High-Resolution Simulations of Nonhelical MHD Turbulence

Abstract

According to the kinematic theory of nonhelical dynamo action, the magnetic energy spectrum increases with wavenumber and peaks at the resistive cutoff wavenumber. It has previously been argued that even in the dynamical case, the magnetic energy peaks at the resistive scale. Using high resolution simulations (up to 1024³ meshpoints) with no large-scale imposed field, we show that the magnetic energy peaks at a wavenumber that is independent of the magnetic Reynolds number and about five times larger than the forcing wavenumber. Throughout the inertial range, the spectral magnetic energy exceeds the kinetic energy by a factor of two to three. Both spectra are approximately parallel. The total energy spectrum seems to be close to k ^−3/2, but there is a strong bottleneck effect and we suggest that the asymptotic spectrum is instead k ^−5/3. This is supported by the value of the second-order structure function exponent that is found to be ζ₂ = 0.70, suggesting a k ^−1.70 spectrum. The third-order structure function scaling exponent is very close to unity,—in agreement with Goldreich–Sridhar theory.

Adding an imposed field tends to suppress the small-scale magnetic field. We find that at large scales the magnetic energy spectrum then follows a k ⁻¹ slope. When the strength of the imposed field is of the same order as the dynamo generated field, we find almost equipartition between the magnetic and kinetic energy spectra.