Universal cascade and relaxation of strong anisotropic turbulence in fusion plasmas

Abstract

Starting from the governing equations, exact relations have been derived for three-dimensional reduced magnetohydrodynamic turbulence corresponding to the inertial range cascade of energy and cross-helicity. Justifications are provided for not attempting to recover the said exact relations as a limit of the exact relations previously derived for incompressible magnetohydrodynamic turbulence. Assuming axial symmetry, anisotropic energy spectrum has been predicted from the exact relation and is found to be consistent with the critical balance thus leading to a -5/3 perpendicular energy spectrum. In the case of a strong alignment between the velocity and the magnetic field fluctuations, the derived exact relation implies a generalized anisotropic spectrum with a -3/2 power-law dependence in the direction of alignment. Using the alternative form of the exact relations, it is shown that the flow naturally relaxes towards a state of dynamic alignment in the limit of negligible kinetic and magnetic pressure. Finally, despite having different equations of dynamics, the exact relations for energy and cross-helicity and the relaxed states of a two-dimensional MHD are found to be identical to those in reduced magnetohydrodynamic flow.