von Kármán–Howarth equation for magnetohydrodynamics and its consequences on third-order longitudinal structure and correlation functions

A derivation in variable dimension of the scaling laws for mixed third-order longitudinal structure and correlation functions for incompressible magnetized flows is given for arbitrary correlation between the velocity and magnetic field with full isotropy, homogeneity, and incompressibility assumed. When close to equipartition between kinetic and magnetic energy, the scaling relations involve only structure functions in a manner similar to the “$\frac{4}{5}$ law” of Kolmogorov.