Fig. A.2
Attached movie shows the nonlinear wave propagation by means of acoustic (left panel) and magnetic (right panel) energy flux proxies. These quantities are the same as shown in Figs. 1 and 2 and the units are given in 
. The equipartition layers (β = 1 layer) are indicated with black dashed lines, while the transition region is shown with a red solid line.
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