Dynamics of buoyant bubbles in clusters of galaxies

We present a phenomenological model of the dynamics of buoyant bubbles in the atmosphere of a cluster of galaxies. The derived equations describe velocity, size, mass, temperature and density of the buoyant bubbles as functions of time based on several simple approximations. The constructed model is then used to interpret results of a numerical experiment of heating of the cluster core with buoyant bubbles in a hydrodynamical approximation (i.e. in the absence of magnetic fields, viscosity, and thermal diffusion). Based on the model parameters we discuss possible limitations of the numerical treatment of the problem, and highlight the main physical processes that govern the dynamics of bubbles in the intracluster medium.