Broadening of Cloud Droplet Spectra through Eddy Hopping: Why Did We All Have It Wrong?

In situ aircraft observations in adiabatic and close-to-adiabatic cloudy volumes suggest that cloud droplet spectra are often broader than predicted by growth of a droplet population rising from the cloud base. Cloud turbulence has been suggested as one of the possible mechanisms for the observed spectral broadening. This paper reviews computational studies of the impact of cloud turbulence on the diffusional growth of cloud droplets in adiabatic cloudy volumes. These studies typically apply direct numerical simulation (DNS) or scaled-up DNS approach to represent diffusional growth of cloud droplets embedded within homogeneous isotropic air turbulence. There is also a theory that predicts that the droplet spectral width continuously increases in time because of the individual droplet growth or evaporation within turbulent eddies. This mechanism has been referred to as eddy hopping. This paper expands the discussion in Prabhakaran et al. and illustrates the fundamental flaw of past computational and theoretical studies. These studies do not consider vertical dispersion of droplet positions that leads to growth of droplets that in the mean move upward and to evaporation of those that move downward. The theoretical prediction comes from confusing spectral broadening with the vertical dispersion of droplet positions when periodic lateral boundaries are used in DNS. Computational examples using a stochastic model mimicking eddy hopping show that droplet spectral width does not continuously increase in time, but it saturates at a small spread. Methodologies for appropriate numerical studies of the adiabatic spectral width evolution in natural clouds are discussed.