Fluctuation dynamo and turbulent induction at low magnetic Prandtl numbers

doi:10.1088/1367-2630/9/8/300 Abstract. This paper is a detailed report on a programme of direct numerical simulations of incompressible nonhelical randomly forced magnetohydrody-namic (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 versus 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 com-pared 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 simula-tions 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 ∝Rm1/2 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 Rm-independent value comparable to the turnover rate of the outer-scale motions. The magnetic-energy spectrum in the low-Pm regime is qualitatively different from the Pm 1 case 6 Author to whom any correspondence should be addressed.