ANOMALOUS SCALINGS FOR FLUCTUATIONS OF INERTIAL PARTICLES CONCENTRATION AND LARGE-SCALE DYNAMICS

Small-scale fluctuations and mean-field dynamics of the number density of inertial particles in turbulent fluid flow are studied. Anomalous scaling for the second-order correlation function of the number densit y of inertial particles is found. The mechanism for the anomalous scal ing is associated with the inertia of particles that results in a dive rgent velocity field of particles. The anomalous scaling appears alrea dy in the second moment when the degree of compressibility sigma>1/27 (where a is the ratio of the energies in the compressible and the inco mpressible components of the particles velocity). The delta-correlated in time random process is used to describe a turbulent velocity held. However, the results remain valid also for the velocity field with a finite correlation time, if all moments of the number density of the p articles vary slowly in comparison with the correlation time of the tu rbulent velocity field. The mechanism of formation of large-scale inho mogeneous structures in spatial distribution of inertial particles adv ected by a low-Mach-number compressible turbulent fluid flow with a no nzero mean temperature gradient is discussed as well. The effect of in ertia causes an additional nondiffusive turbulent flux of particles th at is proportional to the mean temperature gradient. Inertial particle s are concentrated in the vicinity of the minimum (or maximum) of the mean temperature of the surrounding fluid depending on the ratio of th e material particle density to that of the surrounding fluid. The equa tion for the turbulent flux of particles advected by a low-Mach-number compressible turbulent fluid flow is derived. The large-scale dynamic s of inertial particles is studied by considering the stability of the equilibrium solution of the derived equation for the mean number dens ity of the particles. A modified Rayleigh-Ritz variational method is u sed for the analysis of the large-scale instability.