A Spectral Clustering Approach to Lagrangian Vortex Detection

TL;DR

This paper introduces a spectral clustering method to identify coherent vortices in turbulent flows by analyzing Lagrangian trajectories, enabling automated vortex detection in complex fluid dynamics.

Contribution

The paper presents a novel spectral graph theory-based approach for extracting multiple coherent vortices simultaneously from Lagrangian trajectory data.

Findings

Successfully identified vortices in 2D and 3D flows

Demonstrated potential for automated vortex tracking

Effective in complex turbulent flow scenarios

Abstract

One of the ubiquitous features of real-life turbulent flows is the existence and persistence of coherent vortices. Here we show that such coherent vortices can be extracted as clusters of Lagrangian trajectories. We carry out the clustering on a weighted graph, with the weights measuring pairwise distances of fluid trajectories in the extended phase space of positions and time. We then extract coherent vortices from the graph using tools from spectral graph theory. Our method locates all coherent vortices in the flow simultaneously, thereby showing high potential for automated vortex tracking. We illustrate the performance of this technique by identifying coherent Lagrangian vortices in several two- and three-dimensional flows.