  The interstellar medium in star-forming galaxies is a multiphase gas in which
turbulent support is at least as important as thermal pressure. Sustaining this
configuration requires continuous radiative cooling, such that the overall
average cooling rate matches the decay rate of turbulent energy into the
medium. Here we carry out a set of numerical simulations of a stratified,
turbulently stirred, radiatively cooled medium, which uncover a fundamental
transition at a critical one-dimensional turbulent velocity of ~ 35 km/s. At
turbulent velocities below ~35 km/s, corresponding to temperatures below
300,000 K, the medium is stable, as the time for gas to cool is roughly
constant as a function of temperature. On the other hand, at turbulent
velocities above the critical value, the gas is shocked into an unstable regime
in which the cooling time increases strongly with temperature, meaning that a
substantial fraction of the interstellar medium is unable to cool on a
turbulent dissipation timescale. This naturally leads to runaway heating and
ejection of gas from any stratified medium with a one-dimensional turbulent
velocity above ~35 km/s, a result that has implications for galaxy evolution at
all redshifts.
