{
  "id": "2008.05018",
  "version": "v1",
  "published": "2020-08-11T22:19:32.000Z",
  "updated": "2020-08-11T22:19:32.000Z",
  "title": "Effect of spatial dimension in a model of fluid turbulence",
  "authors": [
    "Daniel Clark",
    "Richard Ho",
    "Arjun Berera"
  ],
  "comment": "15 pages, 8 figures",
  "categories": [
    "physics.flu-dyn"
  ],
  "abstract": "A numerical study of the $d$-dimensional Eddy Damped Quasi-Normal Markovian equations is performed to investigate the dependence on spatial dimension of homogeneous isotropic fluid turbulence. Relationships between structure functions and energy and transfer spectra are derived for the $d$-dimensional case. Additionally, an equation for the $d$-dimensional enstrophy analogue is derived and related to the velocity derivative skewness. Comparisons are made to recent four dimensional direct numerical simulation results. Measured energy spectra show a magnified bottleneck effect which grows with dimension whilst transfer spectra show a varying peak in the non-linear energy transfer as the dimension is increased. These results are consistent with an increased forward energy transfer at higher dimensions, further evidenced by measurements of a larger asymptotic dissipation rate with growing dimension. The enstrophy production term, related to the velocity derivative skewness, is seen to reach a maximum at around five dimensions and may reach zero in the limit of infinite dimensions, raising interesting questions about the nature of turbulence in this limit.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-11T22:19:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fluid turbulence",
      "spatial dimension",
      "direct numerical simulation results",
      "eddy damped quasi-normal markovian",
      "damped quasi-normal markovian equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}