Fluctuation dynamo and turbulent induction at low magnetic Prandtl numbers

Details Fluctuation dynamo and turbulent induction at low magnetic Prandtl numbers Fluctuation dynamo and turbulent induction at low magnetic Prandtl numbers

2007-04-16

arxiv.org/abs/0704.2002v1

New J. Phys. 9, 300 (2007)

Physics

Fluid Dynamics

IoP latex, 27 pages, 25 figures, 3 tables. Accepted by New J. Physics

Scientific paper

10.1088/1367-2630/9/8/300

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 11. 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

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