Fluctuation dynamo and turbulent induction at low magnetic Prandtl numbers

This paper is a detailed report on a programme of direct numerical simulations of incompressible nonhelical randomly forced magnetohydrodynamic ( 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 numberRm >> 1 and small magnetic Prandtl number Pm << 1. The dependence of the critical Rm(c) for dynamo versus the hydrodynamic Reynolds number Re is obtained for 1 less than or similar to Re less than or similar to 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 less than or similar to 200 for Re greater than or similar to 6000 compared to Rmc similar to 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 proportional to 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 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 and appears to develop a negative spectral slope, although current resolutions are insufficient to determine its asymptotic form. At Rm is an element of ( 1, Rm(c)), the magnetic fluctuations induced via the tangling by turbulence of a weak mean field are investigated and the possibility of a k(-1) spectrum above the resistive scale is examined. At low Rm < 1, the induced fluctuations are well described by the quasistatic approximation; the k(-11/3) spectrum is confirmed for the first time in direct numerical simulations. Applications of the results on turbulent induction to understanding the nonlocal energy transfer from the dynamo-generated magnetic field to smaller-scale magnetic fluctuations are discussed. The results reported here are of fundamental importance for understanding the genesis of small-scale magnetic fields in cosmic plasmas.