Numerical analysis of magnetic field amplification by turbulence

We apply a Fourier spectral numerical method to the study of three-dimensio nal incompressible MHD turbulence with a magnetic Prandtl number Pr greater than or equal to 1. We examine the processes by which an initially weak, l arge-scale seed magnetic field and an initially weak, small-scale, impulse- like seed magnetic field are amplified. We find that in both cases the magn etic energy spectrum grows at all scales. The growth rates at different amp lification stages are analyzed. For a large-scale seed magnetic field, the magnetic energy density grows as similar tot(2) for the first few turbulenc e eddy turnover times, followed by a dynamic growth stage, where nonlinear interactions between different scales of the turbulence contribute to an ex ponential growth rate that is largely determined by the turbulence eddy tur nover time. For a seed magnetic field that is initially set up at a small s cale in the turbulence, during the kinematic development stage, the growth rate of magnetic energy is proportional to1/tau (max), where tau (max) is t he eddy turnover time of the smallest eddies of the turbulence. The kinemat ic growth stage is followed by a dynamic growth stage, where nonlinearity p lays important role. During such dynamic growth stage, the growth rate of t otal magnetic energy is determined by both the magnetic energy amplificatio n within the turbulence inertial range and that within the turbulence dissi pation range.