  We use numerical hydrodynamic simulations to investigate prestellar core
formation in the dynamic environment of giant molecular clouds, focusing on
planar post-shock layers produced by colliding turbulent flows. A key goal is
to test how core evolution and properties depend on the velocity dispersion in
the parent cloud; our simulation suite consists of 180 models with inflow Mach
numbers Ma=v/c_s=1.1-9. At all Mach numbers, our models show that turbulence
and self-gravity collect gas within post-shock regions into filaments at the
same time as overdense areas within these filaments condense into cores. This
morphology, together with the subsonic velocities we find inside cores, is
similar to observations. We extend previous results showing that core collapse
develops in an ``outside-in'' manner, with density and velocity approaching the
Larson-Penston asymptotic solution. The time for the first core to collapse
varies as 1/sqrt(v), consistent with analytic estimates. Core building takes 10
times as long as core collapse, consistent with observed prestellar core
lifetimes. Core shapes change from oblate to prolate as they evolve. To define
cores, we use isosurfaces of the gravitational potential. We compare to cores
defined using the potential computed from projected surface density, finding
good agreement for core masses and sizes; this offers a new way to identify
cores in observed maps. Cores with masses varying by three orders of magnitude
(0.05 - 50 M_sun) are identified in our simulations. Stability analysis of
post-shock layers predicts that the first core to collapse will have mass M
\propto v^-1/2, and that the minimum mass for cores formed at late times will
have M\propto v^-1. From our simulations, the median mass lies between these
two relations.
