A Voronoi-tessellation-based approach for detection of coherent structures in sparsely-seeded flows

TL;DR

This paper introduces a Voronoi-tessellation-based algorithm for detecting coherent structures in sparse Lagrangian flow data, effectively identifying flow features even with limited particle information.

Contribution

It presents a novel method combining Voronoi tessellation and spectral graph theory to detect coherent structures from sparse particle tracking data.

Findings

Successfully identified coherent structures in synthetic and experimental data.

Effective at mean inter-particle distances comparable to flow length scales.

Proven to work in high Reynolds number flow behind a bluff body.

Abstract

A novel algorithm to detect coherent structures with sparse Lagrangian particle tracking data, using Voronoi tessellation and techniques from spectral graph theory, is tested. Neighbouring tracer particles are naturally identified through the Voronoi tessellation of the tracers' distribution. The method examines the \textit{neighbouring time} of tracer trajectories, defined as the total flow time two Voronoi cells share a common Voronoi edge, by converting this information into a Cartesian distance in the graph representation of the Voronoi diagram. Coherence is assigned to groups of Voronoi cells whose neighbouring time remains high throughout the time interval of analysis. The technique is first tested on the two-dimensional synthetic data of a double-gyre flow, and then with challenging, large-scale three-dimensional Lagrangian particle tracking data behind a bluff body at high Reynolds number. The tested technique proves to be successful at identifying coherence with realistic experimental data. Specifically, it is shown that coherent tracer motion is identifiable for mean inter-particle distances of the order of the largest length scales in the flow.