Horizontal averaged quantities as a function of height. We show temperature T (panel a), density ρ (panel b), and the vertical component of the Poynting flux S_z (panel c). The colors represent the different runs as indicated in the legend (cf. Table 1). The quantities are averaged horizontally for each snapshot and then in time for 1 h (between the time-point at 3.5 and that at 4.5 h, as indicatedin Fig. 4 by the vertical dashed lines. For the Poynting flux we omitted the first three grid points that show boundary effects. See Sect. 4.3.