  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.
