Does a particle swept by a turbulent liquid diffuse?

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.