regime, are analyzed. The concentration spectrum is predicted to obey, above the scale of eddies with lifetime equal to the Stokes time, a power law with universal $-4/3$ exponent, and to be otherwise independent of the nature of the turbulent flow. A preference of the solid particle to lie in less energetic regions of the flow is observed.

PACS numbers: 47.27.Qb 47.55.Kf 02.50.Ey

**I. Introduction**

One of the differences between high Reynolds number turbulence and other examples of random fields with power law scaling, is the Lagrangian nature of time correlations [@kraichnan64]. From the theoretical point of view, the need for a Lagrangian treatment of time correlations has been one of the main difficulties in the realization of statistical turbulent closures [@kraichnan65]. Because of this, many such theories assume from the start that the turbulence dynamics be equivalent to that of a random velocity field with identical energy spectrum but Eulerian time statistics, i.e. the fluctuations decay without being transported by the larger vortices [@kraichnan71; @orszag77; @yakhot86]. Such an assumption does not work in the case of particle transport: both relative and self-diffusion are affected by the way in which time correlations are defined.

Concerning self-diffusion, in Kolmogorov turbulence, fluctuations 