Universal alignment in turbulent pair dispersion.

Area of Science:

• Fluid Dynamics and Turbulence
• Statistical Physics
• Geophysics and Environmental Science

Background:

• Turbulent fluctuations in advected matter concentrations are crucial in natural and industrial processes.
• Particle pair dispersion, describing the change in separation between particles, is traditionally modeled by Richardson's cubic-in-time growth theory for small separations.

Purpose of the Study:

• To reveal a universal, scale-invariant geometric property of turbulent pair dispersion.
• To connect this property to Richardson's theory and validate it experimentally and numerically.
• To establish a new framework for understanding turbulent transport and mixing.

Main Methods:

• Analysis of the alignment between relative velocity and position vectors of dispersing particles.
• Theoretical connection of the mean alignment angle to turbulence constants.
• Validation using data from numerical simulations and laboratory experiments.

Main Results:

• A universal, scale-invariant alignment between relative velocity and position vectors of dispersing particles was discovered.
• The mean alignment angle was identified as a universal constant of turbulence.
• This constant angle was found to be consistent with Richardson's theory and empirical data, manifesting across the entire inertial range of turbulence.

Conclusions:

• The study reveals the universal nature of turbulent pair dispersion through a novel geometric paradigm.
• The discovered universal angle provides a framework for understanding and modeling turbulent transport and mixing processes.
• The findings extend beyond the limitations of Richardson's classical theory, offering broader applicability.