2002/04/12 by Tov Elperin, T. Elperin, Nathan Kleeorin +7 · 2 citations
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Aeolian processes and effects #Fluid Dynamics and Turbulent Flows #Particle Dynamics in Fluid Flows #nlin.CD #physics.flu-dyn
paper · pdf · doi:10.1103/physreve.66.036302
published as Phys. Rev. E, 66, 036302 (2002) · REVTeX 4, 15 pages, 2 figures(included), PRE submitted
arxiv created 2002/04/12 · openalex publication_date 2002/09/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 the 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 cluster formation is more than 20 microm.