The clustering instability of inertial particles spatial distribution in turbulent flows

A theory of clustering of inertial particles advected by a turbulent velocity field caused by an instability of their spatial distribution is suggested. The reason for the clustering instability is a combined effect of the particles inertia and a finite correlation time of the velocity field. The crucial parameter for the clustering instability is a size of the particles. The critical size is estimated for a 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 weak clustering associated with the growth of the second and higher moments. A new concept of compressibility of the turbulent diffusion tensor caused by a finite correlation time of an incompressible velocity field is introduced. In this model of the velocity field, the field of Lagrangian trajectories is not divergence-free. A mechanism of saturation of the clustering instability associated with the particles collisions in the clusters is suggested. Applications of the analyzed effects to the dynamics of droplets in the turbulent atmosphere are discussed. An estimated nonlinear level of the saturation of the droplets number density in clouds exceeds by the orders of magnitude their mean number density. The critical size of cloud droplets required for clusters formation is more than $20 \mu$m.Comment: REVTeX 4, 15 pages, 2 figures(included), PRE submitte

Inclined lidar observations of boundary layer aerosol particles above the Kongsfjord, Svalbard

An inclined lidar with vertical resolution of 0.4 m was used for detailed boundary layer studies and to link observations at Zeppelin Mountain (474 m) and Ny-Ålesund, Svalbard. We report on the observation of aerosol layers directly above the Kongsfjord. On 29 April 2007, a layer of enhanced backscatter was observed in the lowest 25 m above the open water surface. The low depolarization ratio indicated spherical particles. In the afternoon, this layer disappeared. The ultrafine particle concentration at Zeppelin and Corbel station (close to the Kongsfjord) was low. On 1 May 2007, a drying process in the boundary layer was observed. In the morning, the atmosphere up to Zeppelin Mountain showed enhanced values of the backscatter coefficient. Around noon, the top of the highly reflecting boundary layer decreased from 350 to 250 m. The top of the boundary layer observed by lidar was confirmed by radiosonde data