Relative Fluid Stretching and Rotation for Sparse Trajectory Observations

TL;DR

This paper introduces a new frame-indifferent method to quantify fluid stretching and rotation from sparse trajectory data, improving the detection of flow structures in unsteady, sparsely sampled flows like ocean buoy data.

Contribution

The paper presents a novel approach using relative Lagrangian velocities to extend objective flow diagnostics to sparse and unsteady flow data, accounting for mean flow behavior.

Findings

Method effectively identifies flow structures in sparse data

Improves interpretability over frame-dependent diagnostics

Maintains accuracy in extremely sparse sampling scenarios

Abstract

As most mathematically justifiable Lagrangian coherent structure detection methods rely on spatial derivatives, their applicability to sparse trajectory data has been limited. For experimental fluid dynamicists and natural scientists working with Lagrangian trajectory data via passive tracers in unsteady flows (e.g. Lagrangian particle tracking or ocean buoys), obtaining material measures of fluid rotation or stretching is currently only possible for trajectory concentrations that are often out-of-reach. To facilitate frame-indifferent investigations in unsteady and sparsely sampled flows, we present a novel approach to quantify fluid stretching and rotation via relative Lagrangian velocities. This technique provides a formal objective extension of quasi-objective metrics to unsteady flows by accounting for mean flow behavior. For extremely sparse experimental data, fluid structures may be significantly undersampled, and the mean flow behavior becomes difficult to quantify. We provide a means to maintain the accuracy of our novel sparse flow diagnostics in extremely sparse sampling scenarios, such as ocean buoy data and Lagrangian particle tracking. We use data from multiple numerical and experimental flows to show that our methods can identify structures beyond existing limits of sparse, frame-indifferent diagnostics, and exhibit improved interpretability over common frame-dependent diagnostics.