tokens: in other directions form gas circulations in the meridional planes, and near the bottom of the AGN bubble, meridional vortexes also appear. At t 700Myr, one can clearly see that the trailing flow is falling back to the cluster centre (see the overplotted velocity vectors), suggesting that the outflow does not leave the cluster eventually, but instead it is confined to the cluster. Figure 8. Temporal evolution of the concentration distribution ( Z ) of the tracer fluid in a simulation where the initial value of Z at t 0 is 1 if r 100kpc and 0 if r 100kpc. Arrows over-plotted in each panel indicate directions of gas velocities. From top to bottom, the time of each panel is t 300, 400, 500, 700Myr. The top colour bar represents Z in linear scale. It is clear that trailing flows behind the AGN bubble form real outflows in the ICM, which fall back to the cluster centre at later times, e.g. at t 700Myr. Trailing outflows play an important role in suppressing or delaying the central cooling catastrophe. As the rarefaction wave propagates away to large radii, gas inflows resume in the inner core region, as can be clearly seen in Figs 3 and 8 and discussed in Section 3.2 . If there are no trailing outflows, the gas density in the cluster centre would rise rapidly and a central cooling catastrophe would then develop. Trailing outflows uplifted by AGN bubbles transport gas from the inner cluster core to outer regions, suppressing gas accumulation at the cluster centre resulting from inflows along other directions and thus averting the central cooling catastrophe, which is delayed until trailing outflows fall back to the cluster centre at later times (see Section 3.6 ). Observational evidence for trailing outflows has been found in some cool-core clusters where the spatial distributions of heavy elements are anisotropic and preferentially aligned with the large-scale radio and cavity axes (Kirkpatrick, McNamara Cavagnolo 2011 ; Kirkpatrick McNamara 2015 ), suggesting that hot metal-rich outflows are indeed lifted up by AGN jets. Hydrodynamic simulations following both the jet and metallicity evolution in galaxy clusters would be helpful to further explore this scenario (e.g. Barai etal. 2016 , which however does not investigate the angular distribution of metals). Along the axes of trailing outflows, gas density is relatively high, as can be seen in the bottom two rows of Fig. 3 , and cold gas may drop out due to local thermal instability, forming cold filaments found in some galaxy clusters (e.g. Mittal etal. 2012 ; Tremblay etal. 2015 ). 3.6 Emerging picture of cyclic cool cores What is the long-term evolution of cool cluster cores after powerful AGN feedback events? After the onset of the AGN jet event, the cool core in our simulation is quickly overheated by shock dissipation, and rarefied by the rarefaction wave which transports energy to large radii. As the bow shock weakens and propagates further away, the inner core region starts to contract again
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