  Condensational growth of cloud droplets due to supersaturation fluctuations
is investigated by solving the hydrodynamic and thermodynamic equations using
direct numerical simulations with droplets being modeled as Lagrangian
particles. The supersaturation field is calculated directly by simulating the
temperature and water vapor fields instead of being treated as a passive
scalar. Thermodynamic feedbacks to the fields due to condensation are also
included for completeness. We find that the width of droplet size distributions
increases with time, which is contrary to the classical theory without
supersaturation fluctuations, where condensational growth leads to
progressively narrower size distributions. Nevertheless, in agreement with
earlier Lagrangian stochastic models of the condensational growth, the standard
deviation of the surface area of droplets increases as $t^{1/2}$. Also, for the
first time, we explicitly demonstrate that the time evolution of the size
distribution is sensitive to the Reynolds number, but insensitive to the mean
energy dissipation rate. This is shown to be due to the fact that temperature
fluctuations and water vapor mixing ratio fluctuations increases with
increasing Reynolds number, therefore the resulting supersaturation
fluctuations are enhanced with increasing Reynolds number. Our simulations may
explain the broadening of the size distribution in stratiform clouds
qualitatively, where the mean updraft velocity is almost zero.
