Within-Cluster Variability Exponent for Identifying Coherent Structures in Dynamical Systems

TL;DR

This paper introduces a clustering-based method to identify coherent structures in dynamical systems by analyzing particle trajectories, considering their complete history, and offering adaptive and on-the-fly extensions for efficiency.

Contribution

It presents a novel clustering approach using the within-cluster variability exponent to detect coherent structures, incorporating complete trajectory history and adaptive computation extensions.

Findings

Effective identification of coherent flow structures.

Enhanced computational efficiency with adaptive sampling.

Real-time updating capability during data collection.

Abstract

We propose a clustering-based approach for identifying coherent flow structures in continuous dynamical systems. We first treat a particle trajectory over a finite time interval as a high-dimensional data point and then cluster these data from different initial locations into groups. The method then uses the normalized standard deviation or mean absolute deviation to quantify the deformation. Unlike the usual finite-time Lyapunov exponent (FTLE), the proposed algorithm considers the complete traveling history of the particles. We also suggest two extensions of the method. To improve the computational efficiency, we develop an adaptive approach that constructs different subsamples of the whole particle trajectory based on a finite time interval. To start the computation in parallel to the flow trajectory data collection, we also develop an on-the-fly approach to improve the solution as we continue to provide more measurements for the algorithm. The method can efficiently compute the WCVE over a different time interval by modifying the available data points.