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Jets from active galactic nuclei in the centers of galaxy clusters inflatecavities of low density relativistic plasma and drive shock and sound wavesinto the intracluster medium. When these waves overrun previously inflatedcavities, they form a differentially rotating vortex through theRichtmyer-Meshkov instability. The dissipation of energy captured in the vortexcan contribute to the feedback of energy into the atmospheres of cool coreclusters. Using a series of hydrodynamic simulations we investigate theefficiency of this process: we calculate the kinetic energy in the vortex bydecomposing the velocity field into its irrotational and solenoidal parts.Compared to the two-dimensional case, the 3-dimensional Richtmyer-Meshkovinstability is about a factor of 2 more efficient. The energy in the vortexfield for weak shocks is E_vortex ~ rho_ICM v_shock^2 V_bubble (with dependenceon the geometry, density contrast, and shock width). For strong shocks, thevortex becomes dynamically unstable, quickly dissipating its energy via aturbulent cascade. We derive a number of diagnostics for observations andlaboratory experiments of shock-bubble interactions, like the shock-vortexstandoff 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 dissipatethe vortex energy within the cooling radius of the cluster for a reasonablerange of vortex parameters. For sufficiently large filling factors (of order afew percent or larger), this process could thus contribute significantly to AGNfeedback in galaxy clusters.

All Curled Up: A Numerical Investigation of Shock-Bubble Interactions and the Role of Vortices in Heating Galaxy Clusters