Comparison between the numerical and analytical results for the simulations shown in Fig. 4. Left: profile of vertical velocity along x = 0 for P-s. Right: local dispersion relation corresponding to the simulations shown in Fig. 4. The complex vertical wavenumber k_z(z) values calculated from the P-s simulation are overplotted on the dispersion diagram with the black dotted lines, up to the equipartition height, and they are clearly in perfect agreement with the upward fast wave (in green).