Weakly nonlinear magnetohydrodynamic wave interactions

Equations describing weakly nonlinear magnetohydrodynamic (MHD) wave interactions in one Cartesian space dimension are discussed. For wave propagation in uniform media, the wave interactions of interest consist of: (a) three-wave resonant interactions in which high frequency waves, may evolve on long space and time scales if the wave phases satisfy the resonance conditions; (b) Burgers self-wave steepening for the magnetoacoustic waves, and (c) mean wave field effects, in which a particular wave interacts with the mean wave field of the other waves. For wave propagation in non-uniform media, further linear wave mixing terms appear in the equations. The equations describe four types of resonant triads: slow-fast magnetosonic wave interaction; Alfven-entropy wave interaction; Alfven-magnetosonic wave interaction; and magnetosonic-entropy wave interaction. The formalism is restricted to coherent wave interactions. copyright 1999 American Institute of Physics