Large-scale clustering of inertial particles in a rotating, stratified and inhomogeneous turbulence

Abstract

We develop a theory of various kinds of large-scale clustering of inertial particles in a rotating density stratified or inhomogeneous turbulent fluid flows. The large-scale particle clustering occurs in scales which are much larger than the integral scale of turbulence, and it is described in terms of the effective pumping velocity in a turbulent flux of particles. We show that for a fast rotating strongly anisotropic turbulence, the large-scale clustering occurs in the plane perpendicular to rotation axis in the direction of the fluid density stratification. We apply the theory of the large-scale particle clustering for explanation of the formation of planetesimals (progenitors of planets) in accretion protoplanetary discs. We determine the radial profiles of the radial and azimuthal components of the effective pumping velocity of particles which have two maxima corresponding to different regimes of the particle--fluid interactions: at the small radius it is the Stokes regime, while at the larger radius it is the Epstein regime. With the decrease the particle radius, the distance between the maxima increases. This implies that smaller-size particles are concentrated nearby the central body of the accretion disk, while larger-size particles are accumulated far from the central body. The dynamic time of the particle clustering is about $\tau_{\rm dyn} \sim 10^5$--$10^6$ years, while the turbulent diffusion time is about $10^7$ years, that is much larger than the characteristic formation time of large-scale particle clusters ($\sim \tau_{\rm dyn}$).