Theory of incompressible MHD turbulence with scale-dependent alignment and cross-helicity

TL;DR

This paper develops an anisotropic theory of incompressible MHD turbulence incorporating scale-dependent alignment and cross-helicity, extending Boldyrev's model by including probabilistic alignment states and observationally motivated invariants.

Contribution

It introduces a generalized theoretical framework for MHD turbulence that accounts for nonvanishing cross-helicity and alignment probabilities, expanding upon Boldyrev's original theory.

Findings

The theory depends on ratios w+/w-, epsilon+/epsilon-, and p/q.

Reduces to Boldyrev's theory under specific conditions.

Incorporates observational evidence of constant cross-helicity and alignment probability.

Abstract

(Abridged) An anisotropic theory of MHD turbulence with nonvanishing cross-helicity is constructed based on Boldyrev's alignment hypothesis and probabilities p and q for fluctuations v and b to be positively or negatively aligned. Guided by observations suggesting that the normalized cross-helicity and the probability p are approximately constant in the inertial range, a generalization of Boldyrev's theory is derived that depends on the three ratios w+/w-, epsilon+/epsilon-, and p/q. The theory reduces to Boldyrev's original theory when w+ = w-, epsilon+ = epsilon-, and p = q.