Third-order Elsasser moments in axisymmetric MHD turbulence

Incompressible MHD turbulence is investigated under the presence of a uniform magnetic field B(0). Such a situation is described in the correlation space by a divergence relation which expresses the statistical conservation of the Elsasser energy flux through the inertial range. The ansatz is made that the development of anisotropy, observed when B(0) is strong enough, implies a foliation of space correlation. A direct consequence is the possibility to derive a vectorial law for third-order Elsasser moments which is parametrized by the intensity of anisotropy. We use the so-called critical balance assumption to fix this parameter and find a unique expression. (c) 2010 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.