TY - JOUR

T1 - Network-based study of Lagrangian transport and mixing

AU - Padberg-Gehle, Kathrin

AU - Schneide, Christiane

N1 - Funding Information: Acknowledgements. We thank Gábor Drótos and the second anonymous reviewer for insightful comments and suggestions that helped improve and clarify this paper. This work is supported by the Priority Programme SPP 1881 Turbulent Superstructures of the Deutsche Forschungsgemeinschaft (PA 1972/3-1). Kathrin Padberg-Gehle also acknowledges funding from EU Marie-Skłodowska-Curie ITN Critical Transitions in Complex Systems (H2020-MSCA-2014-ITN 643073 CRITICS). We thank Naratip Santitissadeekorn for sharing code for the Antarctic polar vortex computations. Publication is supported by the Office of Naval Research under grant no. N00014-16-1-2492. Publisher Copyright: © Author(s) 2017.

PY - 2017/10/20

Y1 - 2017/10/20

N2 - 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.

AB - 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.

KW - Mathematics

KW - Didactics of Mathematics

UR - http://www.scopus.com/inward/record.url?scp=85031903057&partnerID=8YFLogxK

U2 - 10.5194/npg-24-661-2017

DO - 10.5194/npg-24-661-2017

M3 - Journal articles

VL - 24

SP - 661

EP - 671

JO - Nonlinear Processes in Geophysics

JF - Nonlinear Processes in Geophysics

SN - 1023-5809

IS - 4

ER -