A WKB method was recently used to extend rapid distortion theory (RDT) to initially inhomogeneous turbulence strained by irrotational mean flows [S.V. Nazarenko, N. Kevlahan, B. Dubrulle, J. Fluid Mech. 390 (1999) 325]. This theory takes into account the feedback of turbulence on the mean flow, and it was used by Nazarenko et al. to explain the effect of strain reduction caused by turbulence ob...

Direct numerical simulation of uniform shear flow is used to study the anisotropy of fluctuating motion in a stably stratified medium with uniform mean shear. Turbulence is found to be three dimensional over a wjde range of gradient Richardson numbers in the two Bows investigated here: vertical mean shear ($$-) and horizontal mean shear (g). The role of the turbulent F’roude number in establish...

The transition from weak to strong turbulence when passing from large to small scales in magnetohydrodynamic (MHD) turbulence with guide field is a cornerstone of anisotropic turbulence theory. We present the first check of this transition, using the Shell-RMHD, which combines a shell model of perpendicular nonlinear coupling and linear propagation along the guide field. This model allows us to...

Theoretical approaches to low-frequency magnetized turbulence in collisionless and weakly collisional astrophysical plasmas are reviewed. The proper starting point for an analytical description of these plasmas is kinetic theory, not fluid equations. The anisotropy of the turbulence is used to systematically derive a series of reduced analytical models. Above the ion gyroscale, it is shown rigo...

Recent advances in understanding of the basic properties of compressible Magnetohydrodynamic (MHD) turbulence call for revisions of some of the generally accepted concepts. First, MHD turbulence is not so messy as it is usually believed. In fact, the notion of strong non-linear coupling of compressible and incompressible motions is not tenable. Alfven, slow and fast modes of MHD turbulence foll...