  We compare the distribution of internal velocity dispersions of galaxy
clusters for an observational sample to those obtained from a set of N-body
simulations of seven COBE-normalised cosmological scenarios: the standard CDM
(SCDM) and a tilted (n=0.85) CDM (TCDM) model, a CHDM model with 25% of massive
neutrinos, two low-density LCDM models with Omega_0=0.3 and 0.5, two open OCDM
models with Omega_0=0.4 and 0.6. Simulated clusters are observed in projection
so as to reproduce the main observational biases and are analysed by applying
the same algorithm for interlopers removal and velocity dispersion estimate as
for the reference observational sample. Velocity dispersions for individual
clusters can be largely affected by observational biases in a model-dependent
way: models in which clusters had less time to virialize show larger
discrepancies between 3D and projected velocity dispersions. From the
comparison with real clusters we find that both SCDM and TCDM largely
overproduce clusters. The CHDM model marginally overproduces clusters and
requires a somewhat larger sigma_8 than a purely CDM model in order to produce
the same cluster abundance. The LCDM model with Omega_0=0.3 agrees with data,
while the open model with Omega_0=0.4 and 0.6 underproduces and marginally
overproduces clusters, respectively.
