  We consider the non-radial motions, originating in the outskirts of clusters
of galaxies and we show how it may reduce the discrepancy between Cold Dark
Matter (CDM) predicted X-ray temperature distribution function of clusters of
galaxies and that really observed, so resolving the problem of the X-ray
clusters abundance over-production predicted by the CDM model. We construct the
X-ray temperature distribution function using Press-Schechter's (1974) theory
and Evrard's (1990) prescriptions for the mass-temperature relation, taking
also account of the non-radial motions originating from the gravitational
interaction of the quadrupole moment of the protocluster. Then, we compare our
X-ray temperature distribution function with the tidal field of the matter of
the neighboring protostructures. We find that the model produces a reasonable
cluster temperature distribution.
