{
  "id": "1106.4157",
  "version": "v1",
  "published": "2011-06-21T09:58:09.000Z",
  "updated": "2011-06-21T09:58:09.000Z",
  "title": "Low-dimensional model of turbulent Rayleigh-Benard convection in a Cartesian cell with square domain",
  "authors": [
    "Jorge Bailon-Cuba",
    "Joerg Schumacher"
  ],
  "comment": "23 pages, 18 Postscript figures, Figures 6,7,8,9,17,18 in reduced quality",
  "journal": "Phys. Fluids 23 (2011) 077101",
  "doi": "10.1063/1.3610395",
  "categories": [
    "physics.flu-dyn",
    "nlin.CD"
  ],
  "abstract": "A low-dimensional model (LDM) for turbulent Rayleigh-Benard convection in a Cartesian cell with square domain, based on the Galerkin projection of the Boussinesq equations onto a finite set of empirical eigenfunctions, is presented. The empirical eigenfunctions are obtained from a joint Proper Orthogonal Decomposition (POD) of the velocity and temperature fields using the Snapshot Method on the basis of a direct numerical simulation (DNS). The resulting LDM is a quadratic inhomogeneous system of coupled ordinary differential equations which we use to describe the long-time temporal evolution of the large-scale mode amplitudes for a Rayleigh number of 1e5 and a Prandtl number of 0.7. The truncation to a finite number of degrees of freedom, that does not exceed a number of 310 for the present, requires the additional implementation of an eddy viscosity-diffusivity to capture the missing dissipation of the small-scale modes. The magnitude of this additional dissipation mechanism is determined by requiring statistical stationarity and a total dissipation that corresponds with the original DNS data. We compare the performance of two models, a constant so-called Heisenberg viscosity--diffusivity and a mode-dependent or modal one. The latter viscosity--diffusivity model turns out to reproduce the large-scale properties of the turbulent convection qualitatively well, even for a model with only a few hundred POD modes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-06-21T09:58:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47.27.te",
      "02.60.Cb",
      "47.11.-j",
      "47.20.Bp",
      "47.27.ek",
      "47.27.tb"
    ],
    "keywords": [
      "turbulent rayleigh-benard convection",
      "cartesian cell",
      "low-dimensional model",
      "square domain",
      "joint proper orthogonal decomposition"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "Physics of Fluids",
      "year": 2011,
      "month": "Jul",
      "volume": 23,
      "number": 7,
      "pages": 7101
    },
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011PhFl...23g7101B"
    }
  }
}