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 delta v(perpendicular to). and delta b(perpendicular to) 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 sigma(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(-), is an element of(+)/is an element of(-), 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 sigma(c) = 0, is an element of(+) = is an element of(-), and p = q and extends the theory of Perez and Boldyrev when sigma(c) not equal 0. The theory is also an anisotropic generalization of the theory of Dobrowolny, Mangeney, and Veltri.