Universal cascade and relaxation of strong anisotropic turbulence in plasma fluids

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, an 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 perpendicular energy spectra with −5/3 and −3/2 power-law dependence along and transverse to the alignment, respectively. Using the alternative form of the exact relations, it is shown that the flow naturally relaxes toward 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 two-dimensional magnetohydrodynamics are found to be identical to those in reduced magnetohydrodynamic flow.