  We use N-body simulations to study the shape of mean cluster density and
velocity profiles formed via gravitational instability. The dependence of the
final structure on both cosmology and initial density field is examined, using
a grid of cosmologies and scale-free initial power spectra P\propto k^n. For
each model, we stack clusters to define an average density profile in the
non-linear regime. The profiles are well fit by a power law over 99% of the
cluster volume, with a clear trend toward steeper slopes with both increasing n
and decreasing Omega_o. For models with a Omega_o = 0.2, the profile slopes are
consistently higher than those for Omega-1.0. Cluster density profiles are thus
potentially useful cosmological diagnostics. We find no evidence for a constant
density core in any of the models, although the density profiles do tend to
flatten at small radii. Much of the flattening is due to the force softening
required by the simulations, and an attempt is made to recover the unsoftened
profiles assuming angular momentum invariance. The recovered profiles in the
Omega=1 cosmologies are consistent with a pure power law up to the highest
density contrasts (10^6) accessible with our resolution. The low density models
show significant deviations from a power law above density contrasts \sim 10^5.
We interpret this curvature as reflecting the non scale-invariant nature of the
background cosmology in these models.

Astrophysics