### abstract

- Turbulent transport of aerosols and droplets in a random velocity field with a finite correlation time is studied. We derived a mean-field equation and an equation for the second moment for a number density of aerosols. The finite correlation time of random velocity field results in the appearance of the high-order spatial derivatives in these equations. The finite correlation time and compressibility of the velocity field can cause a depletion of turbulent diffusion and a modification of an effective mean drift velocity. The coefficient of turbulent diffusion in the vertical direction can be depleted by 25 % due to the finite correlation time of a turbulent velocity field. The latter result is in compliance with the known anisotropy of the coefficient of turbulent diffusion in the atmosphere. The effective mean drift velocity is caused by a compressibility of particles velocity field and results in formation of large-scale inhomogeneities in spatial distribution of aerosols in the vicinity of the atmospheric temperature inversion. Results obtained by Saffman (1960) for the effect of molecular diffusivity in turbulent diffusion are generalized for the case of compressible and anisotropic random velocity field. A mechanism of formation of small-scale inhomogeneities in particles spatial distribution is also discussed. This mechanism is associated with an excitation of a small-scale instability of the second moment of number density of particles. The obtained results are important in the analysis of various atmospheric phenomena, e.g., atmospheric aerosols, droplets and smog formation.