A developed stage of Alfven wave phase mixing

Alfven wave phase mixing is an extensively studied mechanism for dissipatin g wave energy in an inhomogeneous medium. It is common in the vast majority of phase mixing papers to assume that even though short scale lengths and steep gradients develop as a result of phase mixing, nonlinear wave couplin g does not occur. However, weakly nonlinear studies have shown that phase m ixing generates magnetoacoustic modes. Numerical results are presented whic h show the nonlinear generation of magnetosonic waves by Alfven wave phase mixing. The efficiency of the effect is determined by the wave amplitude, t he frequency of the Alfven waves and the gradient in the background Alfven speed. Weakly nonlinear theory has shown that the amplitude of the fast mag netosonic wave grows linearly in time. The simulations presented in this pa per extend this result to later times and show saturation of the fast magne tosonic component at amplitudes much lower than that of the Alfven wave. Fo r the case when Alfven waves are driven at the boundary, simulating photosp heric footpoint motion, a clear modulation of the saturated amplitude is ob served. All the results in this paper are for a low amplitude (less than or equal to 0.1), single frequency Alfven wave and a uniform background magne tic field in a two dimensional domain. For this simplified geometry, and wi th a monochromatic driver, we concluded that the nonlinear generation of fa st modes has little effect on classical phase mixing.