{
  "id": "1412.2686",
  "version": "v1",
  "published": "2014-12-08T18:21:05.000Z",
  "updated": "2014-12-08T18:21:05.000Z",
  "title": "Universal Statistical Properties of Inertial-particle Trajectories in Three-dimensional, Homogeneous, Isotropic, Fluid Turbulence",
  "authors": [
    "Akshay Bhatnagar",
    "Anupam Gupta",
    "Dhrubaditya Mitra",
    "Prasad Perlekar",
    "Rahul Pandit"
  ],
  "categories": [
    "physics.flu-dyn",
    "nlin.CD"
  ],
  "abstract": "We uncover universal statistical properties of the trajectories of heavy inertial particles in three-dimensional, statistically steady, homogeneous, and isotropic turbulent flows by extensive direct numerical simulations. We show that the probability distribution functions (PDFs) $P(\\phi)$, of the angle $\\phi$ between the Eulerian velocity ${\\bf u}$ and the particle velocity ${\\bf v}$, at this point and time, shows a power-law region in which $P(\\phi) \\sim \\phi^{-\\gamma}$, with a new universal exponent $\\gamma \\simeq 4$. Furthermore, the PDFs of the trajectory curvature $\\kappa$ and modulus $\\theta$ of the torsion $\\vartheta$ have power-law tails that scale, respectively, as $P(\\kappa) \\sim \\kappa^{-h_\\kappa}$, as $\\kappa \\to \\infty$, and $P(\\theta) \\sim \\theta^{-h_\\theta}$, as $\\theta \\to \\infty$, with exponents $h_\\kappa \\simeq 2.5$ and $h_\\theta \\simeq 3$ that are universal to the extent that they do not depend on the Stokes number ${\\rm St}$ (given our error bars). We also show that $\\gamma$, $h_\\kappa$ and $h_\\theta$ can be obtained by using simple stochastic models. We characterize the complexity of heavy-particle trajectories by the number $N_{\\rm I}(t,{\\rm St})$ of points (up until time $t$) at which $\\vartheta$ changes sign. We show that $n_{\\rm I}({\\rm St}) \\equiv \\lim_{t\\to\\infty} \\frac{N_{\\rm I}(t,{\\rm St})}{t} \\sim {\\rm St}^{-\\Delta}$, with $\\Delta \\simeq 0.4$ a universal exponent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-08T18:21:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fluid turbulence",
      "inertial-particle trajectories",
      "trajectory",
      "three-dimensional",
      "universal exponent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.2686B"
    }
  }
}