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Coherent vortices in turbulent flows are identified as clusters of fluid particle trajectories. This novel method uses spectral graph theory for automated vortex tracking in complex fluid dynamics.

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Area of Science:

  • Fluid dynamics
  • Turbulence research
  • Complex systems analysis

Background:

  • Coherent vortices are persistent structures in real-world turbulent flows.
  • Identifying and tracking these vortices is crucial for understanding fluid behavior.
  • Existing methods may struggle with simultaneous detection and tracking.

Purpose of the Study:

  • To develop a novel method for extracting coherent vortices from turbulent flows.
  • To utilize Lagrangian trajectories and spectral graph theory for vortex identification.
  • To demonstrate the potential for automated and simultaneous vortex tracking.

Main Methods:

  • Clustering Lagrangian trajectories based on pairwise distances in phase space (position and time).
  • Constructing a weighted graph representing fluid trajectory relationships.
  • Applying spectral graph theory techniques to extract coherent vortex clusters from the graph.

Main Results:

  • Successfully extracted coherent vortices as distinct clusters of Lagrangian trajectories.
  • The method identifies all coherent vortices within the flow simultaneously.
  • Demonstrated effectiveness in various two- and three-dimensional flow scenarios.

Conclusions:

  • The proposed method offers a powerful tool for automated vortex tracking in turbulent flows.
  • Spectral graph theory provides an effective framework for analyzing Lagrangian data.
  • This approach enhances the understanding and analysis of complex fluid dynamics.