Scale invariance of normalized cross-helicity throughout the inertial range of solar wind turbulence

Solar wind measurements over the period from 1995 through 2006 are used to study fluctuations in the plasma bulk velocity and magnetic field over the range of magnetohydrodynamic (MHD) scales commonly referred to as the inertial range. Power spectra of the solar wind velocity, magnetic field, proton density, total energy (kinetic plus magnetic), and cross-helicity are analyzed for 176 time intervals in which the interplanetary magnetic field is restricted to a single magnetic sector. The data yield measurements of the normalized cross-helicity σ_c, the ratio of the cross-helicity spectrum to the energy spectrum, that span the entire inertial range at 1 AU and extend previous measurements by more than one decade in wavenumber. The results show that σ_c is approximately constant throughout the inertial range, independent of wavenumber, consistent with existing theoretical ideas. At the highest frequencies measured, |σ_c| is observed to decrease toward zero, however, this decrease is caused by measurement noise and is not a real physical effect. Other new results obtained in this study are (1) the average spectral index for the total energy—kinetic plus magnetic—is found to be closer to 3/2 than 5/3 with an average value 1.540±0.033 for highly Alfvénic wind, in agreement with simulations of incompressible MHD turbulence with a strong ambient magnetic field; (2) the spectral index for the total energy is a function of |σ_c| that varies from roughly 5/3 when σ_c≈0 to approximately 3/2 when |σ_c|≈1; (3) the spectral index for the total energy exhibits a solar cycle dependence during solar cycle 23 with above average values (steeper spectra) in the early rising phase of the cycle and below average values (shallower spectra) during the declining phase of the cycle—the controlling parameter for this solar cycle dependence appears to be |σ_c|.