High-redshift clusters of galaxies show an over-abundance of spirals by a
factor of 2-3, and the corresponding under-abundance of S0 galaxies, relative
to the nearby clusters. This morphological evolution can be explained by tidal
interactions with neighboring galaxies and with the hierarchically growing
cluster halo. The efficiency of tidal interactions depends on the size and
structure of the cluster, as well as on the epoch of its formation. I simulate
the formation and evolution of Virgo-type clusters in three cosmologies: a
critical density model Omega_0=1, an open model Omega_0=0.4, and a flat model
Omega_0=0.4 with a cosmological constant. The orbits of identified halos are
traced with a high temporal resolution (~10^7 yr). Halos with low relative
velocities merge only shortly after entering the cluster; after virialization
mergers are suppressed. The dynamical evolution of galaxies is determined by
the tidal field along their trajectories. The maxima of the tidal force do not
always correspond to closest approach to the cluster center. They are produced
to a large extent by the local density structures, such as the massive galaxies
and the unvirialized remnants of infalling groups of galaxies. Collisions of
galaxies are intensified by the substructure, with about 10 encounters within
10 kpc per galaxy in the Hubble time. These very close encounters add an
important amount (10-50%) of the total heating rate. The integrated effect of
tidal interactions is insufficient to transform a spiral galaxy into an
elliptical, but can produce an S0 galaxy. Overall, tidal heating is stronger in
the low Omega_0 clusters