Clustering of heavy particles in random self-similar flow

A statistical description of heavy particles suspended in incompressible rough self-similar flows is developed. It is shown that, differently from smooth flows, particles do not form fractal clusters. They rather distribute inhomogeneously with a statistics that only depends on a local Stokes number, given by the ratio between the particles' response time and the turnover time associated with the observation scale. Particle clustering is reduced by the fluid roughness. Heuristic arguments supported by numerics explain this effect in terms of the algebraic tails of the probability density function of the velocity difference between two particles.