{
  "id": "1609.00743",
  "version": "v1",
  "published": "2016-09-02T20:37:26.000Z",
  "updated": "2016-09-02T20:37:26.000Z",
  "title": "Extended self-similarity in moment-generating-functions in wall-bounded turbulence at high Reynolds number",
  "authors": [
    "Xiang I. A. Yang",
    "Charles Meneveau",
    "Ivan Marusic",
    "Luca Biferale"
  ],
  "journal": "Physical Review Fluids vol 1, 044405 (2016)",
  "doi": "10.1103/PhysRevFluids.1.044405",
  "categories": [
    "physics.flu-dyn"
  ],
  "abstract": "In wall-bounded turbulence, the moment generating functions (MGFs) of the streamwise velocity fluctuations $\\left<\\exp(qu_z^+)\\right>$ develop power-law scaling as a function of the wall normal distance $z/\\delta$. Here $u$ is the streamwise velocity fluctuation, $+$ indicates normalization in wall units (averaged friction velocity), $z$ is the distance from the wall, $q$ is an independent variable and $\\delta$ is the boundary layer thickness. Previous work has shown that this power-law scaling exists in the log-region {\\small $3Re_\\tau^{0.5}\\lesssim z^+$, $z\\lesssim 0.15\\delta$}, where $Re_\\tau$ is the friction velocity-based Reynolds numbers. Here we present empirical evidence that this self-similar scaling can be extended, including bulk and viscosity-affected regions $30<z^+$, $z<\\delta$, provided the data are interpreted with the Extended-Self-Similarity (ESS), i.e. self-scaling of the MGFs as a function of one reference value, $q_o$. ESS also improves the scaling properties, leading to more precise measurements of the scaling exponents. The analysis is based on hot-wire measurements from boundary layers at $Re_\\tau$ ranging from $2700$ to $13000$ from the Melbourne High-Reynolds-Number-Turbulent-Boundary-Layer-Wind-Tunnel. Furthermore, we investigate the scalings of the filtered, large-scale velocity fluctuations $u^L_z$ and of the remaining small-scale component, $u^S_z=u_z-u^L_z$. The scaling of $u^L_z$ falls within the conventionally defined log region and depends on a scale that is proportional to {\\small $l^+\\sim Re_\\tau^{1/2}$}; the scaling of $u^{S}_z$ extends over a much wider range from $z^+\\approx 30$ to $z\\approx 0.5\\delta$. Last, we present a theoretical construction of two multiplicative processes for $u^L_z$ and $u^S_z$ that reproduce the empirical findings concerning the scalings properties as functions of $z^+$ and in the ESS sense.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-02T20:37:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "high reynolds number",
      "wall-bounded turbulence",
      "extended self-similarity",
      "streamwise velocity fluctuation",
      "moment-generating-functions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}