Strong Anisotropic MHD Turbulence with Cross Helicity

This paper proposes a new phenomenology for strong incompressible MHD turbulence with nonzero cross helicity. This phenomenology is then developed into a quantitative Fokker-Planck model that describes the time evolution of the anisotropic power spectra of the fluctuations propagating parallel and anti-parallel to the background magnetic field. It is found that in steady state the power spectra of the magnetic field and total energy are steeper than a Kolmogorov spectrum and become increasingly steep as C/E increases, where C is the cross helicity and E is the fluctuation energy. Increasing C with fixed E increases the time required for energy to cascade to smaller scales, reduces the cascade power, and increases the anisotropy of the small-scale fluctuations. The implications of these results for the solar wind and solar corona are discussed in some detail.