Third-Order Law for MHD Turbulence Varying the Dissipation Mechanisms

The phenomenon of energy cascade in Alfvénic solar wind turbulence has traditionally been studied assuming ideal plasmas, where viscosity (ν) and resistivity (η) are equal and very small. However, recent observations suggest that in the solar wind, viscous-like effects related to velocity act on much larger scales compared to magnetic dissipation. The main novelty of this study lies in assuming phenomenological distinctions among dissipation mechanisms and hence assuming different values for ν and η.

In this work, we investigate the third-order Yaglom law for magnetohydrodynamic (MHD) turbulence through a combination of theoretical analysis and simulations. Specifically, we study the energy budget law for visco-resistive MHD and explore how differing viscosities and resistivities affect the energy cascade. The Yaglom relation, rewritten in terms of Elsässer variables, deviates from the ideal case due to the assumption ν ≠ η. This relation, which involves a third-order moment calculated from velocity and magnetic fields, provides a direct measure of the energy transfer rate across scales.

Our preliminary results, supported by direct numerical simulations, indicate that these findings could enhance the interpretation of solar wind and magnetosheath observations. The third-order moment is indeed particularly relevant as it enables a detailed comparison of energy transfer mechanisms, highlighting the differences that arise when the dissipation processes in the velocity and the magnetic field are different.