  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.
