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Transport and mixing processes in fluid flows are crucially influenced by coherent structures and the characterization of these\udLagrangian objects is a topic of intense current research. While established\udmathematical approaches such as variational methods or transfer-operator-based\udschemes require full knowledge of the flow field or at least high-resolution\udtrajectory data, this information may not\udbe available in applications. Recently, different computational methods have been proposed to identify coherent behavior in flows\uddirectly from Lagrangian trajectory data, that is, numerical or measured time\udseries of particle positions in a fluid flow. In this\udcontext, spatio-temporal clustering algorithms have been proven to be very effective for the extraction of coherent sets from sparse\udand possibly incomplete trajectory data. Inspired by these recent approaches, we consider an unweighted, undirected network, where\udLagrangian particle trajectories serve as network nodes. A link is established between two nodes if the respective trajectories come\udclose to each other at least once in the course of time. Classical graph concepts are then employed to analyze the resulting\udnetwork. In particular, local network measures such as the node degree, the average degree of neighboring nodes, and the clustering\udcoefficient serve as indicators of highly mixing regions, whereas spectral graph partitioning schemes allow us to extract coherent\udsets. The proposed methodology is very fast to run and we demonstrate its applicability in two geophysical flows – the Bickley jet as\udwell as the Antarctic stratospheric polar vortex

Network-based study of Lagrangian transport and mixing