Statistics of the relative velocity of particles in turbulent flows: Monodisperse particles.

We use direct numerical simulations to calculate the joint probability density function of the relative distance R and relative radial velocity component VR for a pair of heavy inertial particles suspended in homogeneous and isotropic turbulent flows. At small scales the distribution is scale invariant, with a scaling exponent that is related to the particle-particle correlation dimension in phase space, D2. It was argued [K. Gustavsson and B. Mehlig, Phys. Rev. E 84, 045304 (2011); J. Turbul. 15, 34 (2014)] that the scale invariant part of the distribution has two asymptotic regimes: (1) |VR|«R, where the distribution depends solely on R, and (2) |VR|»R, where the distribution is a function of |VR| alone. The probability distributions in these two regimes are matched along a straight line: |VR|=z*R. Our simulations confirm that this is indeed correct. We further obtain D2 and Z* as a function of the Stokes number, St. The former depends nonmonotonically on St with a minimum at about St≈0.7 and the latter has only a weak dependence on St. [ABSTRACT FROM AUTHOR]