Identification of individual coherent sets associated with flow trajectories using Coherent Structure Coloring

TL;DR

This paper introduces a spectral graph theory-based method to identify coherent flow structures from sparse particle trajectory data, enabling analysis of complex unsteady flows and potential applications beyond fluid dynamics.

Contribution

The paper presents a novel spectral graph theory approach using Coherent Structure Coloring to identify coherent structures from sparse trajectory data, applicable to various dynamical systems.

Findings

Successfully identifies coherent structures in unsteady flows

Can assess the relative coherence of flow structures

Applicable to other dynamical systems beyond fluid flows

Abstract

We present a method for identifying the coherent structures associated with individual Lagrangian flow trajectories even where only sparse particle trajectory data is available. The method, based on techniques in spectral graph theory, uses the Coherent Structure Coloring vector and associated eigenvectors to analyze the distance in higher-dimensional eigenspace between a selected reference trajectory and other tracer trajectories in the flow. By analyzing this distance metric in a hierarchical clustering, the coherent structure of which the reference particle is a member can be identified. This algorithm is proven successful in identifying coherent structures of varying complexities in canonical unsteady flows. Additionally, the method is able to assess the relative coherence of the associated structure in comparison to the surrounding flow. Although the method is demonstrated here in the context of fluid flow kinematics, the generality of the approach allows for its potential application to other unsupervised clustering problems in dynamical systems such as neuronal activity, gene expression, or social networks.