Itzhak Fouxon (Yonsei University, South Korea). Clustering of particles in turbulence.

This talk describes recent progress in describing clustering of particles in turbulence. This is demonstrated to be universal consequence of small deviations of particles' trajectories from those of the fluid. The mechanisms that cause the deviations differ: inertia, search of living phytoplankton cells for optimal living conditions, drift in gradients of temperature, salinity or nutrients and others. In all these situations the motion of particles in space can be described as smooth weakly compressible random flow. We demonstrate this frame brings log-normal distribution of particles on multifractal sets in space. Pair correlations obey power law with negative exponent diverging at zero separation. The predictions hold without modeling the (unknown) statistics of turbulence and are confirmed by direct numerical simulations of motion of particles in Navier-Stokes turbulence and experiments. Implications for the problem of formation of rain will be discussed.