Homogeneous and Inhomogeneous Mixing in Cumulus Clouds: Dependence on Local Turbulence Structure

The helicopter-borne instrument payload known as the Airborne Cloud Turbulence Observation System (ACTOS) was used to study the entrainment and mixing processes in shallow warm cumulus clouds. The characteristics of the mixing process are determined by the Damköhler number, defined as the ratio of the mixing and a thermodynamic reaction time scale. The definition of the reaction time scale is refined by investigating the relationship between the droplet evaporation time and the phase relaxation time. Following arguments of classical turbulence theory, it is concluded that the description of the mixing process through a single Damköhler number is not sufficient and instead the concept of a transition length scale is introduced. The transition length scale separates the inertial subrange into a range of length scales for which mixing between ambient dry and cloudy air is inhomogeneous, and a range for which the mixing is homogeneous. The new concept is tested on the ACTOS dataset. The effect of entrained subsaturated air on the droplet number size distribution is analyzed using mixing diagrams correlating droplet number concentration and droplet size. The data suggest that homogeneous mixing is more likely to occur in the vicinity of the cloud core, whereas inhomogeneous mixing dominates in more diluted cloud regions. Paluch diagrams are used to support this hypothesis. The observations suggest that homogeneous mixing is favored when the transition length scale exceeds approximately 10 cm. Evidence was found that suggests that under certain conditions mixing can lead to enhanced droplet growth such that the largest droplets are found in the most diluted cloud regions.