Modeling of the turbulent magnetohydrodynamic residual-energy equation using a statistical theory

The difference between the kinetic and magnetic energies in a conducting fluid is investigated in the framework of magnetohydrodynamics. The deviation from equipartition is measured by the turbulent residual energy KR. With the aid of the two-scale direct-interaction approximation, a statistical analytical theory for inhomogeneous turbulence, expressions for the correlation tensors appearing in the evolution equation for the residual energy are derived. Using these results, we propose a model equation for KR evolution. Examination of the structure of this equation shows that the evolution of the scaled residual energy is related to the cross helicity (velocity-magnetic-field correlation) of turbulence coupled with the mean-field shears. An application to the solar wind shows that the scaled ∣KR∣ can be increased near the outside of the Alfvén point in the inner heliosphere whereas the almost stationary behavior of ∣KR∣ is suggested in the outer heliosphere. These results are consistent with observations of solar-wind turbulence.