  We study motions of galaxies in galaxy clusters formed in the concordance
LCDM 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 ~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 faster than the dark matter particles in clusters. The magnitude
of the velocity bias, b_v~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 ~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.
