The Turbulent Magnetohydrodynamic Cascade: Applications of Third-Moment Theory to the Solar Wind at 1 AU

Velocity and magnetic field fluctuations in the solar wind show evidence that non-linear turbulent dynamics are present in the interplanetary medium. The cascade of energy created by these turbulent processes may provide a mechanism for in situ heating of the solar wind plasma. We perform three studies analyzing the turbulent energy cascade at 1AU using 10 years of data from the Advanced Composition Explorer spacecraft. These studies employ magnetohydrodynamic analogues to traditional hydrodynamic third-moment expressions. In the first analysis, we compute energy cascade rates and compare them to proton heating rates as inferred from the radial gradient of the solar wind proton temperature. We find good agreement between energy cascade rates and proton heating rates. There is a moderate excess of energy in the cascade (∼ 25–50%) which is consistent with previous estimates for thermal electron heating in the solar wind. In the second analysis, we apply third-moment theory to compute energy cascade rates as a function of the normalized cross-helicity. We find, in contrast to intervals of smaller cross-helicity forming the bulk of the observations, large cross-helicity intervals experience a significant back-transfer of energy from small to large scales. This occurs in such a way as to reinforce the dominance of outward-propagating fluctuations. We conclude this backtransfer process must be a short-lived, transient phenomena in order to be in keeping with solar wind observations. Finally, we extend newly developed magnetohydrodynamic third-moment expressions, which take into account the effects of large-scale velocity shear, to the solar wind. Limited success is achieved with the new formalism when applied to solar wind data. The best agreement is found for rarefaction intervals where the solar wind speed is decreasing as it passes the spacecraft. We find that cascade rates increase with increasing shear magnitude and that only a small amount of shear induced anisotropy is necessary to be consistent with proton heating rates. We conclude the shear formalism is necessary when analyzing data with a persistent shear of a single sign, but unnecessary when considering equal amounts of positive and negative shear.