{
  "id": "0704.2002",
  "version": "v1",
  "published": "2007-04-16T12:37:39.000Z",
  "updated": "2007-04-16T12:37:39.000Z",
  "title": "Fluctuation dynamo and turbulent induction at low magnetic Prandtl numbers",
  "authors": [
    "A. A. Schekochihin",
    "A. B. Iskakov",
    "S. C. Cowley",
    "J. C. McWilliams",
    "M. R. E. Proctor",
    "T. A. Yousef"
  ],
  "comment": "IoP latex, 27 pages, 25 figures, 3 tables. Accepted by New J. Physics",
  "journal": "New J. Phys. 9, 300 (2007)",
  "doi": "10.1088/1367-2630/9/8/300",
  "categories": [
    "physics.flu-dyn",
    "astro-ph",
    "nlin.CD",
    "physics.plasm-ph"
  ],
  "abstract": "This paper is a detailed report on a programme of simulations used to settle a long-standing issue in the dynamo theory and demonstrate that the fluctuation dynamo exists in the limit of large magnetic Reynolds number Rm>>1 and small magnetic Prandtl number Pm<<1. The dependence of the critical Rm_c vs. the hydrodynamic Reynolds number Re is obtained for 1<Re<6700. In the limit Pm<<1, Rm_c is ~3 times larger than for Pm>1. The stability curve Rm_c(Re) (and, it is argued, the nature of the dynamo) is substantially different from the case of the simulations and liquid-metal experiments with a mean flow. It is not as yet possible to determine numerically whether the growth rate is ~Rm^{1/2} in the limit Re>>Rm>>1, as should be the case if the dynamo is driven by the inertial-range motions. The magnetic-energy spectrum in the low-Pm regime is qualitatively different from the Pm>1 case and appears to develop a negative spectral slope, although current resolutions are insufficient to determine its asymptotic form. At 1<Rm<Rm_c, the magnetic fluctuations induced via the tangling by turbulence of a weak mean field are investigated and the possibility of a k^{-1} spectrum above the resistive scale is examined. At low Rm<1, the induced fluctuations are well described by the quasistatic approximation; the k^{-11/3} spectrum is confirmed for the first time in direct numerical simulations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-04-16T12:37:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "low magnetic prandtl numbers",
      "fluctuation dynamo",
      "turbulent induction",
      "small magnetic prandtl number pm",
      "large magnetic reynolds number"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "New Journal of Physics",
      "year": 2007,
      "month": "Aug",
      "volume": 9,
      "number": 8,
      "pages": 300
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 776452,
      "adsabs": "2007NJPh....9..300S"
    }
  }
}