  Heat input roughly balances radiative cooling in the gaseous cores of galaxy
clusters even when the central cooling time is short, implying that cooling
triggers a feedback loop that maintains thermal balance. Furthermore, cores
with short cooling times tend to have multiphase structure, suggesting that the
intracluster medium (ICM) becomes locally thermally unstable for cooling times
< 1 Gyr. In this work, we use 2D and 3D hydrodynamic simulations to study the
onset of condensation in idealized galaxy-cluster cores. In particular, we look
at how the condensation process depends on the ratio of cooling time to
freefall time and on the geometry of the gravitational potential. We conclude
that the ICM can always evolve to a state in which condensation occurs if given
enough time, but that an initial timescale ratio tcool /tff < 10 is needed for
thermal instability to grow quickly enough to affect realistic cluster cores
within a timescale that is relevant for cosmological structure formation. We
find that instability leads to convection and that perturbations continue to
grow while the gas convects. Condensation occurs when the timescale ratio in
the low-entropy tail of the perturbation distribution drops below tcool /tff <
3, even if the volume-averaged timescale ratio is substantially greater. In our
simulations, the geometry of the gravitational potential does not have a strong
effect on thermal stability. Finally, we find that if condensation is powering
feedback, a conversion efficiency of around 10^-3 for converting the condensed
mass into thermal energy is sufficient to maintain thermal balance in the ICM.
