Coupling between nonlinear Alfven waves and reduced magnetohydrodynamics for compressible fluids

A reduced description of magnetohydrodynamic (MHD) turbulence in a plasma p ermeated by a strong uniform magnetic field is derived using a reductive pe rturbative expansion method. This leads to a coupled system of equations fo r the velocity and magnetic fields in the planes perpendicular to the ambie nt field, described by the usual reduced MHD equations [Zank and W. H. Matt haeus, J. Plasma Phys. 48, 85-100 (1992)] and for parallel propagating Alfv en waves, which on the characteristic time and length scale of the transver se flow, undergo cumulative nonlinear effects described by a generalized De rivative Nonlinear Schrodinger equation (DNLS). The cases beta far from uni ty and beta approximate to 1 are addressed separately. In the latter case, the nonlinear Alfven waves drive a mean longitudinal velocity whose magnitu de is comparable to that of the transverse components. A modulational analy sis for a quasi-monochromatic plane Alfven wave at beta far from unity illu strates the effect of the transverse MHD flow on the Alfven wave filamentat ion. (C) 1999 American Institute of Physics. [S1070-664X(99)03507-7].