of galaxy formation, cooling flows, and during the transition of gas clouds from quasi-hydrostatic contraction to dynamical collapse. It is a natural consequence of thermal instability, which generally leads to the emergence of a population of relatively cool, dense clouds (warm, fragmentary clouds, or WFC’s) that are pressure confined by an ambient hot, tenuous gas (residual hot gas, or RHG). In such a state, the hot gas establishes a quasistatic equilibrium with the background gravitational potential, and the cold clouds settle into it under the action of their negative buoyancy. In the present investigation, we neglect the self-gravity of the gas, and consider the potential to be due to a time-invariant background distribution of dark matter or stars.

Through a series of numerical simulations, we demonstrate the following evolutionary outcomes.

1\) During their descent, the WFC’s break up on the same timescale as is required for them to attain a terminal speed.

2\) Most of the energy released from the sedimentation of the WFC’s into the background gravitational potential is deposited into the RHG.

These results provide justifications for the assumptions we made in our earlier model for the evolution of multi-phase medium during the epoch of galaxy formation (Lin 