Abstract
We use direct numerical simulations to calculate the joint probability density function of the relative distance and relative radial velocity component 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, . 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) , where the distribution depends solely on , and (2) , where the distribution is a function of alone. The probability distributions in these two regimes are matched along a straight line: . Our simulations confirm that this is indeed correct. We further obtain and as a function of the Stokes number, . The former depends nonmonotonically on with a minimum at about and the latter has only a weak dependence on .
2 More- Received 16 October 2017
DOI:https://doi.org/10.1103/PhysRevE.97.023105
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