Inverse cascade of magnetic helicity in magnetohydrodynamic turbulence

Abstract

The nonlinear dynamics of magnetic helicity HM, which is responsible for large-scale magnetic structure formation in electrically conducting turbulent media, is investigated in forced and decaying three-dimensional magnetohydrodynamic turbulence. This is done with the help of high-resolution direct numerical simulations and statistical closure theory. The numerically observed spectral scaling of HM is at variance with earlier work using a statistical closure model [Pouquet et al., J. Fluid Mech. 77, 321 (1976)]. By revisiting this theory, a universal dynamical balance relation is found that includes the effects of kinetic helicity as well as kinetic and magnetic energies on the inverse cascade of HM and explains the above-mentioned discrepancy. Consideration of the result in the context of mean-field dynamo theory suggests a nonlinear modification of the α-dynamo effect, which is important in the context of magnetic-field excitation in turbulent plasmas.