The phenomenon of energy cascade in Alfvénic solar wind turbulence is a central topic in space plasma physics, as it governs how energy injected at large scales is transferred toward smaller scales where dissipation occurs. Traditionally, theoretical studies have assumed ideal plasma conditions, in which viscosity (ν) and resistivity (η) are taken to be equal and very small. Under this assumption, the dissipative processes affecting velocity and magnetic fields are treated symmetrically. However, recent observations of the solar wind suggest that viscous-like effects associated with velocity fluctuations may act over larger spatial scales compared to magnetic dissipation. This motivates a more general approach in which the two dissipation mechanisms are treated independently, allowing for ν ≠ η.

The main objective of this study is to investigate the impact of distinct dissipation mechanisms on the energy cascade in magnetohydrodynamic (MHD) turbulence. In particular, we focus on the third-order Yaglom law, a fundamental exact relation that links third-order statistical moments of turbulent fluctuations to the mean energy transfer rate. We derive and analyze the energy budget equation for visco-resistive MHD turbulence, extending the classical formulation to the case where viscosity and resistivity differ. The Yaglom relation, rewritten in terms of Elsässer variables, shows deviations from the ideal symmetric case when ν ≠ η.

This third-order law involves mixed velocity and magnetic field increments and provides a direct and model-independent estimate of the energy cascade rate across scales. Through theoretical analysis and direct numerical simulations, we examine how unequal dissipation coefficients modify the structure of the energy transfer and the scaling properties of the third-order moment. Our results demonstrate that separating the dissipative contributions leads to measurable differences in the cascade behavior.

These findings are particularly relevant for the interpretation of in-situ observations in the solar wind and the magnetosheath, where dissipation processes may not act symmetrically on velocity and magnetic fluctuations. By accounting for distinct dissipation mechanisms, this work contributes to a more accurate understanding of turbulent energy transfer in space plasmas and provides a framework for comparing theoretical predictions with spacecraft data.

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