Central jetted active galactic nuclei (AGN) appear to heat the core regions
of the intracluster medium (ICM) in cooling-core galaxy clusters and groups,
thereby preventing a cooling catastrophe. However, the physical mechanism(s) by
which the directed flow of kinetic energy is thermalized throughout the ICM
core remains unclear. We examine one widely discussed mechanism whereby the AGN
induces subsonic turbulence in the ambient medium, the dissipation of which
provides the ICM heat source. Through controlled inviscid 3-d hydrodynamic
simulations, we verify that explosive AGN-like events can launch gravity waves
(g-modes) into the ambient ICM which in turn decay to volume-filling
turbulence. In our model, however, this process is found to be inefficient,
with less than 1% of the energy injected by the AGN activity actually ending up
in the turbulence of the ambient ICM. This efficiency is an order of magnitude
or more too small to explain the observations of AGN-feedback in galaxy
clusters and groups with short central cooling times. Atmospheres in which the
g-modes are strongly trapped/confined have an even lower efficiency since, in
these models, excitation of turbulence relies on the g-modes' ability to escape
from the center of the cluster into the bulk ICM. Our results suggest that, if
AGN-induced turbulence is indeed the mechanism by which the AGN heats the ICM
core, its driving may rely on physics beyond that captured in our ideal
hydrodynamic model
