The Turbulent Cascade for High Cross-helicity States at 1 au. II. Minor Energy

The application of third moments to turbulence can determine the rate of the energy cascade. This approach is most readily done for statistically homogeneous turbulence in a uniform incompressible medium. Solar wind conditions near 1 au appear to fulfill these requirements sufficiently well to demonstrate that an energy cascade is active among interplanetary fluctuations with a rate sufficient for the inferred amount of proton heating. Fluctuation and solar-wind parameter ranges have been found where average cascade rates are calculated to have negative values that correspond to back-transfer of energy implying no proton heating. Additionally, individual outward and inward pseudo-energy cascade rates are anti-correlated rather than correlated, as they are for a power spectral cascade rate prediction. These negative rates and behaviors are shown here to be organized by inward pseudo-energy, which is generally the minor component of energy, and they occur below a threshold of inward pseudo-energy per unit mass of about 800 km2 s−2 for 12 hr intervals. Inward pseudo-energy is also shown to correlate with ambient solar-wind intervals that have decreasing wind speed and so correspond to rarefactions. These results imply that the average negative cascade rates may be the outcome of effects that are significant enough in these rarefactions to require a third-moment analysis that includes the effects of a nonuniform medium, principally flow gradients.