Numerical Analysis of Magnetic Field Amplification by Turbulence

Abstract

We apply a Fourier spectral numerical method to 3D incompressible MHD turbulence with a magnetic Prandtl number $Pr\ge 1$. We examine the processes by which an initially weak, large-scale seed magnetic field and an initially weak, small-scale, impulse-like seed magnetic field are amplified. We find that in both cases the magnetic energy spectrum grows at all scales. The growth rates at different amplification stages are analyzed. For a large-scale seed magnetic field, the magnetic energy density grows as $\sim t^2$ for the first few turbulence eddy turnover times, followed by a dynamic growth stage, where nonlinear interactions between different scales of the turbulence contribute to an exponential growth rate that is largely determined by the turbulence eddy turnover time. For a seed magnetic field that is initially set up at a small scale in the turbulence, during the kinematic development stage, the growth rate of magnetic energy is $\propto 1/{\tau }_{max}$, where ${\tau }_{max}$ is the eddy turnover time of the smallest eddies of the turbulence. The kinematic growth stage is followed by a dynamic growth stage, where nonlinearity plays important role. During such dynamic growth stage, the growth rate of total magnetic energy is determined by both the magnetic energy amplification within the turbulence inertial range and that within the turbulence dissipation range.

41 pages, 12 figures, to be published in ApJ (vol. 556)

Cited by in corpus (14)

• Simulations of small-scale turbulent dynamo
• Simulations of nonhelical hydromagnetic turbulence
• Statistical Theory of Magnetohydrodynamic Turbulence: Recent Results
• A model of nonlinear evolution and saturation of the turbulent MHD dynamo
• Spectra and Growth Rates of Fluctuating Magnetic Fields in the Kinematic Dynamo Theory with Large Magnetic Prandtl Numbers
• The small-scale structure of magnetohydrodynamic turbulence with large magnetic Prandtl numbers
• Turbulent dynamo in a conducting fluid and partially ionized gas
• Systematics of the magnetic-Prandtl-number dependence of homogeneous, isotropic magnetohydrodynamic turbulence
• Effect of Fractional Kinetic Helicity on Turbulent Magnetic Dynamo Spectra
• Energy transfers and magnetic energy growth in small-scale dynamo
• The effect of hyperdiffusivity on turbulent dynamos with helicity
• Energy transfers in dynamos with small magnetic Prandtl numbers
• Amplification of large-scale magnetic field in nonhelical magnetohydrodynamics
• Dynamo Onset as a First-Order Transition: Lessons from a Shell Model for Magnetohydrodynamics