{
  "id": "1209.4154",
  "version": "v2",
  "published": "2012-09-19T05:56:04.000Z",
  "updated": "2012-09-20T08:37:29.000Z",
  "title": "Logarithmic distribution of mean velocity and turbulent kinetic energy in a pipe flow",
  "authors": [
    "Xi Chen",
    "Fazle Hussain",
    "Zhen-Su She"
  ],
  "comment": "6 pages, 4 figures",
  "categories": [
    "physics.flu-dyn"
  ],
  "abstract": "A Lie-group based similarity theory is developed for both momentum and energy distributions in a turbulent pipe flow, leading to asymptotic logarithmic profiles of mean velocity and turbulent kinetic energy. Both channel and pipe data over a wide range of Re yield 0.45 to be the universal Karman constant. A new spatial invariant characterizing outer dynamics is discovered and validated by reliable experimental data. The theory predicts the mean velocity profile (MVP) with 99% accuracy for high Re experimental data (up to 40 millions), and offers a quantitative explanation for recent observation of logarithmic kinetic energy distribution by Hullmak et al. (Phys. Rev. Lett. 108, 094501).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-09-20T08:37:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "turbulent kinetic energy",
      "mean velocity",
      "logarithmic distribution",
      "logarithmic kinetic energy distribution",
      "experimental data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.4154C"
    }
  }
}