Intermittent distribution of heavy particles in a turbulent flow

The retardation of weakly inertial particles depends on the acceleration of the ambient fluid, so the particle concentration n is determined by the divergence of Lagrangian acceleration which we study by direct numerical simulations. We demonstrate that the second moment of the concentration coarse-grained over the scale r behaves as an approximate power law: <(n) over bar (2)(r)>similar tor(alpha). We study the dependencies of the exponent alpha on the Reynolds number, of the Stokes number, and on the settling velocity. We find numerically that the theoretical lower bound previously suggested [Falkovich , Nature 419, 151 (2002)] correctly estimates the order of magnitude (within a factor 2 to 4) as well as the dependencies on the Reynolds, Stokes, and Froude numbers. The discrepancy grows with the Reynolds number and the Froude number. We analyze the possible physical mechanism responsible for that behavior. (C) 2004 American Institute of Physics.