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 B0. It is found that in steady state the power spectra of the magnetic field and total energy are steeper than k−5/3 ⊥ and become increasingly steep as C/E increases, where C = Z d3x v ·B is the cross helicity, E is the fluctuation energy, and k⊥ is the wavevector component perpendicular to B0. 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. Subject headings: turbulence — magnetic fields — magnetohydrodynamics — solar wind — solar corona — solar flares