Theory of Incompressible Magnetohydrodynamic Turbulence With Scale-Dependent Alignment and Cross-Helicity

A phenomenological anisotropic theory of MHD turbulence with nonvanishing cross-helicity is constructed based on Boldyrev's phenomenology and probabilities p and q for fluctuations and to be positively or negatively aligned. The positively aligned fluctuations occupy a fractional volume p and the negatively aligned fluctuations occupy a fractional volume q . Guided by observations suggesting that the normalized cross-helicity σ c and the probabilities p and q are approximately scale invariant in the inertial range, a generalization of Boldyrev's theory is derived that depends on the three ratios w + / w − , + / − , and p / q . It is assumed that the cascade processes for positively and negatively aligned fluctuations are both in a state of critical balance and that the eddy geometries are scale invariant. The theory reduces to Boldyrev's original theory when σ c = 0, + = − , and p = q and extends the theory of Perez and Boldyrev when σ c ≠ 0. The theory is also an anisotropic generalization of the theory of Dobrowolny, Mangeney, and Veltri.