Network Measures of Mixing

TL;DR

This paper explores how graph-based network measures derived from particle trajectories can reveal flow structures and classify dynamical behaviors in fluid mixing processes.

Contribution

It analytically links local network measures to flow structures and demonstrates their use in classifying trajectory groups through manifold learning.

Findings

Local network measures relate to flow structures

Network measures can classify dynamical behavior

Analytical connection between graph measures and fluid flow

Abstract

Transport and mixing processes in fluid flows can be studied directly from Lagrangian trajectory data, such as obtained from particle tracking experiments. Recent work in this context highlights the application of graph-based approaches, where trajectories serve as nodes and some similarity or distance measure between them is employed to build a (possibly weighted) network, which is then analyzed using spectral methods. Here, we consider the simplest case of an unweighted, undirected network and analytically relate local network measures such as node degree or clustering coefficient to flow structures. In particular, we use these local measures to divide the family of trajectories into groups of similar dynamical behavior via manifold learning methods.