Dissipation of non-linear circularly polarized Alfven waves

We study propagating Alfven waves by solving the time-dependent equations of magnetohydrodynamics (MHD) in one dimension numerically. In a homogeneous medium the circularly polarized Alfven wave is an exact solution of the ideal MHD equations, and therefore it does not suffer from any dissipation. A high-amplitude linearly polarized Alfven wave, on the other hand, steepens and form current sheets, in which the Poynting flux is lost. In a stratified medium, however, a high-amplitude circularly polarized Alfven wave can also lose a significant fraction of its Poynting flux.