Spectral-clustering approach to Lagrangian vortex detection

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.