Acceleration of raindrop formation due to the tangling-clustering instability in a turbulent stratified atmosphere

Abstract

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 µm 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 µm size droplets to 40-50 µm size droplets within 15-20 minutes.

The role of turbulence in thunderstorm, snowstorm, and dust storm electrification

“…The projection of each particle motion on z axis can be described by the following equations [ Elperin et al , ; Belan et al , ]: where τ St1,2 are the Stokes times for large and small particles, v T is a turbulent velocity, and g is the acceleration of gravity. We can use expressions in complex amplitudes because the equations are linear and the turbulent velocity can be represented as a Fourier integral.…”

“…The projection of each particle motion on z axis can be described by the following equations [Elperin et al, 2015;Belan et al, 2016]:…”

A model study of the effect of clustering on the last stage of drizzle formation

“…Saffman and Turner () showed that the rapid growth of “small” cloud droplets (of sub‐Kolmogorov size and whose Stokes number ( St ) ≪ 1; the latter is the ratio of droplet response time to Kolmogorov time‐scale (Davidson, ) demands turbulence with a dissipation rate ∼2, 000 cm 2 ·s −3 which rather lies at the higher end of the dissipation rates for cumulus clouds. However, Maxey () showed that inertial particles in a turbulent flow leave high‐vorticity regions to accumulate in high‐strain regions, which phenomenon is now called clustering (or preferential concentration or accumulation effect); since then more mechanisms for inertial particle clustering have been proposed (Mehlig and Wilkinson, ; Coleman and Vassilicos, ; Bec et al ., ; Bragg et al ., ; Elperin et al ., ), see Gustavsson and Mehlig () or Pumir and Wilkinson () for a review. Droplet clustering further enhances the collision rate because the number density in the vicinity of a droplet is now statistically higher; the enhancement is measured either by comparison with Saffman and Turner ()'s formula (because droplets do not cluster when St → 0 or St → ∞ ) or by computing the radial distribution function at contact between droplets (Sundaram and Collins, ).…”

Mechanism of unconfined dust explosions: Turbulent clustering and radiation-induced ignition

“…(42)- (47) in [26] and Eqs. (17) and (18) in [27]. The correlation function (R) takes into account particle clustering.…”

“…Recent analytical studies [26,27] and laboratory experiments [28] have shown that the particle clustering can be much more effective in the presence of a mean temperature gradient. In this case, the turbulence is temperature stratified and the turbulent heat flux is not zero.…”