{
  "id": "1601.03697",
  "version": "v1",
  "published": "2016-01-14T18:52:12.000Z",
  "updated": "2016-01-14T18:52:12.000Z",
  "title": "Intermittency in Fractal Fourier Hydrodynamics: Lessons from the Burgers Equation",
  "authors": [
    "Michele Buzzicotti",
    "Luca Biferale",
    "Uriel Frisch",
    "Samriddhi Sankar Ray"
  ],
  "comment": "9 pages, 7 figures",
  "categories": [
    "physics.flu-dyn",
    "nlin.CD"
  ],
  "abstract": "We present theoretical and numerical results for the one-dimensional stochastically forced Burgers equation decimated on a fractal Fourier set of dimension $D$. We investigate the robustness of the energy transfer mechanism and of the small-scale statistical fluctuations by changing $D$. We find that a very small percentage of mode-reduction ($D \\lesssim 1$) is enough to destroy most of the characteristics of the original non-decimated equation. In particular, we observe a suppression of intermittent fluctuations for $D <1$ and a quasi-singular transition from the fully intermittent ($D=1$) to the non-intermittent case for $D \\lesssim 1$. Our results indicate that the existence of strong localized structures (shocks) in the one-dimensional Burgers equation is the result of highly entangled correlations amongst all Fourier modes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-14T18:52:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fractal fourier hydrodynamics",
      "intermittency",
      "fractal fourier set",
      "one-dimensional burgers equation",
      "energy transfer mechanism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}