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Fluctuation dynamo and turbulent induction at low magnetic Prandtl numbers, New J. Phys. 9, 300 (2007) D.S. Shapovalov, E.T. Vishniac, Simulations of Turbulent Dynamos Driven by the Magnetic Helicity Flux, Astrophys

By A A Schekochihin, A B Iskakov, S C Cowley, J C Mcwilliams, M R E Proctor and T A Yousef


Abstract. This paper is a detailed report on a programme of direct numerical simulations of incompressible nonhelical randomly forced MHD turbulence that are used to settle a long-standing issue in the turbulent 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 for dynamo vs. the hydrodynamic Reynolds number Re is obtained for 1 � Re � 6700. In the limit Pm ≪ 1, Rmc is at most three times larger than for the previously well established dynamo at large and moderate Prandtl numbers: Rmc � 200 for Re � 6000 compared to Rmc ∼ 60 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 of the magnetic energy 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 at the resistive scale, or tends to an Rmindependent value comparable to the turnover rate of the outer-scale motions. Th

Year: 2011
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