{
  "id": "1505.07984",
  "version": "v1",
  "published": "2015-05-29T10:33:47.000Z",
  "updated": "2015-05-29T10:33:47.000Z",
  "title": "Turbulence on a Fractal Fourier set",
  "authors": [
    "Alessandra Sabina Lanotte",
    "Roberto Benzi",
    "Luca Biferale",
    "Shiva Kumar Malapaka",
    "Federico Toschi"
  ],
  "categories": [
    "physics.flu-dyn",
    "nlin.CD"
  ],
  "abstract": "The dynamical effects of mode reduction in Fourier space for three dimensional turbulent flows is studied. We present fully resolved numerical simulations of the Navier-Stokes equations with Fourier modes constrained to live on a fractal set of dimension D. The robustness of the energy cascade and vortex stretching mechanisms are tested at changing D, from the standard three dimensional case to a strongly decimated case for D = 2.5, where only about $3\\%$ of the Fourier modes interact. While the direct energy cascade persist, deviations from the Kolmogorov scaling are observed in the kinetic energy spectra. A model in terms of a correction with a linear dependency on the co-dimension of the fractal set, $E(k)\\sim k^{- 5/3 + 3 -D }$, explains the results. At small scales, the intermittent behaviour due to the vorticity production is strongly modified by the fractal decimation, leading to an almost Gaussian statistics already at D ~ 2.98. These effects are connected to a genuine modification in the triad-to-triad nonlinear energy transfer mechanism.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-29T10:33:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fractal fourier set",
      "triad-to-triad nonlinear energy transfer mechanism",
      "direct energy cascade persist",
      "turbulence",
      "fractal set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}