2007/04/16 by A. A. Schekochihin, A. B. Iskakov, S. C. Cowley +3
Physics and Astronomy · #physics.flu-dyn #astro-ph #nlin.CD #physics.plasm-ph
paper · pdf · doi:10.1088/1367-2630/9/8/300
published as New J.Phys.9:300,2007 · IoP latex, 27 pages, 25 figures, 3 tables. Accepted by New J. Physics
arxiv created 2007/04/16 · arxiv updated 2014/11/18
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 Rmc vs. the hydrodynamic Reynolds number Re is obtained for 1<Re<6700. In the limit Pm<<1, Rmc is ~3 times larger than for Pm>1. The stability curve Rmc(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 ~Rm1/2 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<Rmc, 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.