  We analyze three-dimensional hydrodynamical simulations of the interaction of
jets and the bubbles they inflate with the intra-cluster medium (ICM), and show
that the heating of the ICM by mixing hot bubble gas with the ICM operates over
tens of millions of years, and hence can smooth the sporadic activity of the
jets. The inflation process of hot bubbles by propagating jets forms many
vortices, and these vortices mix the hot bubble gas with the ICM. The mixing,
hence the heating of the ICM, starts immediately after the jets are launched,
but continues for tens of millions of years. We suggest that the smoothing of
the active galactic nucleus (AGN) sporadic activity by the long-lived vortices
accounts for the recent finding of a gentle energy coupling between AGN heating
and the ICM.
