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

We propose a clustering-based approach for identifying coherent flow struc-tures 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 dif-ferent 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 im-prove 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 mea-surements for the algorithm. The method can efficiently compute the WCVE over a different time interval by modifying the available data points.