Abstract
Abstract. Transport and mixing processes in fluid flows are crucially influenced by coherent structures and the characterization of these Lagrangian objects is a topic of intense current research. While established mathematical approaches such as variational methods or transfer-operator-based schemes require full knowledge of the flow field or at least high-resolution trajectory data, this information may not be available in applications. Recently, different computational methods have been proposed to identify coherent behavior in flows directly from Lagrangian trajectory data, that is, numerical or measured time series of particle positions in a fluid flow. In this context, spatio-temporal clustering algorithms have been proven to be very effective for the extraction of coherent sets from sparse and possibly incomplete trajectory data. Inspired by these recent approaches, we consider an unweighted, undirected network, where Lagrangian particle trajectories serve as network nodes. A link is established between two nodes if the respective trajectories come close to each other at least once in the course of time. Classical graph concepts are then employed to analyze the resulting network. In particular, local network measures such as the node degree, the average degree of neighboring nodes, and the clustering coefficient serve as indicators of highly mixing regions, whereas spectral graph partitioning schemes allow us to extract coherent sets. The proposed methodology is very fast to run and we demonstrate its applicability in two geophysical flows – the Bickley jet as well as the Antarctic stratospheric polar vortex.
Highlights
The notion of coherence in time-dependent dynamical systems is used to describe mobile sets that do not freely mix with the surrounding regions in phase space
Transport and mixing processes in fluid flows are crucially influenced by coherent structures and the characterization of these Lagrangian objects is a topic of intense current research
Coherent behavior has a crucial impact on transport and mixing processes in fluid flows
Summary
The notion of coherence in time-dependent dynamical systems is used to describe mobile sets that do not freely mix with the surrounding regions in phase space. In addition to considering local network measures, we will apply spectral graph partitioning schemes for the solution of a balanced cut problem (Shi and Malik, 2000) This allows us to efficiently extract coherent sets of the underlying flow, similar in spirit to the approaches proposed in Hadjighasem et al (2016) and Banisch and Koltai (2017), who considered weighted networks, which are constructed based on using different metrics for determining the distance between two trajectories. We close the paper with a discussion and an outlook on future work
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