{
  "id": "physics/9708016",
  "version": "v1",
  "published": "1997-08-13T22:27:42.000Z",
  "updated": "1997-08-13T22:27:42.000Z",
  "title": "The persistence of viscous effects in the overlap region, and the mean velocity in turbulent pipe and channel flows",
  "authors": [
    "Katepalli R. Sreenivasan",
    "Anupam Sahay"
  ],
  "comment": "15 pages, Latex, 7 eps figures, label positions will need adjustment if the text height or width is changed. To appear in `Self-Sustaining Mechanisms of Wall Turbulence', ed. R. L. Panton, Comp. Mech. Pub., 1997",
  "categories": [
    "physics.flu-dyn",
    "chao-dyn",
    "cond-mat.stat-mech",
    "nlin.CD"
  ],
  "abstract": "We argue that important elements of the dynamics of wall-bounded flows reside at the wall-normal position $y_p^+$ corresponding to the peak of the Reynolds shear stress. Specializing to pipe and channel flows, we show that the mean momentum balance in the neighborhood of $y_p^+$ is distinct in character from those in the classical inner and outer layers. We revisit empirical data to confirm that $y_p^+ = O(R^{1/2})$ and show that, in a neighborhood of order $R^{1/2}$ around $y_p^+$, only the viscous effects balance pressure-gradient terms. Here, R is the Reynolds number based on friction velocity and pipe radius (or channel half-width). This observation provides a mechanism by which viscous effects play an important role in regions traditionally thought to be inviscid or inertial; in particular, it throws doubt on the validity of the classical matching principle. Even so, it is shown that the classical semi-logarithmic behavior for the mean velocity distribution can be a useful approximation. It is argued that the recently advanced power-law profiles possess a rich underlying structure, and could be good approximations to the data over an extended region (but they too are unlikely to be exact).",
  "revisions": [
    {
      "version": "v1",
      "updated": "1997-08-13T22:27:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mean velocity",
      "channel flows",
      "overlap region",
      "turbulent pipe",
      "persistence"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1997physics...8016S"
    }
  }
}