Articles | Volume 24, issue 4
https://doi.org/10.5194/npg-24-661-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
https://doi.org/10.5194/npg-24-661-2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
the Creative Commons Attribution 3.0 License.
Research article
| 
20 Oct 2017
Research article |
| 20 Oct 2017
Network-based study of Lagrangian transport and mixing
Kathrin Padberg-Gehle
CORRESPONDING AUTHOR
Leuphana Universität Lüneburg, Institute of Mathematics and its Didactics, Applied Mathematics Group, Universitätsallee 1, 21335 Lüneburg, Germany
Christiane Schneide
Leuphana Universität Lüneburg, Institute of Mathematics and its Didactics, Applied Mathematics Group, Universitätsallee 1, 21335 Lüneburg, Germany
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Cited
46 citations as recorded by crossref.
- Crossroads of the mesoscale circulation A. Baudena et al. https://doi.org/10.1016/j.jmarsys.2018.12.005
- Deep Lagrangian Connectivity in the Global Ocean Inferred from Argo Floats R. Abernathey et al. https://doi.org/10.1175/JPO-D-21-0156.1
- Assessing Lagrangian coherence in atmospheric blocking H. Schoeller et al. https://doi.org/10.5194/npg-32-51-2025
- Open-flow mixing and transfer operators A. Klünker et al. https://doi.org/10.1098/rsta.2021.0028
- Graph convolutional networks applied to unstructured flow field data F. Ogoke et al. https://doi.org/10.1088/2632-2153/ac1fc9
- Detecting flow features in scarce trajectory data using networks derived from symbolic itineraries: an application to surface drifters in the North Atlantic D. Wichmann et al. https://doi.org/10.5194/npg-27-501-2020
- Trajectory‐based computational study of coherent behavior in flows K. Padberg‐Gehle & C. Schneide https://doi.org/10.1002/pamm.201710004
- Lagrangian heat transport in turbulent three-dimensional convection P. Vieweg et al. https://doi.org/10.1103/PhysRevFluids.6.L041501
- Ocean Surface Connectivity in the Arctic: Capabilities and Caveats of Community Detection in Lagrangian Flow Networks D. Reijnders et al. https://doi.org/10.1029/2020JC016416
- Influence of excitation amplitude on mixing characteristics and Lagrangian coherent structures of a supercritical nitrogen jet X. LI et al. https://doi.org/10.1016/j.cja.2026.104376
- Impact of Climate Change on Surface Stirring and Transport in the Mediterranean Sea E. Ser‐Giacomi et al. https://doi.org/10.1029/2020GL089941
- Lagrangian analysis of long‐term dynamics of turbulent superstructures C. Schneide et al. https://doi.org/10.1002/pamm.202000197
- Preface: Current perspectives in modelling, monitoring, and predicting geophysical fluid dynamics A. Mancho et al. https://doi.org/10.5194/npg-25-125-2018
- Ordering of trajectories reveals hierarchical finite-time coherent sets in Lagrangian particle data: detecting Agulhas rings in the South Atlantic Ocean D. Wichmann et al. https://doi.org/10.5194/npg-28-43-2021
- Detecting Lagrangian coherent structures from sparse and noisy trajectory data S. Mowlavi et al. https://doi.org/10.1017/jfm.2022.652
- Lagrangian gradient regression for the detection of coherent structures from sparse trajectory data T. Harms et al. https://doi.org/10.1098/rsos.240586
- Sparse eigenbasis approximation: Multiple feature extraction across spatiotemporal scales with application to coherent set identification G. Froyland et al. https://doi.org/10.1016/j.cnsns.2019.04.012
- A long short-term memory neural network-based error estimator for three-dimensional dynamically adaptive mesh generation X. Wu et al. https://doi.org/10.1063/5.0172020
- Evolution of clusters of turbulent reattachment due to shear layer instability in flow past a circular cylinder G. Chopra et al. https://doi.org/10.1063/5.0187414
- Probing turbulent superstructures in Rayleigh-Bénard convection by Lagrangian trajectory clusters C. Schneide et al. https://doi.org/10.1103/PhysRevFluids.3.113501
- Lagrangian network analysis of turbulent mixing G. Iacobello et al. https://doi.org/10.1017/jfm.2019.79
- Experimental investigation of vertical turbulent transport of a passive scalar in a boundary layer: Statistics and visibility graph analysis G. Iacobello et al. https://doi.org/10.1103/PhysRevFluids.4.104501
- Spectral-Clustering of Lagrangian Trajectory Graphs: Application to Abdominal Aortic Aneurysms A. Darwish et al. https://doi.org/10.1007/s13239-021-00590-3
- Graph theoretic methods for assessing the effects of a background shear current on internal solitary waves I. Membrere & M. Stastna https://doi.org/10.1017/jfm.2024.743
- Efficient numerical methods for the Maxey-Riley-Gatignol equations with Basset history term J. Urizarna-Carasa et al. https://doi.org/10.1016/j.cpc.2025.109502
- Lagrangian coherent sets in turbulent Rayleigh-Bénard convection C. Schneide et al. https://doi.org/10.1103/PhysRevE.100.053103
- Fast and robust computation of coherent Lagrangian vortices on very large two-dimensional domains D. Karrasch & N. Schilling https://doi.org/10.5802/smai-jcm.63
- Clustering time-evolving networks using the spatiotemporal graph Laplacian M. Trower et al. https://doi.org/10.1063/5.0228419
- Explicit and implicit network connectivity: Analytical formulation and application to transport processes E. Ser-Giacomi et al. https://doi.org/10.1103/PhysRevE.103.042309
- Evolutionary clustering of Lagrangian trajectories in turbulent Rayleigh–Bénard convection flows C. Schneide et al. https://doi.org/10.1063/5.0076035
- Unsteady Mass Transfer in Bubble Wakes Analyzed by Lagrangian Coherent Structures in a Flat-Bed Reactor L. Kursula et al. https://doi.org/10.3390/pr10122686
- Transport structure of two-dimensional homogeneous Rayleigh–Bénard convection L. Moczarski & W. Müller https://doi.org/10.1017/jfm.2026.11351
- Spectral Early-Warning Signals for Sudden Changes in Time-Dependent Flow Patterns M. Ndour et al. https://doi.org/10.3390/fluids6020049
- Lagrangian studies of coherent sets and heat transport in constant heat flux-driven turbulent Rayleigh–Bénard convection P. Vieweg et al. https://doi.org/10.1016/j.euromechflu.2023.08.007
- Relevance of the Basset history term for Lagrangian particle dynamics J. Urizarna-Carasa et al. https://doi.org/10.1063/5.0225926
- Quantitative analysis of the kinematics and induced aerodynamic loading of individual vortices in vortex-dominated flows: A computation and data-driven approach K. Menon & R. Mittal https://doi.org/10.1016/j.jcp.2021.110515
- Wall-induced anisotropy effects on turbulent mixing in channel flow: A network-based analysis D. Perrone et al. https://doi.org/10.1103/PhysRevE.102.043109
- Particle clustering and subclustering as a proxy for mixing in geophysical flows R. Chakraborty et al. https://doi.org/10.5194/npg-26-307-2019
- Generalized Lagrangian coherent structures S. Balasuriya et al. https://doi.org/10.1016/j.physd.2018.01.011
- Computational study of three-dimensional Lagrangian transport and mixing in a stirred tank reactor C. Weiland et al. https://doi.org/10.1016/j.ceja.2023.100448
- Network measures of mixing R. Banisch et al. https://doi.org/10.1063/1.5087632
- A Geometric Heat-Flow Theory of Lagrangian Coherent Structures D. Karrasch & J. Keller https://doi.org/10.1007/s00332-020-09626-9
- An Inflated Dynamic Laplacian to Track the Emergence and Disappearance of Semi-material Coherent Sets J. Atnip et al. https://doi.org/10.1007/s00332-026-10301-8
- A review on turbulent and vortical flow analyses via complex networks G. Iacobello et al. https://doi.org/10.1016/j.physa.2020.125476
- Network-based analysis of fluid flows: Progress and outlook K. Taira & A. Nair https://doi.org/10.1016/j.paerosci.2022.100823
- Analyzing two-dimensional cellular detonation flows from numerical simulations with proper orthogonal decomposition and Lagrangian descriptors C. Yan et al. https://doi.org/10.1007/s12650-024-01024-7
46 citations as recorded by crossref.
- Crossroads of the mesoscale circulation A. Baudena et al. https://doi.org/10.1016/j.jmarsys.2018.12.005
- Deep Lagrangian Connectivity in the Global Ocean Inferred from Argo Floats R. Abernathey et al. https://doi.org/10.1175/JPO-D-21-0156.1
- Assessing Lagrangian coherence in atmospheric blocking H. Schoeller et al. https://doi.org/10.5194/npg-32-51-2025
- Open-flow mixing and transfer operators A. Klünker et al. https://doi.org/10.1098/rsta.2021.0028
- Graph convolutional networks applied to unstructured flow field data F. Ogoke et al. https://doi.org/10.1088/2632-2153/ac1fc9
- Detecting flow features in scarce trajectory data using networks derived from symbolic itineraries: an application to surface drifters in the North Atlantic D. Wichmann et al. https://doi.org/10.5194/npg-27-501-2020
- Trajectory‐based computational study of coherent behavior in flows K. Padberg‐Gehle & C. Schneide https://doi.org/10.1002/pamm.201710004
- Lagrangian heat transport in turbulent three-dimensional convection P. Vieweg et al. https://doi.org/10.1103/PhysRevFluids.6.L041501
- Ocean Surface Connectivity in the Arctic: Capabilities and Caveats of Community Detection in Lagrangian Flow Networks D. Reijnders et al. https://doi.org/10.1029/2020JC016416
- Influence of excitation amplitude on mixing characteristics and Lagrangian coherent structures of a supercritical nitrogen jet X. LI et al. https://doi.org/10.1016/j.cja.2026.104376
- Impact of Climate Change on Surface Stirring and Transport in the Mediterranean Sea E. Ser‐Giacomi et al. https://doi.org/10.1029/2020GL089941
- Lagrangian analysis of long‐term dynamics of turbulent superstructures C. Schneide et al. https://doi.org/10.1002/pamm.202000197
- Preface: Current perspectives in modelling, monitoring, and predicting geophysical fluid dynamics A. Mancho et al. https://doi.org/10.5194/npg-25-125-2018
- Ordering of trajectories reveals hierarchical finite-time coherent sets in Lagrangian particle data: detecting Agulhas rings in the South Atlantic Ocean D. Wichmann et al. https://doi.org/10.5194/npg-28-43-2021
- Detecting Lagrangian coherent structures from sparse and noisy trajectory data S. Mowlavi et al. https://doi.org/10.1017/jfm.2022.652
- Lagrangian gradient regression for the detection of coherent structures from sparse trajectory data T. Harms et al. https://doi.org/10.1098/rsos.240586
- Sparse eigenbasis approximation: Multiple feature extraction across spatiotemporal scales with application to coherent set identification G. Froyland et al. https://doi.org/10.1016/j.cnsns.2019.04.012
- A long short-term memory neural network-based error estimator for three-dimensional dynamically adaptive mesh generation X. Wu et al. https://doi.org/10.1063/5.0172020
- Evolution of clusters of turbulent reattachment due to shear layer instability in flow past a circular cylinder G. Chopra et al. https://doi.org/10.1063/5.0187414
- Probing turbulent superstructures in Rayleigh-Bénard convection by Lagrangian trajectory clusters C. Schneide et al. https://doi.org/10.1103/PhysRevFluids.3.113501
- Lagrangian network analysis of turbulent mixing G. Iacobello et al. https://doi.org/10.1017/jfm.2019.79
- Experimental investigation of vertical turbulent transport of a passive scalar in a boundary layer: Statistics and visibility graph analysis G. Iacobello et al. https://doi.org/10.1103/PhysRevFluids.4.104501
- Spectral-Clustering of Lagrangian Trajectory Graphs: Application to Abdominal Aortic Aneurysms A. Darwish et al. https://doi.org/10.1007/s13239-021-00590-3
- Graph theoretic methods for assessing the effects of a background shear current on internal solitary waves I. Membrere & M. Stastna https://doi.org/10.1017/jfm.2024.743
- Efficient numerical methods for the Maxey-Riley-Gatignol equations with Basset history term J. Urizarna-Carasa et al. https://doi.org/10.1016/j.cpc.2025.109502
- Lagrangian coherent sets in turbulent Rayleigh-Bénard convection C. Schneide et al. https://doi.org/10.1103/PhysRevE.100.053103
- Fast and robust computation of coherent Lagrangian vortices on very large two-dimensional domains D. Karrasch & N. Schilling https://doi.org/10.5802/smai-jcm.63
- Clustering time-evolving networks using the spatiotemporal graph Laplacian M. Trower et al. https://doi.org/10.1063/5.0228419
- Explicit and implicit network connectivity: Analytical formulation and application to transport processes E. Ser-Giacomi et al. https://doi.org/10.1103/PhysRevE.103.042309
- Evolutionary clustering of Lagrangian trajectories in turbulent Rayleigh–Bénard convection flows C. Schneide et al. https://doi.org/10.1063/5.0076035
- Unsteady Mass Transfer in Bubble Wakes Analyzed by Lagrangian Coherent Structures in a Flat-Bed Reactor L. Kursula et al. https://doi.org/10.3390/pr10122686
- Transport structure of two-dimensional homogeneous Rayleigh–Bénard convection L. Moczarski & W. Müller https://doi.org/10.1017/jfm.2026.11351
- Spectral Early-Warning Signals for Sudden Changes in Time-Dependent Flow Patterns M. Ndour et al. https://doi.org/10.3390/fluids6020049
- Lagrangian studies of coherent sets and heat transport in constant heat flux-driven turbulent Rayleigh–Bénard convection P. Vieweg et al. https://doi.org/10.1016/j.euromechflu.2023.08.007
- Relevance of the Basset history term for Lagrangian particle dynamics J. Urizarna-Carasa et al. https://doi.org/10.1063/5.0225926
- Quantitative analysis of the kinematics and induced aerodynamic loading of individual vortices in vortex-dominated flows: A computation and data-driven approach K. Menon & R. Mittal https://doi.org/10.1016/j.jcp.2021.110515
- Wall-induced anisotropy effects on turbulent mixing in channel flow: A network-based analysis D. Perrone et al. https://doi.org/10.1103/PhysRevE.102.043109
- Particle clustering and subclustering as a proxy for mixing in geophysical flows R. Chakraborty et al. https://doi.org/10.5194/npg-26-307-2019
- Generalized Lagrangian coherent structures S. Balasuriya et al. https://doi.org/10.1016/j.physd.2018.01.011
- Computational study of three-dimensional Lagrangian transport and mixing in a stirred tank reactor C. Weiland et al. https://doi.org/10.1016/j.ceja.2023.100448
- Network measures of mixing R. Banisch et al. https://doi.org/10.1063/1.5087632
- A Geometric Heat-Flow Theory of Lagrangian Coherent Structures D. Karrasch & J. Keller https://doi.org/10.1007/s00332-020-09626-9
- An Inflated Dynamic Laplacian to Track the Emergence and Disappearance of Semi-material Coherent Sets J. Atnip et al. https://doi.org/10.1007/s00332-026-10301-8
- A review on turbulent and vortical flow analyses via complex networks G. Iacobello et al. https://doi.org/10.1016/j.physa.2020.125476
- Network-based analysis of fluid flows: Progress and outlook K. Taira & A. Nair https://doi.org/10.1016/j.paerosci.2022.100823
- Analyzing two-dimensional cellular detonation flows from numerical simulations with proper orthogonal decomposition and Lagrangian descriptors C. Yan et al. https://doi.org/10.1007/s12650-024-01024-7
Saved (final revised paper)
Latest update: 10 Aug 2026
Short summary
Transport and mixing processes in fluid flows are crucially influenced by coherent structures, such as eddies, gyres, or jets in geophysical flows. We propose a very simple and computationally efficient approach for analyzing coherent behavior in fluid flows. The central object is a flow network constructed directly from particle trajectories. The network's local and spectral properties are shown to give a very good indication of coherent as well as mixing regions in the underlying flow.
Transport and mixing processes in fluid flows are crucially influenced by coherent structures,...
