Intermittency and anomalous scalings of inertial particles distribution in turbulent flow

Small-scale fluctuations of the number density of inertial particles in turbulent fluid flow are studied. Anomalous scaling for the second-order correlation function of the number density of inertial particles is found. The mechanism for the anomalous scaling is associated with the inertia of particles which results in a divergent velocity field of particles. The anomalous scaling appears already in the second moment when the degree of compressibility σ > 1/27 (where σ is the ratio of the energies in compressible and incompressible component of the particles velocity). It is also demonstrated that inertia of particles in a homogeneous and isotropic turbulent fluid flow causes a self-excitation (exponential growth) of fluctuations of particles concentration. The growth rates of the higher moments of particle concentration is higher than those of the lower moments, i.e., the particle spatial distribution is intermittent.