Inverse cascades in helically magnetized turbulence

P. Frick¹ - R. Stepanov^{1, 2} - I. Mizeva¹

¹ Institute of Continuous Media Mechanics, 1 Korolyov str., Perm 614013, Russia
² Perm State National Research Polytechnical University, 29 Komsomolskii ave., Perm 614990, Russia

Abstract
Magnetic helicity is one of three integrals of motion in ideal magnetohydrodynamics of incompressible fluids and can essentially affect spectral transfer in fully developed MHD turbulence. We study the magnetic energy and magnetic helicity cascades provided by the injection of magnetic helicity at different scales, paying attention to the infrared (relative to the scale of forcing) part of the spectrum. A shell model was used for simulations of MHD turbulence in an extended range of scales, which includes two decades of the inertial range and at least two decades of the infrared range. In small scales, the common Kolmogorov turbulence with a direct spectral energy flux is established. In the infrared part of the spectrum, the inverse cascade of magnetic helicity and magnetic energy provides an inertial range with a power law E(k) ∼ k^α−1 with −0.1 < α < 0 depending on the magnetic helicity injection rate. Magnetic helicity and associated magnetic energy are accumulated at largest available scale. This scenario does not change if the magnetic helicity forcing is shifted to smaller scales. Our results demonstrate that a large-scale dynamo can be affected by magnetic helicity generated at small scales. Particularly, the magnetic helicity cascade is followed by the growth of kinetic helicity. Figs 6, Refs 15.