Inverse cascade of hybrid helicity in $B Ω$-MHD turbulence

Abstract

We investigate the impact of a solid-body rotation $Ω_0$ on the large-scale dynamics of an incompressible magnetohydrodynamic turbulent flow in presence of a background magnetic field $\bf B_0$ and at low Rossby number. Three-dimensional direct numerical simulations are performed in a periodic box, at unit magnetic Prandtl number and with a forcing at intermediate wavenumber $k_f=20$. When $Ω_0$ is aligned with $\bf B_0$ (i.e. $θ\equiv \widehat{\left(Ω_{0}, \bf B_0 \right)} = 0$), inverse transfer is found for the magnetic spectrum at $k 0$ and becomes weak when $θ\ge 35^o$. These properties are understood as the consequence of an inverse cascade of hybrid helicity which is an inviscid/ideal invariant of this system when $θ=0$. Hybrid helicity emerges, therefore, as a key element for understanding rotating dynamos. Implication of these findings on the origin of the alignment of the magnetic dipole with the rotation axis in planets and stars is discussed.