Radiative energy losses of the hot gas in galaxy clusters occur on timescales
significantly shorter than the Hubble time, leading to massive accumulation of cold gas
and vigorous star formation, in contradiction to observations. Several sources of heat
have been discussed, most promising being heating by the SMBH in central galaxies
through inflation of bubbles of relativistic plasma. The missing link in this scenario
is the mechanisms, by which energy from bubbles is transported to the hot
gas. Dissipation of gas turbulence, induced by bubbles during their buoyant rise and
expansion, is a possible mechanisms. However, direct measurements of gas velocities will
be possible only with future X-ray calorimeter on board the Astro-H observatory. We
recently overcame this problem, by analyzing long Chandra observations of the X-ray
brightest clusters of galaxies and measuring statistical properties of density
fluctuations, which allowed us to constrain the velocity power spectrum of gas motions
in the ICM indirectly. I will show that the heating rate due to dissipation of
turbulence is indeed sufficient to balance the radiative cooling locally at each radius
within the cores. Turbulent dissipation, therefore, might be the key element in
resolving the gas cooling problem in cluster cores and other X-ray gas-rich systems.