Survival and mass growth of cold gas in a turbulent, multiphase medium

Astrophysical gases are commonly multiphase and highly turbulent. In this work, we investigate the survival and growth of cold gas in such a turbulent, multi-phase medium using three-dimensional hydrodynamical simulations. Similar to previous work simulating coherent flow (winds), we find that cold gas survives if the cooling time of the mixed gas is shorter than the Kelvin-Helmholtz time of the cold gas clump (with some weak additional Mach number dependence). However, there are important differences. Near the survival threshold, the long-term evolution is highly stochastic, and subject to the existence of sufficiently large clumps. In a turbulent flow, the cold gas continuously fragments, enhancing its surface area. This leads to exponential mass growth, with a growth time given by the geometric mean of the cooling and the mixing time. The fragmentation process leads to a large number of small droplets which follow a scale-free $\mathrm{d} N/\mathrm{d} m \propto m^{-2}$ mass distribution, and dominate the area covering fraction. Thus, whilst survival depends on the presence of large `clouds', these in turn produce a `fog' of smaller droplets tightly coupled to the hot phase which are probed by absorption line spectroscopy. We show with the aid of Monte-Carlo simulations that the simulated mass distribution emerges naturally due to the proportional mass growth and the coagulation of droplets. We discuss the implications of our results for convergence criteria of larger scale simulations and observations of the circumgalactic medium.