Kinetic, Magnetic and Cross-helicity Contributions to the Turbulent Cascade in the Solar Wind

In classic Kolmogorov theory of inertial-range turbulence, the third moment of velocity fluctuations at spatial lag L, is proportional to L times the rate of energy input at large scales (= epsilon = dissipation rate). Furthermore, the turbulent power is proportional to the 2/3 power of epsilon. In the MHD solar wind, energy and energy cascade involve both velocity and magnetic fluctuations, and the third moment related to energy dissipation has three terms: (1) the same hydrodynamic term, of correlations between velocity fluctuations and kinetic energy, (2) correlations between velocity fluctuations and magnetic energy, and (3) correlations between magnetic fluctuations and cross-helicity. We used ACE MAG/SWEPAM merged data set for the last decade, to separately determine these three third moments at lags from 64 seconds to 2 hours to see how each term varies with L, and contributes to the energy cascade, and how they add up. Moments were calculated for 12-hour intervals. Mean values and error bars were calculated for intervals in 12 types of solar wind sorted by their turbulent energy level and their bulk cross-helicity, or “imbalance”. With calculated accuracy, we report that when the cross-helicity is small, 1. Energy dissipation rate is proportional to turbulent power^3/2, as Kolmogorov theory predicts 2. The magnetic energy term is approximately equal to the kinetic energy (hydrodynamic) term; however 3. The cross-helicity term nearly cancels the magnetic energy term, so that the energy third moment is only slightly larger than the hydrodynamic term alone. When the cross-helicity is large, 1. All three Energy third moments are dramatically suppressed. 2. Energy dissipation rate deduced from third moment scaling is small or possibly negative, and does NOT agree with Kolmogorov, implying that 3. Most of the energy in fluctuating fields is NOT part of a direct inertial cascade.