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
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