### abstract

- Department of Physics, Moscow State University, Moscow 117234, Russia(February 8, 2008)We suggested a theory of clustering of inertial particlesadvected by a turbulent velocity ﬁeld caused by an instabilityof their spatial distribution. The reason of the clustering in-stability is a combined eﬀect of the particle inertia and ﬁnitecorrelation time of the velocity ﬁeld. The crucial parame-ter for the instability is a size of the particles. The criticalsize is estimated for a strong clustering (with a ﬁnite frac-tion of particles in clusters) associated with the growth of themean absolute value of the particles number density and for aweak clustering associated with the growth of the second andhigher moments. A nonlinear mechanism for a saturation ofthe clustering instability (particles collisions in the clusters)is suggested. Applications of the analyzed eﬀects to the dy-namics of aerosols and droplets in the turbulent atmosphereare discussed. The critical size of atmospheric aerosols anddroplets in clustering is of the order of (20 − 30)µm, and alower estimate of the number of particles in a cluster is abouthundreds.I. INTRODUCTION