Comparison between turbulent helical dynamo simulations and a non-linear three-scale theory

Progress towards understanding principles of non-linear growth and saturation of large-scale magnetic fields has emerged from comparison of theoretical models that incorporate the evolution of magnetic helicity with numerical simulations for problems that are more idealized than expected in astrophysical circumstances, but still fully non-linear. We carry out a new comparison of this sort for the magnetic field growth from forced isotropic helical turbulence in a periodic box. Previous comparisons between analytic theory and simulations of this problem have shown that a two-scale model compares well with the simulations in agreeing that the driver of large-scale field growth is the difference between kinetic and current helicities associated with the small-scale field, and that the backreaction slows the growth of the large-scale field as the small-scale current helicity grows. However, the two-scale model artificially restricts the small-scale current helicity to reside at the same scale as the driving kinetic helicity. In addition, previous comparisons have focused on the late-time saturation regime and less on the early-time growth regime. Here, we address these issues by comparing a three-scale model to new simulations for both early- and late-time growth regimes. We find that the minimalist extension to three scales provides a better model for the field evolution than the two-scale model because the simulations show that the small-scale current helicity does not reside at the same scale as that of the driving kinetic helicity. The simulations also show that the peak of the small-scale current helicity migrates towards lower wavenumbers as the growth evolves from the fast to saturated growth regimes.