3.1. Numerical simulations
The most direct way to study such a complex set of fluid dynamical processes is through numerical simulations. A variety of 2D and 3D simulations have now been published, addressing the heating of the ICM by buoyant plumes. These calculations illustrate several of the requirements for gentle, distributed heating to occur:
The plumes spread laterally as well as radially, a result of the `mushroom cloud' effect (Churazov et al. 2001; Ruszkowski et al. 2003). This is necessary in order to distribute the energy in solid angle, if it is initially injected by jets.
The bubbles persist long after the observable radio lobes have faded (Reynolds et al. 2002; Basson & Alexander 2002; Brüggen et al. 2002), and may drift far from the initial injection axis. Since radio emission fades rapidly once the bubbles begin to rise, this provides a straightforward explanation for `ghost cavities' (M. Ruszkowski, C. Kaiser & M. Begelman 2003, unpublished work).
The rising bubbles and associated mixing do not necessarily smear out abundance gradients in the ICM (Brüggen 2002).
Rising and expanding bubbles increase the potential, thermal and kinetic energy of the ICM (Reynolds et al. 2002; Quilis et al. 2001; Churazov et al. 2002; Brüggen & Kaiser 2002). If the AGN is intermittent they can generate sound waves (Ruszkowski et al. 2003), which may have been detected in the Perseus (Fabian et al. 2003) and the Virgo (Forman et al. 2003) clusters.