Top panels: temperature projection of the gas. The dashed circle indicates the sphere within which the VSF are computed, whose position is kept fixed throughout the run. The round marker at the top of the temperature projection indicates the position of the SMBH particle and the arrow shows the jet injection axis. The projection depth is 1 kpc. Middle panels: Velocity structure functions of the cold (gray curves) and hot (red curves) phases. The dashed orange lines indicate the fit of the power-law index of the hot phase VSF. Lower panel: Time evolution of the cold and hot phases power-law index. Here, t₀ refers to the restarting time of the simulation.