{
  "id": "1112.6310",
  "version": "v2",
  "published": "2011-12-29T13:58:53.000Z",
  "updated": "2011-12-30T05:47:55.000Z",
  "title": "Karman constant and accurate mean flow prediction in a turbulent pipe",
  "authors": [
    "Zhen-Su She",
    "Xi Chen",
    "You Wu",
    "Fazle Hussain"
  ],
  "comment": "20 pages, 6 figures",
  "categories": [
    "physics.flu-dyn"
  ],
  "abstract": "The Karman constant \\kappa - widely used in atmospheric science and engineering turbulence modelling, and proposed by Prandtl in 1925 and von Karman in 1930 to describe the mean velocity of a turbulent wall-bounded flow - leads to a logarithmic profile in an overlap region near the wall. For over eighty years, its value was believed to be ~0.41. But more recently, many argue that it is not a constant, because of measured variations in different flows and at different Reynolds numbers (Re). Here, a multi-layer analytic theory is shown to lead to a re-interpretation of \\kappa as a global constant for both the overlap region and outer flow, and to yield a new method for its measurement. The newly determined value is 0.45 for both channel and pipe. It is shown that this new \\kappa, together with other wall constants, yields a 99% accuracy in the prediction of mean velocity data at all points in high Re (up to 40 million) pipe flow. The theory also describes finite Re effect, and discovers a transition at the friction Re (i.e. Re_\\tau)=5000. An accurate model for the prediction of turbulent transport in canonical pipe and channel flows is achieved here, and we propose the model to be valid for a wide class of turbulent flows.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-12-30T05:47:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "accurate mean flow prediction",
      "karman constant",
      "turbulent pipe",
      "overlap region",
      "mean velocity data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.6310S"
    }
  }
}