All Curled Up: A Numerical Investigation of Shock-Bubble Interactions
  and the Role of Vortices in Heating Galaxy Clusters
  Jets from active galactic nuclei in the centers of galaxy clusters inflate
cavities of low density relativistic plasma and drive shock and sound waves
into the intracluster medium. When these waves overrun previously inflated
cavities, they form a differentially rotating vortex through the
Richtmyer-Meshkov instability. The dissipation of energy captured in the vortex
can contribute to the feedback of energy into the atmospheres of cool core
clusters. Using a series of hydrodynamic simulations we investigate the
efficiency of this process: we calculate the kinetic energy in the vortex by
decomposing the velocity field into its irrotational and solenoidal parts.
Compared to the two-dimensional case, the 3-dimensional Richtmyer-Meshkov
instability is about a factor of 2 more efficient. The energy in the vortex
field for weak shocks is E_vortex ~ rho_ICM v_shock^2 V_bubble (with dependence
on the geometry, density contrast, and shock width). For strong shocks, the
vortex becomes dynamically unstable, quickly dissipating its energy via a
turbulent cascade. We derive a number of diagnostics for observations and
laboratory experiments of shock-bubble interactions, like the shock-vortex
standoff distance, which can be used to derive lower limits on the Mach number.
The differential rotation of the vortex field leads to viscous dissipation,
which is sufficiently efficient to react to cluster cooling and to dissipate
the vortex energy within the cooling radius of the cluster for a reasonable
range of vortex parameters. For sufficiently large filling factors (of order a
few percent or larger), this process could thus contribute significantly to AGN
feedback in galaxy clusters.
