Stochastic effects of cloud droplet hydrodynamic interaction in a turbulent flow

M. Pinsky, A. Khain*, M. Shapiro

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

72 Scopus citations


The collision efficiencies of small cloud droplets are calculated in a turbulent flow. A flow velocity field was generated using a model of isotropic turbulence [Pinsky, M.B., Khain, A.P., 1995. A model of homogeneous isotropic turbulence flow and its application for simulation of cloud drop tracks. Geophys. Astrophys. Fluid Dyn. 81, 33-55; Pinsky, M.B., Khain, A.P., 1996. Simulations of drops' fall in a homogeneous isotropic turbulence flow. Atmos. Res. 40, 223-259]. The results indicate that in a turbulent flow the collision efficiency is a random value with high dispersion. The collision efficiencies depend on the initial (at the infinity) interparticle velocities and angles of droplet approach. The mean values of the collision efficiency and the mean values of the collision kernel in a turbulent flow exceed the values measured or calculated for still air conditions. For instance, under turbulent intensity typical of early cumulus clouds, the mean values of the collision efficiency for a 10 μm drop-collector are 5 to 9 times as large as the values in the pure gravity case. In case of a 20-μm-radius drop-collector the mean collision efficiencies are greater than the corresponding gravity values by a factor ranging from 1.2 to about 6, depending on the size ratios of colliding droplets. The collision efficiencies in a turbulent flow are shown to be very sensitive to relative droplet velocities. Even a small variation (of about 10%) of the interdrop relative velocity can result in values of the collision efficiencies twice as large as in the calm air. Possible effects of the stochastic nature of the collision process on the evolution of the "mean" cloud structure are discussed. It is shown that drop concentration inhomogeneity accelerates the rate of droplet collisions, which are effective in the areas of the increased droplet concentration. To illustrate the effect of the mean increase of the collision efficiency on the drop size spectrum evolution, we solved the stochastic kinetic equation of collision. It was shown that the increase of the collision efficiency of small cloud droplets controls the broadening of the initially narrow droplet size spectrum and accelerates the process of rain formation. The results indicate that the increase of the collision efficiency of small cloud droplets in a turbulent flow is, possibly, the mechanism responsible for in situ observed broadening of droplet spectra in undiluted cores of cumulus clouds. In numerical simulations of drop collisions within a turbulent flow, a new effect was discovered, namely, in some cases the collision efficiencies in a turbulent flow appeared to be equal to zero (no collisions). Analysis shows that in the case the ratio of droplet fall velocities is less than a certain critical value (which depends on the ratio of particle sizes) the falling particles form a tandem, in which particles fall with equal velocities.

Original languageAmerican English
Pages (from-to)131-169
Number of pages39
JournalAtmospheric Research
Issue number1-3
StatePublished - 2000

Bibliographical note

Funding Information:
This study was partially supported by the Germany–Israel Science Foundation (grant 0407-008.08/95), and by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities (grant 572/97).


  • Cloud microphysics
  • Droplet spectrum formation
  • Stochastical processes in clouds
  • Turbulence effects


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