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

It is shown that the inertia of small droplets leads to the formation of dr op velocity flux divergence, with the maximum of the spatial spectrum at sc ales from 1 cm to 2.5 cm or different values of the dissipation rate. The s pace length of correlation of the divergence field, calculated using the Ba tchelor model of isotropic and homogeneous turbulence, is also of centimetr e 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 's pots' of enhanced and decreased drop concentration. Because of temporal and spatial changes of the turbulent flow structure, droplets appear alternate ly within the areas of positive or negative drop-flux velocity divergence a nd tend to leave the areas of the positive and enter the areas of negative drop-flux velocity divergence. Drop motions through the interface between t wo cloudy, or cloudy and clear-air, volumes lead to drop exchange between t hese volumes (inertial drop mixing). The characteristic time of this proces s was shown to be of the same order as the characteristic time-scales of mo lecular diffusion, droplet evaporation and gravitational sedimentation. Pos sible 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 clo ud updraught. Drop exchange between the centimetre-scale volumes, together with the generation of supersaturation in the ascending volumes, leads to t he 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 pron ounced in cases of cloudy and clear-air volumes mixing, especially when fre sh nucleation is assumed. It is shown that inertial mixing leads to the hom ogenization of the drop spectrum, i.e. to the formation of the same drop sp ectrum 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.