{
  "id": "1710.04917",
  "version": "v1",
  "published": "2017-10-13T13:35:18.000Z",
  "updated": "2017-10-13T13:35:18.000Z",
  "title": "Statistics of the relative velocity of particles in turbulent flows : monodisperse particles",
  "authors": [
    "Akshay Bhatnagar",
    "K. Gustavsson",
    "Dhrubaditya Mitra"
  ],
  "categories": [
    "physics.flu-dyn"
  ],
  "abstract": "We use direct numerical simulations to calculate the joint probability density function of the relative distance $R$ and relative radial velocity component $V_R$ 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, $D_2$. It was argued [1, 2] that the scale invariant part of the distribution has two asymptotic regimes: (1) $|V_R| \\ll R$ where the distribution depends solely on $R$; and (2) $|V_R| \\gg R$ where the distribution is a function of $|V_R|$ alone. The probability distributions in these two regimes are matched along a straight line $|V_R| = z^\\ast R$. Our simulations confirm that this is indeed correct. We further obtain $D_2$ and $z^\\ast$ as a function of the Stokes number, ${\\rm St}$. The former depends non-monotonically on ${\\rm St}$ with a minimum at about ${\\rm St} \\approx 0.7$ and the latter has only a weak dependence on ${\\rm St}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-13T13:35:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "monodisperse particles",
      "relative velocity",
      "distribution",
      "statistics",
      "joint probability density function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}