{
  "id": "1312.3459",
  "version": "v2",
  "published": "2013-12-12T12:07:46.000Z",
  "updated": "2014-12-13T12:30:16.000Z",
  "title": "Three-dimensional Iroshnikov-Kraichnan turbulence in a mean magnetic field",
  "authors": [
    "Roland Grappin",
    "Wolf-Christian Müller",
    "Andrea Verdini",
    "Özgür Gürcan"
  ],
  "comment": "Major re-write of manuscript",
  "categories": [
    "astro-ph.SR",
    "physics.plasm-ph"
  ],
  "abstract": "Forced, weak MHD turbulence with guide field is shown to adopt different regimes, depending on the magnetic excess of the large forced scales. When the magnetic excess is large enough, the classical perpendicular cascade with $5/3$ scaling is obtained, while when equipartition is imposed, an isotropic $3/2$ scaling appears in all directions with respect to the mean field (\\cite{2010PhRvE..82b6406G} or GM10). We show here that the $3/2$ scaling of the GM10 regime is not ruled by a small-scale cross-helicity cascade, and propose that it is a 3D extension of a perpendicular weak Iroshnikov-Kraichnan (IK) cascade. We analyze in detail the structure functions in real space and show that they closely follow the critical balance relation both in the local frame and the global frame: we show that there is no contradiction between this and the isotropic $3/2$ scaling of the spectra. We propose a scenario explaining the spectral structure of the GM10 regime, that starts with a perpendicular weak IK cascade and extends to 3D by using quasi-resonant couplings. The quasi-resonance condition happens to reduce the energy flux in the same way as is done in the weak perpendicular cascade, so leading to a $3/2$ scaling in all directions. We discuss the possible applications of these findings to solar wind turbulence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-12T12:07:46.000Z",
      "abstract": "As shown by M\\\"uller et al. (2003), the 1D energy spectra deduced from structure functions in simulations of MHD turbulence with mean field $B_0$ show varying scalings, passing from $k_\\bot^{-5/3}$ to $k_\\bot^{-3/2}$ when $B_0$ increases, while the parallel scaling remains $k_\\|^{-2}$. To explain this, Boldyrev (2005, 2006) proposed, as an alternative to the Iroshnikov-Kraichnan (IK) scenario which predicts an isotropic $k^{-3/2}$ scaling, a scenario with a strong perpendicular $k_\\bot^{-3/2}$ cascade constrained by small-scale dynamic alignment, and critical balance controlling the parallel extent of the spectrum (Goldreich and Sridhar, 1995). Since then however, a more complete analysis of the 3D energy spectra by Grappin and M\\\"uller (2010) showed that the spectral anisotropy is in fact in between the two predictions, with a scaling as $k^{-3/2}$ independent of the direction with respect to the mean field. We reanalyze the data and show that the isotropic scaling is not a consequence of measuring the energy spectrum in a frame of reference defined by the global mean field $B_0$. The structure function scalings actually yield the same results, whether measured in the local or global frame, as soon as $B_0/b_{rms} \\gtrsim 5$. We then show that the 1D parallel scaling $k_\\|^{-2}$ is generated by the scales outside the inertial range, and thus should disappear at larger Reynolds number. To explain the scaling isotropy of the 3D spectrum, as well as the large oblique extent of the spectrum well outside the critical balance domain, we propose here a new theory, involving the ricochet process that generates oblique cascades coupled to a 2D IK perpendicular cascade. We thus conclude that the turbulent regime studied is a 3D extension of the 2D IK regime.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-12-13T12:30:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "three-dimensional iroshnikov-kraichnan turbulence",
      "mean magnetic field",
      "energy spectrum",
      "mean field",
      "2d ik perpendicular cascade"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.3459G"
    }
  }
}