  Condensation of water vapor on active cloud condensation nuclei produces
micron-size water droplets. To form rain, they must grow rapidly into at least
50-100 $\mu$m droplets. Observations show that this process takes only 15-20
minutes. The unexplained physical mechanism of such fast growth, is crucial for
understanding and modeling of rain, and known as "condensation-coalescence
bottleneck in rain formation". We show that the recently discovered phenomenon
of the tangling clustering instability of small droplets in
temperature-stratified turbulence (Phys. Fluids 25, 085104, 2013) results in
the formation of droplet clusters with drastically increased droplet number
densities. The mechanism of the tangling clustering instability is much more
effective than the previously considered by us the inertial clustering
instability caused by the centrifugal effect of turbulent vortices. This is the
reason of strong enhancement of the collision-coalescence rate inside the
clusters. The mean-field theory of the droplet growth developed in this study
can be useful for explanation of the observed fast growth of cloud droplets in
warm clouds from the initial 1 micron size droplets to 40-50 micron size
droplets within 15-20 minutes.
