Separate Exact Laws of Kinetic and Magnetic Energy Cascade in Magnetohydrodynamic Turbulence

Separate exact scaling laws are derived for the cascades of the kinetic and magnetic energy in incompressible homogeneous isotropic magnetohydrodynamic (MHD) turbulence, and validated by numerical simulations. The third-order moments exhibit linear scaling with respect to the spatial displacement scale in both the subviscous region and in the inertial range, and are proportional to the rate of conversion of kinetic energy to magnetic energy in the subviscous region, but to the energy injection rates in the inertial range, highlighting the impact of forcing mechanisms on energy transfer within MHD turbulence. Further analysis demonstrates that the Politano and Pouquet [Phys. Rev. E 57, R21 (1998).PLEEE81063-651X10.1103/PhysRevE.57.R21] 4/5 law emerges as a specific case of our exact laws, when the antisymmetric flux term, closely associated with the nonlocal nature of energy transfer in MHD turbulence, is neglected, which is only valid in the absence of magnetic energy injection. These laws are of fundamental importance in MHD turbulence theory, and offer substantial potential to enhance the predictive capability to estimate the dissipation rates of the solar wind.