Critical analysis of results concerning droplet collisions in turbulent clouds

During the past ten years a large number of studies dedicated to the problem of collisions of inertial particles in turbulent flows have appeared. It is widely accepted now that turbulence enhances the rate of collisions of particles. A wide range of the turbulence collision enhancement factor was reported: from a few percents to several hundred times. There exist three major mechanisms that turbulence affects the collision rate: a) enhancement of relative particle velocity; b) particle clustering, and c) influence of turbulence on the hydrodynamic interaction of particles. The major turbulent effect on collisions is often attributed to the particle clustering in a turbulent flow. Some studies reported the formation of extremely high concentrations of particles forming "fractal" structures at scales below the Kolmogorov microscale. The formation of such droplet structures results in a dramatic increase (up two orders of magnitude) in the collision rate. The results of these studies are often applied to the explanation of rain triggering in actual clouds. The simulations with advanced numerical cloud models indicate that the increase in the collision rate between cloud droplets by factors found in these studies leads to a rapid formation of precipitation from clouds known as non-precipitating. Note that most of these analytical and numerical (DNS) results were obtained for monodisperse (or bi-disperse) high concentration particle suspensions, neglecting differential particle sedimentation and Brownian diffusion effects. We present a critical analysis of the applicability of results of the studies to actual clouds. It is shown that conditions in actual clouds dramatically differ from those used in these studies. Clouds represent very low concentration suspensions of particles (droplets) having a wide range of sizes and sedimentation velocities. The size of the most droplets in clouds is less than 20 microns, i.e. droplets are characterized by the Stokes number St < 0.2. The mean distance between cloud droplets exceeds 1 mm, and it can exceed 1 cm for the largest cloud droplets (St~0.2) and small raindrops (St~1). Small droplet concentration and significant difference in the sedimentation velocity makes the formation of "fractal" droplet structures at sub-Kolmogorov microscale in actual clouds questionable. In case the concentration of large droplets is low, their transport under turbulent-induced centrifugal forces does not lead to a decrease of the mean drop separation distances. In many studies the effect of clustering was assessed by using phenomenological arguments but not by a proper averaging of the Smoluchowski equation over the statistics of the turbulent velocity field. Respectively, the droplet clustering effect seems to be highly overestimated in many studies as concerns actual cloud conditions. Some effects of hydrodynamic droplet interaction related to specific cloud properties are discussed. We argue that low droplet concentration renders such fine effects as multi-particle interactions of the secondary importance. In some studies aimed at the parameterization of turbulent effects on droplet collisions, the collision kernel is represented as a sum of "gravitational" and "turbulent" collision kernels, where the turbulent collision kernel is derived from the DNS performed for high concentration suspensions neglecting gravity effects. We argue that this approach is at least questionable.