Parameter study of decaying magnetohydrodynamic turbulence

It is well known that helical magnetohydrodynamic (MHD) turbulence exhibits an inverse transfer of magnetic energy from small to large scales, which is related to the approximate conservation of magnetic helicity. Recently, several numerical investigations noticed the existence of an inverse energy transfer also in nonhelical MHD flows. We run a set of fully resolved direct numerical simulations and perform a wide parameter study of the inverse energy transfer and the decaying laws of helical and nonhelical MHD. Our numerical results show only a small inverse transfer of energy that grows as with increasing Prandtl number (Pm). This latter feature may have interesting consequences for cosmic magnetic field evolution. Additionally, we find that the decaying laws $E \sim t^{-p}$ are independent of the scale separation and depend solely on Pm and Re. In the helical case we measure a dependence of the form $p_b \approx 0.6 + 14/Re$. We also make a comparison between our results and previous literature and discuss the possible reason for the observed disagreements