On the turbulent energy cascade in anisotropic magnetohydrodynamic turbulence

TL;DR

This paper reviews the energy cascade process in anisotropic magnetohydrodynamic turbulence, deriving a Yaglom relation that links third-order moments of velocity and magnetic fields, aiding interpretation of spacecraft observations.

Contribution

It provides a formal derivation of a Yaglom relation for anisotropic MHD turbulence, clarifying the energy cascade in solar wind plasmas.

Findings

Derivation of a Yaglom relation from anisotropic MHD equations.

The relation involves third-order moments of Elsässer fields.

Useful for analyzing spacecraft turbulence data.

Abstract

The problem of the occurrence of an energy cascade for Alfv\'enic turbulence in solar wind plasmas was hystorically addressed by using phenomenological arguments based to the weakness of nonlinear interactions and the anisotropy of the cascade in wave vectors space. Here, this paradox is reviewed through the formal derivation of a Yaglom relation from anisotropic Magnetohydrodynamic equation. The Yaglom relation involves a third-order moment calculated from velocity and magnetic fields and involving both Els\"asser vector fields, and is particularly useful to be used as far as spacecraft observations of turbulence are concerned.