Formation of inhomogeneity in drop concentration induced by the inertia of drops falling in a turbulent flow, and the influence of the inhomogeneity on the drop-spectrum broadening

M. Pinsky, A. Khain*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


The mechanisms of drop-concentration inhomogeneity formation are studied using both a numerical simulation with a model of isotropic and homogeneous turbulence, and analytical methods. It is shown that atmospheric turbulence can create a significant drop-concentration inhomogeneity due to the effects of drop inertia. Two types of area in the turbulent flow are revealed. Drops tend to leave the areas of 'drop vortices' and collect within the zones out of the vortices. As a result, the zones of drop-track collection turn out to be the zones of enhanced drop concentration. The rate of concentration enhancement is studied for drops of different sizes using the Monte Carlo method. It is shown that the drop flux velocity divergence and droplet-concentration variations reach their maximum at 100 μm drop radius. Zones of enhanced drop concentrations are stretched along the drop tracks. Characteristic scales of drop-concentration fluctuations along the drop tracks are of the order of several metres or even a few tens of metres. Across the drop tracks, the characteristic scale of concentration pulsations is of the order of a few centimetres. The existence of the areas of drop-concentration enhancement and the areas of decreased concentration means that drop collisions are not distributed uniformly, but are concentrated within the areas with greater drop concentration. The possible effects of droplet inhomogeneity is simulated by solving a stochastic coalescence equation for the water drop-size-distribution function in areas of enhanced and decreased droplet concentration with the subsequent mixing of the corresponding spectra at each 10 s. It is shown that due to the nonlinear nature of collision processes the effects of the increase of collision frequency in the areas of enhanced concentration dominate over those of its decrease. The effects of the drop-concentration inhomogeneity are accumulated with time and lead to substantial acceleration of droplet spectrum broadening. It is supposed that the inhomogeneity of rain rates with time and space can be attributed to these turbulence effects determining drop-track collection and drop-concentration inhomogeneity. These turbulence effects can contribute to the formation of inhomogeneity of ice and aerosol particles as well.

Original languageAmerican English
Pages (from-to)165-186
Number of pages22
JournalQuarterly Journal of the Royal Meteorological Society
Issue number537
StatePublished - Jan 1997


  • Cloud turbulence
  • Drop inertia
  • Droplet collisions
  • Droplet-concentration inhomogeneity
  • Precipitation formation


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