Numerical Demonstration of Fluctuation Dynamo at Low Magnetic Prandtl Numbers

Direct numerical simulations of incompressible nonhelical randomly forced MHD turbulence are used to demonstrate for the first time that the fluctuation dynamo exists in the limit of large magnetic Reynolds number Rm1 and small magnetic Prandtl number Pm1. The dependence of the critical Rmc for dynamo on the hydrodynamic Reynolds number Re is obtained for 1Re6700. In the limit Pm1, Rmc is about 3 times larger than for the previously well-established dynamo at large and moderate Prandtl numbers: Rmc200 for Re6000 compared to Rmc~60 for Pm≥1. It is not yet possible to determine numerically whether the growth rate of the magnetic energy is ∝Rm1/2 in the limit Rm→∞, as it should be if the dynamo is driven by the inertial-range motions at the resistive scale.