On the derivation of the energy flux of linear magnetohydrodynamic waves

Abstract

New light is shed on the derivation of the energy flux of the linear MHD waves. It is shown that, according to a suggestion of Lighthill, the usual perturbation procedure, which starts from the general expression for the energy flux, need not be supplemented by an averaging procedure. As a result, it is shown that to second order in the wave amplitude, a quantity identifiable as the wave energy flux is conserved. Some of the subtleties inherent in the derivation of the pertubation energy equation are discussed.