Universal alignment in turbulent pair dispersion

TL;DR

This paper uncovers a universal, scale-invariant alignment between relative velocity and position in turbulent pair dispersion, linking it to Richardson's theory and demonstrating its consistency across simulations and experiments.

Contribution

It introduces a universal geometric alignment in turbulent pair dispersion, extending Richardson's classical theory beyond small initial separations.

Findings

Universal mean angle between velocity and position vectors in turbulence

Agreement with numerical simulation and laboratory data

Constancy of the angle across the inertial range

Abstract

Countless processes in nature and industry, from rain droplet nucleation to plankton interaction in the ocean, are intimately related to turbulent fluctuations of local concentrations of advected matter. These fluctuations can be described by considering the change of the separation between particle pairs, known as pair dispersion, which is believed to obey a cubic in time growth according to Richardson's theory. Our work reveals a universal, scale-invariant alignment between the relative velocity and position vectors of dispersing particles at a mean angle that we show to be a universal constant of turbulence. We connect the value of this mean angle to Richardson's traditional theory and find agreement with data from a numerical simulation and a laboratory experiment. While the Richardson's cubic regime has been observed for small initial particle separations only, the constancy of the mean angle manifests throughout the entire inertial range of turbulence. Thus, our work reveals the universal nature of turbulent pair dispersion through a geometrical paradigm whose validity goes beyond the classical theory, and provides a novel framework for understanding and modeling transport and mixing processes.