Strong Imbalanced Turbulence

We consider stationary, forced, imbalanced, or cross-helical MHD Alfvénic 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 a 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 old formulation in the balanced case. We also provide phenomenological model of energy cascading and discuss possibility of self-similar solutions in a realistic setup of driven turbulence. Subject headings: MHD – turbulence – ISM: kinematics and dynamics 1. INTRODUCTION MHD turbulence appears in the dynamics of conductive fluid in a generalized settings with large Reynolds numbers, or low physical dissipation. It is ubiquitous in the interstellar and intracluster medium, Earth magne-tosphere, solar wind, accretion disks, etc. In fact, it is laminar flows that constitute exception in astrophysics, while, generically, astrophysical fluids are turbulent. The study of MHD turbulence has been an old challenge. First attempts to address it were classical papers by Iroshnikov (1963) and Kraichnan (1965) (henceforth IK model). A good account for the state of the field could be found in Biskamp (2003). Usually turbulence is subdivided into weak and strong, depending on the strength of non-linear interaction. While weak MHD turbulence allows analytical perturbative treatment (Ng & Bhat-tacharjee 1996, Galtier et al 2002, Chandran 2005), the progress in understanding strong turbulence came primarily from phenomenological and closure models which were tested by numerical simulations. Important theoretical works on strong MHD tur-Those clarified the anisotropic nature of the energy cascade and paved the way for further advancement in the field. The study by Goldreich & Sridhar (1995, henceforth GS95) identified the balance between perturbations parallel and perpendicular to the local direction of magnetic field, i.e. " critical balance " , as the key component of dynamics in strong magnetic turbulence. Although it dealt with incompressible MHD turbulence, GS95 also influenced further studies of compressible turbulence (e.g. Lithwick & Goldreich 2003). In particular, it identified the dominant role of Alfvénic perturbations for cascading of slow modes, which later confirmed with numerical simulations in both weakly and strongly com-pressive media (Cho & Lazarian …