A Simple Model of Droplet Spectral Evolution during Turbulent Mixing

Abstract

The mixing of cloudy, saturated air with cloud-free, subsaturated air is examined with a simple one-dimensional model of the mixing process. The model incorporates (i) a one-dimensional parameterization of turbulent deformation, (ii) molecular diffusion, (iii) sedimentation of droplets and (iv) droplet evaporation in the changing humidity field. The model predicts droplet spectral shapes after homogenization of the two air masses. The turbulent deformation parameterization is based on inertial subrange arguments. It yields a crude estimate of the time development of the vapor and temperature fields in a single characteristic eddy in one dimension rather than the full range of eddy scales in three dimensions. For the high turbulence levels commonly found in cumuli the evaporation process appears close to that described earlier as homogeneous, which may in part be due to the approximations in our treatment. For all other conditions the calculations show total evaporation of some drops accompanied by some change in droplet spectral shape.