Scaling laws and diffuse locality of balanced and imbalanced MHD turbulence

The search of ways to generalize the theory of strong MHD turbulence for the case of non-zero cross-helicity (or energy imbalance) has attracted considerable interest recently. In our earlier publications we performed three-dimensional numerical simulations and showed that some of existing models are inconsistent with numerics. In this paper we focused our attention on low-imbalance limit and performed new high-resolution simulations. The results strongly suggest that in the limit of small imbalances we smoothly transition to a standard Goldreich-Sridhar (1995) balanced model. We also claim that Perez-Boldyrev (2009) model that predicts the same nonlinear timescale for both components due to so-called "dynamic alignment" strongly contradicts numerical evidence.