Understanding Nonlinear Cascades in Magnetohydrodynamic Turbulence by Statistical Closure Theory

It is shown that supposedly universal scaling relations between second-order statistical moments of magnetohydrodynamic turbulence can be found with the help of the eddy-damped quasi-normal statistical closure theory (EDQNM). As an example, the inertial range scaling behaviour of the spectrum of magnetic helicity in direct numerical simulations of three-dimensional mapletohydrodynamic turbulence driven at small scales is theoretically studied. Using hypothesis of dynamical equilibrium the inertial range spectrum is found to depend on various quantities: kinetic and magnetic energy as well as kinetic helicity. The influence of kinetic helicity explains numerical results that are in apparent contradiction to previous theoretical and numerical work. A similar approach towards the residual energy spectrum in magnetohydrodynamic turbulence is also touched upon.