Title: Identification of individual coherent sets associated with flow trajectories using Coherent Structure Coloring,
Abstract: We present a method for identifying the coherent structures associated with
individual Lagrangian flow trajectories even where only sparse particle
trajectory data is available. The method, based on techniques in spectral graph
theory, uses the Coherent Structure Coloring vector and associated eigenvectors
to analyze the distance in higher-dimensional eigenspace between a selected
reference trajectory and other tracer trajectories in the flow. By analyzing
this distance metric in a hierarchical clustering, the coherent structure of
which the reference particle is a member can be identified. This algorithm is
proven successful in identifying coherent structures of varying complexities in
canonical unsteady flows. Additionally, the method is able to assess the
relative coherence of the associated structure in comparison to the surrounding
flow. Although the method is demonstrated here in the context of fluid flow
kinematics, the generality of the approach allows for its potential application
to other unsupervised clustering problems in dynamical systems such as neuronal
activity, gene expression, or social networks.