Strong imbalanced turbulence

We consider stationary, forced, imbalanced, or cross helical MHD Alfvenic turbulence where the waves traveling in one direction have higher amplitudes than the opposite waves. This paper is dedicated to so-called strong turbulence, which cannot be treated perturbatively. Our main result is that the anisotropy of the weak waves is stronger than the anisotropy of strong waves. We propose that critical balance, which was originally conceived as a causality argument, has to be amended by what we call a propagation argument. This revised formulation of critical balance is able to handle the imbalanced case and reduces to the old formulation in the balanced case. We also provide a phenomenological model of energy cascading and discuss the possibility of self-similar solutions in a realistic setup of driven turbulence.