On the turbulent energy cascade in anisotropic magnetohydrodynamic turbulence

The problem of the occurrence of an energy cascade for Alfvenic turbulence in solar wind plasmas was historically addressed by using phenomenological arguments based to the sweeping of Alfvenic fluctuations by the large-scale magnetic field and the anisotropy of the cascade in wave vectors space. Here, this paradox is reviewed through the formal derivation of a Yaglom relation from the anisotropic magnetohydrodynamic equation. The Yaglom relation involves a third-order moment calculated from velocity and magnetic fields and involving both Elsasser vector fields, and is particularly useful to be used as far as spacecraft obervations of turbulence are concerned. Copyright (c) EPLA, 2009