduces quasi-objective measures of local stretching and rotation from single trajectories, enabling detection of coherent structures in fluid flows without needing full velocity fields or multiple trajectories.

Contribution

It develops novel quasi-objective diagnostics that can be computed from individual trajectories, expanding the tools for analyzing flow coherence with sparse data.

Findings

Effectively identifies elliptic and hyperbolic Lagrangian coherent structures.

Works with very sparse trajectory data.

Provides measures that approximate objective diagnostics under certain conditions.

Abstract

We derive measures of local material stretching and rotation that are computable from individual trajectories without reliance on other trajectories or on an underlying velocity field. Both measures are quasi-objective: they approximate objective (i.e., observer-independent) coherence diagnostics in frames satisfying a certain condition. This condition requires the trajectory accelerations to dominate the angular acceleration induced by the spatial mean vorticity. We illustrate in examples how quasi-objective coherence diagnostics highlight elliptic and hyperbolic Lagrangian coherent structures even from very sparse trajectory data.