  (Abridged) We present a parameter study of offset mergers between clusters of
galaxies. Using the Eulerian hydrodynamics/N-body code COSMOS, we simulate
mergers between nonisothermal, hydrostatic clusters with a steep central dark
matter density profile and a beta-model gas profile. We constrain global
properties of the model clusters using observed cluster statistical
relationships. We consider impact parameters between zero and five times the
scale radius and mass ratios of 1:1 and 1:3. The morphological changes,
relative velocities, and temperature jumps we observe agree with previous
studies using the King profile for the dark matter. We observe a larger jump in
X-ray luminosity (~4-10x) than in previous work, and we argue that this
increase is most likely a lower limit due to our spatial resolution. We
emphasize that luminosity and temperature jumps due to mergers may have an
important bearing on constraints on Omega derived from the observation of hot
clusters at high redshift. Shocks are relatively weak in the cluster cores;
hence they do not significantly increase the entropy there. Instead, shocks
create entropy in the outer regions, and this high-entropy gas is mixed with
the core gas during later stages of the merger. Ram pressure initiates mixing
by displacing the core gas from its potential center, causing it to become
convectively unstable. The resulting convective plumes produce large-scale
turbulent motions with eddy sizes up to several 100 kpc. This turbulence is
pumped by dark matter-driven oscillations in the gravitational potential. Even
after nearly a Hubble time these motions persist as subsonic turbulence in the
cluster cores, providing 5-10% of the support against gravity.
