{
  "id": "1810.04659",
  "version": "v1",
  "published": "2018-10-10T17:41:46.000Z",
  "updated": "2018-10-10T17:41:46.000Z",
  "title": "3D simulations and MLT: II. RA-ILES results",
  "authors": [
    "W. David Arnett",
    "Casey Meakin",
    "Raphael Hirschi",
    "Andrea Cristini",
    "Cyril Georgy",
    "Simon Campbell",
    "Laura J. A. Scott",
    "Etienne A. Kaiser"
  ],
  "categories": [
    "astro-ph.SR"
  ],
  "abstract": "In a previous paper (Arnett, et al., 2019) we introduced the use of Reynolds averaged implicit large eddy simulations (Moc\\'ak, et al., 2019) to the classical problem of stellar convection (B\\\"ohm-Vitense, 1958; mixing length theory, MLT). We explored the structure of turbulent boundary layers, multi-modal behavior, intermittency, fluctuations, and composition gradients, and found that the Kolmogorov dissipation length played a role in some respects akin to the B\\\"ohm-Vitense mixing length. We now extend our analysis by extracting the sub-grid dissipation of our method (the \"mixing length\"), and by quantifying errors in resolution of boundary layers. The results for weakly-stratified convection show quantitative agreement with the four-fifths law of Kolmogorov. We examine the differences between weakly and strongly stratified convection (i.e., core convection and surface convection zones, respectively). We find that MLT is a weak-stratification theory (which ignores turbulent kinetic energy), and for precise work should be modified for strong-stratification cases like the solar and stellar atmospheres. We derive the `effective mixing length' for strong-stratification; it is the density scale height, so $\\alpha \\approx \\Gamma \\sim 5/3$, in surprising agreement with many stellar evolution calibrations, but smaller than the preferred values for the Standard Solar Model (SSM), an error we attribute in part to the lack of a turbulent boundary layer, which we find at the bottom of the convection zone but missing in MLT and SSM.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-10T17:41:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ra-iles results",
      "3d simulations",
      "mixing length",
      "turbulent boundary layer",
      "averaged implicit large eddy simulations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}