We study motions of galaxies in galaxy clusters formed in the concordance \Lambda CDM cosmology .
We use high-resolution cosmological simulations that follow dynamics of dark matter and gas and include various physical processes critical for galaxy formation : gas cooling , heating and star formation .
Analysing motions of galaxies and the properties of intracluster gas in the sample of eight simulated clusters at z = 0 , we study velocity dispersion profiles of the dark matter , gas , and galaxies .
We measure the mean velocity of galaxy motions and gas sound speed as a function of radius and calculate the average Mach number of galaxy motions .
The simulations show that galaxies , on average , move supersonically with the average Mach number of \approx 1.4 , approximately independent of the cluster-centric radius .
The supersonic motions of galaxies may potentially provide an important source of heating for the intracluster gas by driving weak shocks and via dynamical friction , although these heating processes appear to be inefficient in our simulations .
We also find that galaxies move slightly faster than the dark matter particles .
The magnitude of the velocity bias , b _ { v } \approx 1.1 , is , however , smaller than the bias estimated for subhalos in dissipationless simulations .
Interestingly , we find velocity bias in the tangential component of the velocity dispersion , but not in the radial component .
Finally , we find significant random bulk motions of gas .
The typical gas velocities are of order \approx 20 - 30 \% of the gas sound speed .
These random motions provide about 10 \% of the total pressure support in our simulated clusters .
The non-thermal pressure support , if neglected , will bias measurements of the total mass in the hydrostatic analyses of the X-ray cluster observations .