  We use SWIFT, a smoothed particle hydrodynamics code, to simulate the
evolution of bubbles inflated by active galactic nuclei (AGN) jets, as well as
their interactions with the ambient intracluster medium (ICM). These jets
inflate lobes that turn into bubbles after the jets are turned off (at $t=50$
Myr). Almost all of the energy injected into the jets is transferred to the ICM
very quickly after they are turned off, with roughly $70$ per cent of it in
thermal form and the rest in kinetic. At late times ($t>500$ Myr) we find the
following: 1) the bubbles draw out trailing filaments of low-entropy gas,
similar to those recently observed, 2) the action of buoyancy and the uplift of
the filaments dominates the energetics of both the bubbles and the ICM and 3)
almost all of the originally injected energy is in the form of gravitational
potential energy, with the bubbles containing $15$ per cent of it, and the rest
contained in the ICM. These findings indicate that feedback proceeds mainly
through the displacement of gas to larger radii. We find that the uplift of
these filaments permanently changes the thermodynamic properties of the ICM by
reducing the central density and increasing the central temperature (within
$30$ kpc). We propose that jet feedback proceeds not only through the heating
of the ICM (which can delay cooling), but also through the uplift-related
reduction of the central gas density. The latter also delays cooling, on top of
reducing the amount of gas available to cool.
