Braids of entangled particle trajectories

Area of Science:

• Fluid Dynamics
• Topology
• Data Analysis

Background:

• Two-dimensional particle trajectories are often available, but underlying fluid flow remains poorly understood.
• Existing methods like dispersion coefficients or Lyapunov exponents incompletely utilize trajectory data.

Purpose of the Study:

• To develop a global method for analyzing fluid flow using all available particle trajectory data.
• To approximate topological entropy as a measure of trajectory entanglement in fluid flows.

Main Methods:

• Utilizing tools from braid theory and the topology of surface mappings.
• Calculating topological entropy from the entanglement patterns of particle trajectories.

Main Results:

• The proposed method uses all trajectory data for a global analysis.
• Topological entropy quantifies the complexity of trajectory entanglement, approaching zero for simple flows like large vortices.

Conclusions:

• The technique offers a novel way to extract quantitative information about fluid flow from particle trajectories.
• This method can potentially identify Lagrangian coherent structures, improving our understanding of oceanic and other fluid systems.