Large and small scale random forcing concept in MHD turbulence

Abstract
Renormalization group approach together with the double-expansion form 2D theory is used to study the properties of MHD turbulence. It has turned out that the turbulence energy forcing into system from region of limit small wave-numbers is not sufficient for stationary energy spectrum in 2D case. The energy forcing from large wave-number region is also necessary. Continuation from 2D up to 3D space displays that this property remains valid in 3D MHD turbulence. Moreover, the used method show another discrepancy with 3D renormalization group (RNG) approach. In contact to the 3D cases, when RNG theory established two stable non-trivial fixed points corresponding to two universal regimes with their specific kinetic and magnetic energy transfer, in presented approach there arises amount of fixed points. Nevertheless, only one of them becomes stable in which the inverse Prandtl number is equal to 1.562. Therefore, the stable magnetic regime in analogy with that found in 3D case does not exist. Refs. 12.