Aspects of the theory of incompressible MHD turbulence with cross-helicity and applications to the solar wind

Solar wind observations have shown that the normalized cross-helicity σ _c, the ratio of the cross-helicity spectrum to the energy spectrum, is approximately constant, independent of wavenumber, throughout the inertial range. This means that the correlation between velocity and magnetic field fluctuations is the same at every scale, that the ratio of the two Elsasser energies (w^{+/w^-)^2} is the same at every scale, and that the ratio of the energy cascade times of the two Elsasser energies τ ^{+/τ ^-} is the same at every scale. In the case when the magnetic Prandtl number is unity, it can be shown from the equations of incompressible MHD that if σ _c is a constant, then the cascade times of the two Elsasser energies are equal so that τ ^{+/τ ^-=1}. This is an important constraint for turbulence theories. Using this result, the Goldreich and Sridhar theory and the Boldyrev theory are generalized to MHD turbulence with nonvanishing cross-helicity in such a way that the scaling laws of the original two theories are unchanged. The derivation and some of the important properties of these more general theories shall be presented. Solar wind measurements in support of these theoretical models will also be discussed. For example, new solar wind measurements of the total energy spectrum (kinetic plus magnetic) show that the power-law exponent is closer to 3/2 than 5/3, consistent with simulations of 3D incompressible MHD turbulence with a strong mean magnetic field that show a 3/2 scaling. For highly Alfvenic, high cross-helicity solar wind turbulence, new measurements presented here show that the average spectral index is 1.540 ± 0.033.