Third-order Els\"asser moments in axisymmetric MHD turbulence

TL;DR

This paper derives a vectorial law for third-order Els"asser moments in anisotropic incompressible MHD turbulence with a strong magnetic field, using the critical balance assumption to relate anisotropy to energy flux conservation.

Contribution

It introduces a new vectorial law for third-order Els"asser moments in anisotropic MHD turbulence, connecting anisotropy development with energy flux conservation.

Findings

Derived a vectorial law for Els"asser moments considering anisotropy.

Connected anisotropy with the energy flux through the inertial range.

Provided a unique expression based on the critical balance assumption.

Abstract

Incompressible MHD turbulence is investigated under the presence of a uniform magnetic field $\bb0$. Such a situation is described in the correlation space by a divergence relation which expresses the statistical conservation of the Els\"asser 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 Els\"asser 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.