Within-Cluster Variability Exponent for Identifying Coherent Structures in Dynamical Systems (Communications in Computational Physics, 2023)
We propose a clustering-based approach for identifying coherent flow structures in continuous dynamical systems. We first treat a particle trajectory over a finitetime interval as a high-dimensional data point and then cluster these data from different initial locations into groups. The method then uses the normalized standarddeviation or mean absolute deviation to quantify the deformation. Unlike the usualfinite-time Lyapunov exponent (FTLE), the proposed algorithm considers the completetraveling history of the particles. We also suggest two extensions of the method. To improve the computational efficiency, we develop an adaptive approach that constructsdifferent subsamples of the whole particle trajectory based on a finite time interval. Tostart the computation in parallel to the flow trajectory data collection, we also developan 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 adifferent time interval by modifying the available data points.
Keywords: Dynamical system; visualization; finite time Lyapunov exponent; numerical methods for differential equations; k-means clustering.