Timescales of Turbulent Relative Dispersion

TL;DR

This paper revisits the timescales of turbulent relative dispersion, showing that acceleration differences decorrelate quickly and lead to a long-time diffusion behavior akin to Brownian motion, challenging traditional explanations.

Contribution

It demonstrates that the long-time dispersion in turbulence is governed by acceleration decorrelation and dissipation timescales, not the scale-dependent diffusivity traditionally assumed.

Findings

Acceleration differences decorrelate on dissipative timescales.

Long-time behavior of dispersion is like Brownian motion.

Convergence time linked to deviations from ballistic regime.

Abstract

Tracers in a turbulent flow separate according to the celebrated $t^{3/2}$ Richardson--Obukhov law, which is usually explained by a scale-dependent effective diffusivity. Here, supported by state-of-the-art numerics, we revisit this argument. The Lagrangian correlation time of velocity differences is found to increase too quickly for validating this approach, but acceleration differences decorrelate on dissipative timescales. This results in an asymptotic diffusion $\propto t^{1/2}$ of velocity differences, so that the long-time behavior of distances is that of the integral of Brownian motion. The time of convergence to this regime is shown to be that of deviations from Batchelor's initial ballistic regime, given by a scale-dependent energy dissipation time rather than the usual turnover time. It is finally argued that the fluid flow intermittency should not affect this long-time behavior of relative