The Turbulent Cascade at 1 AU: Energy Transfer and the Third-Order Scaling for MHD

We perform a test of MHD turbulent cascade theory in the solar wind and directly evaluate the contribution of local turbulence to heating the solar wind at 1 AU. We look at turbulent fluctuations in the solar wind velocity V and magnetic field B, using the vector Elsasser variables Z^± ≡ V ± B/(4πρ)^1/2 as measured at the ACE spacecraft stationed at the Earth's L1 point. We combine the fluctuations δZ^± over time lags in the inertial range, from 64 s to several hours, to form components of the mixed vector third moments, and we adopt the work of Politano & Pouquet, who derive an exact scaling law, similar to the Kolmogorov 4/5 law, but valid in anisotropic MHD turbulence, for these components. We demonstrate that the scaling is reasonably linear, as is expected for the inertial range. The total turbulent energy injection/dissipation rate that we derive this way agrees with the in situ heating of the solar wind that is inferred from the temperature gradient, whereas methods using the power spectra only seldom agree with the heating rates derived from gradients of the thermal proton distribution. We derive expressions of the third-order moments that are applicable to the spectral cascades parallel and perpendicular to the mean magnetic field. We apply these expressions to fast- and slow-wind subsets of the data, with additional subsetting for mean field direction. We find that both the fast wind and the slow wind exhibit an active energy cascade over the inertial range scales. Furthermore, we find that the energy flux in the parallel cascade is consistently smaller than in the perpendicular cascade.