Diffusion of heavy particles in turbulent flows

Relative dispersion of tracers - i.e. very small, neutrally buoyant particles-, is particularly efficient in incompressible turbulent flows. Due to the non smooth behaviour of velocity differences in the inertial range, the separation distance between two trajectories, $R(t) = X_1(t) - X_2(t)$, grows as a power of time superdiffusively, $\langle R^2(t) \rangle~\alpha t^3$, as first observed by L.F. Richardson [1]. This now well established result has no counterpart in the theory of heavy particle suspensions, namely finite-size particles with a mass density much larger that of the carrier fluid. The complete knowledge of particle properties of mixing in turbulent flows -yet an open problem-, is of great importance in cloud physics, or in estimating pollutant dispersion for hazardous safety purposes