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.
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