{
  "id": "1205.5907",
  "version": "v1",
  "published": "2012-05-26T18:35:36.000Z",
  "updated": "2012-05-26T18:35:36.000Z",
  "title": "Heat transport by turbulent Rayleigh-Bénard convection for $\\Pra\\ \\simeq 0.8$ and $4\\times 10^{11} \\alt \\Ra\\ \\alt 2\\times10^{14}$: Ultimate-state transition for aspect ratio $Γ= 1.00$",
  "authors": [
    "Xiaozhou He",
    "Denis Funfschilling",
    "Eberhard Bodenschatz",
    "Guenter Ahlers"
  ],
  "comment": "17 pages, including 2 pages of data tables and 56 references. Submitted to New J. Phys",
  "categories": [
    "physics.flu-dyn",
    "nlin.CD"
  ],
  "abstract": "We report experimental results for heat-transport measurements by turbulent Rayleigh-B\\'enard convection in a cylindrical sample of aspect ratio $\\Gamma \\equiv D/L = 1.00$ ($D = 1.12$ m is the diameter and $L = 1.12$ m the height). They are for the Rayleigh-number range $4\\times10^{11} \\alt \\Ra \\alt 2\\times10^{14}$ and for Prandtl numbers \\Pra\\ between 0.79 and 0.86. For $\\Ra < \\Ra^*_1 \\simeq 2\\times 10^{13}$ we find $\\Nu = N_0 \\Ra^{\\gamma_{eff}}$ with $\\gamma_{eff} = 0.321 \\pm 0.002$ and $N_0 = 0.0776$, consistent with classical turbulent Rayleigh-B\\'enard convection in a system with laminar boundary layers below the top and above the bottom plate and with the prediction of Grossmann and Lohse. For $\\Ra > \\Ra_1^*$ the data rise above the classical-state power-law and show greater scatter. In analogy to similar behavior observed for $\\Gamma = 0.50$, we interpret this observation as the onset of the transition to the ultimate state. Within our resolution this onset occurs at nearly the same value of $\\Ra_1^*$ as it does for $\\Gamma = 0.50$. This differs from an earlier estimate by Roche {\\it et al.} which yielded a transition at $\\Ra_U \\simeq 1.3\\times 10^{11} \\Gamma^{-2.5\\pm 0.5}$. A $\\Gamma$-independent $\\Ra^*_1$ would suggest that the boundary-layer shear transition is induced by fluctuations on a scale less than the sample dimensions rather than by a global $\\Gamma$-dependent flow mode. Within the resolution of the measurements the heat transport above $\\Ra_1^*$ is equal for the two $\\Gamma$ values, suggesting a universal aspect of the ultimate-state transition and properties. The enhanced scatter of \\Nu\\ in the transition region, which exceeds the experimental resolution, indicates an intrinsic irreproducibility of the state of the system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-26T18:35:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "turbulent rayleigh-bénard convection",
      "ultimate-state transition",
      "heat transport",
      "aspect ratio",
      "classical turbulent rayleigh-benard convection"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/1367-2630/14/6/063030",
      "journal": "New Journal of Physics",
      "year": 2012,
      "month": "Jun",
      "volume": 14,
      "number": 6,
      "pages": "063030"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012NJPh...14f3030H"
    }
  }
}