  We simulate the effects of viscous dissipation of waves that are generated by
AGN activity in clusters of galaxies. We demonstrate that the amount of viscous
heating associated with the dissipation of these waves can offset radiative
cooling rates in cooling flow clusters of galaxies. This heating mechanism
leads to spatially distributed and approximately symmetrical dissipation. The
heating waves reach a given distance from the cluster center on a timescale
shorter than the cooling time. This means that this heating mechanism has the
potential of quenching cooling flows in a quasi-stable fashion. Moreover, the
heating is gentle as no strong shocks are present in the simulations. We first
investigated whether a single continuous episode of AGN activity can lead to
adequate dissipation to balance cooling rates. These simulations demonstrated
that, whereas secondary waves generated by the interaction of the rising bubble
with the intracluster medium are clearly present, viscous heating associated
with the dissipation of these waves is insufficient to balance radiative
cooling. It is only when the central source is intermittent that the viscous
dissipation of waves associated with subsequent episodes of activity can offset
cooling. This suggests that the ripples observed in the Perseus cluster can be
interpreted as being due to the AGN duty cycle, i.e., they trace AGN activity
history. The simulations were performed using the PPM adaptive mesh refinement
code FLASH in two dimensions.
