Strong and weak clustering of inertial particles in turbulent flows

We suggested a theory of clustering of inertial particles advected by a turbulent velocity field caused by an instability of their spatial distribution. The reason of the {\em clustering instability} is a combined effect of the particle inertia and finite correlation time of the velocity field. The crucial parameter for the instability is a size of the particles. The critical size is estimated for a {\em strong clustering} (with a finite fraction of particles in clusters) associated with the growth of the mean absolute value of the particles number density and for a {\em weak clustering} associated with the growth of the second and higher moments. A nonlinear mechanism for a saturation of the clustering instability (particles collisions in the clusters) is suggested. Applications of the analyzed effects to the dynamics of aerosols and droplets in the turbulent atmosphere are discussed. The critical size of atmospheric aerosols and droplets in clustering is of the order of $(20 - 30)\mu$m, and a lower estimate of the number of particles in a cluster is about hundreds.