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Area of Science:

  • Fluid Dynamics
  • Network Science
  • Data Analysis

Background:

  • Lagrangian trajectory data offers insights into fluid transport and mixing.
  • Graph-based network analysis is emerging for trajectory data, using spectral methods.
  • Previous work often involves complex weighted networks.

Purpose of the Study:

  • To analytically connect local network measures to fluid flow structures.
  • To simplify graph-based analysis by considering unweighted, undirected networks.
  • To group trajectories with similar dynamical behaviors using manifold learning.

Main Methods:

  • Constructing unweighted, undirected networks from trajectory data.
  • Calculating local network measures (node degree, clustering coefficient).
  • Applying manifold learning techniques to cluster trajectories.

Main Results:

  • Analytical relationships established between local network measures and flow structures.
  • Demonstrated utility of simple network measures for understanding complex flows.
  • Successful grouping of trajectories based on dynamical similarity.

Conclusions:

  • Local network measures in simplified graph representations are effective for analyzing fluid dynamics.
  • This approach provides a new method for identifying flow structures and trajectory groupings.
  • Manifold learning enhances the interpretation of network properties for dynamical systems.