Does a particle swept by a turbulent liquid diffuse?

TL;DR

This paper investigates the motion of a single particle in turbulent liquid, revealing that it exhibits superdiffusive behavior with a correlation time that is infinite, contrasting the traditional diffusive model.

Contribution

It demonstrates that a particle's velocity in turbulence has infinite correlation time, leading to superdiffusive motion characterized by a displacement proportional to T^{6/5}.

Findings

Particle motion is superdiffusive with F proportional to T^{6/5}.

Correlation time of particle velocity is infinite.

Single particle motion differs from the classical diffusive picture.

Abstract

Since the famous 1926 paper by Richardson, the relative diffusion of two particles in a turbulent liquid has attracted a lot of interest. The motion of a single particle on the other hand is usually considered not to be especially interesting. The widely accepted picture is that the velocity of the particle has short-range correlations in time, resulting in motion that is diffusive on time scales large compared to the correlation time. We find, however, that the correlation time is infinite and that the square displacement, F, is not linear in the traversed time, T, which would correspond to diffusion, but rather F is proportional to T^6/5. Namely, the motion is slightly super diffusive.