The role of the inertia of cloud drops in the evolution of the spectra during drop growth by diffusion

Mark B. Pinsky, Alexander P. Khain*, Zev Levin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


It is shown that the inertia of small droplets leads to the formation of drop velocity flux divergence, with the maximum of the spatial spectrum at scales from 1 cm to 2.5 cm for different values of the dissipation rate. The spacelength of correlation of the divergence field, calculated using the Bachelor model of isotropic and homogeneous turbulence, is also of centimetre scale. These results are interpreted in such a way that the drop inertia leads to the formation of the centimetre-scale structure of a cloud with 'spots' of enhananced and decreased drop concentration. Because of temporal and spatial changes of the turbulent flow structure, droplets appear alternately within the areas of positive or negative drop-flux velocity divergence and tend to leave the areas of the positive and enter the areas of negative drop-flux velocity divergence. Drop motions through the interface between two cloudy, or cloudy and clean-air, volumes lead to drop exchange between these volumes (inertial drop mixing). The characteristic time of this process was shown to be of the same order as the characteristic time-scales of molecular diffusion, droplet evaporation and gravitational sedimentation. Possible effects of the inertial mixing are illustrated using a simple model, in which a comparatively large air volume consists of many centimetre-scale volumes of different drop-flux divergence and ascent velocity within a cloud updraught. Drop exchange between the centimetre-scale volumes, together with the generation of supersaturation in the ascending volumes, leads to the evolution of droplet size spectra. The inertial mixing 'itself' leads to a weak droplet spectrum broadening in the case of uniform initial droplet concentration. The droplet spectrum broadening appears to be much more pronounced in cases of cloudy and clear-air volumes mixing, especially when fresh nucleation is assumed. It is shown that inertial mixing leads to the homogenization of the drop spectrum, i.e. to the formation of the same drop spectrum shape in all centimetre-scale volumes. Thus, inertial mixing may be important for the formation of local droplet spectra. At the same time, the inertial mixing may lead to significant fluctuations of drop concentration in these volumes.

Original languageAmerican English
Pages (from-to)553-581
Number of pages29
JournalQuarterly Journal of the Royal Meteorological Society
Issue number554
StatePublished - Jan 1999


  • Condensational growth
  • Droplet concentration inhomogeneity
  • Droplet spectrum formation
  • Effects of cloud turbulence
  • Fine-structure of clouds
  • Inertia of droplets
  • Inertial mixing


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