Measurements of the normalized cross-helicity of solar wind turbulence spanning the entire inertial range

MHD turbulence which is spatially homogeneous and stationary in time is characterized in part by its three dimensional energy spectrum (Fourier spectrum) and its cross-helicity spectrum. The ratio of the cross-helicity spectrum divided by the energy spectrum is the normalized cross-helicity spectrum $\sigma_c$ which takes values between $-1$ and $+1$. Solar wind measurements of the energy spectrum, cross-helicity spectrum, and the normalized cross-helicity spectrum (reduced spectra) have been performed almost since the dawn of the space age 50 years ago. However, measurements of the cross-helicity and the normalized cross-helicity spanning the entire inertial range at 1 AU have only recently been performed for the first time using simultaneous 3-second plasma and magnetic field data from the WIND spacecraft. The new measurements extend the frequency range of previous measurements by 1.5 decades (a factor of $\sim 30$). A large study of over 100 different intervals of solar wind data shows that the normalized cross-helicity is approximately constant throughout the inertial range and, moreover, that this result holds over a wide range of solar wind conditions including both high- and low-speed wind. This result has important implications for theories of imbalanced MHD turbulence as I show in an accompanying poster.