Theory of solar wind turbulence with scale-dependent alignment, anisotropy, and cross-helicity

A theory of incompressible MHD turbulence with nonvanishing cross-helicity is derived based on two new observations from the Wind spacecraft. The first is the observation that the normalized cross-helicity sigma(c), is approximately scale-invariant throughout the inertial range. The second is the observation that the probabilities p and q for velocity and magnetic field fluctuations to be positively or negatively aligned are also approximately scale-invariant. The theory extends the theory of Boldyrev (2006) to turbulence with nonvanishing cross-helicity assuming that the cascades of the two Elsasser energies are both in a state of critical balance.