A unified large/small-scale dynamo in helical turbulence

Abstract

We use high resolution direct numerical simulations (DNS) to show that helical turbulence can generate significant large-scale fields even in the presence of strong small-scale dynamo action. During the kinematic stage, the unified large/small-scale dynamo grows fields with a shape-invariant eigenfunction, with most power peaked at small scales or large $k$, as in \citet{SB14}. Nevertheless, the large-scale field can be clearly detected as an excess power at small $k$ in the negatively polarized component of the energy spectrum for a forcing with positively polarized waves. Its strength $bar{B}$, relative to the total rms field $B_{rms}$, decreases with increasing magnetic Reynolds number, $R_m$. However, as the Lorentz force becomes important, the field generated by the unified dynamo orders itself by saturating on successively larger scales. The magnetic integral scale for the positively polarized waves, characterizing the small-scale field, increases significantly from the kinematic stage to saturation. This implies that the small-scale field becomes as coherent as possible for a given forcing scale, which averts the $R_m$-dependent quenching of $\bar{B}/B_rms$. These results are obtained for $1024^3$ DNS with magnetic Prandtl numbers of $P_m=0.1$ and $10$. For $P_m=0.1$, $\bar{B}/B_{rms}$ grows from about $0.04$ to about $0.4$ at saturation, aided in the final stages by helicity dissipation. For $P_m=10$, $\bar{B}/B_{rms}$ grows from much less than 0.01 to values of the order the $0.2$. Our results confirm that there is a unified large/small-scale dynamo in helical turbulence.