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

Abstract

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 Damkö hler 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 Damkö hler 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. * Deceased.

Observation of a Self-Limiting, Shear-Induced Turbulent Inversion Layer Above Marine Stratocumulus

“…5. Thus, we can suppose that the microphysical response to cloud-top entrainment will undergo transition from inhomogeneous to more homogeneous mixing as the mixed air becomes increasingly 'pre-humidified' (Lehmann et al 2009). …”

Droplet growth in warm turbulent clouds

“…Da = 1). Observations of cumulus by Lehmann et al (2009) show that there are regions of high ε where the transition length scale is greater than 10 cm. Entrainment leads to a decrease in buoyancy of the cloud, which in turn decreases ε.…”

“…The time-scales τ s and τ e can vary quite significantly depending on the choice of parameters. Indeed, Lehmann et al (2009) show that even when τ s and τ e are comparable, the numerical solution of (2) and (3) (with no assumption of constant a or constant s) can yield a time-scale for droplet evaporation (or for s to reach equilibrium) that is substantially different from either τ s or τ e . The first term on the right-hand side of (3) represents the increase in s due to adiabatic cooling in ascent and the second term represents the decrease in s due to the condensation of water vapour on droplets.…”

“…for relative humidities greater than 90%, there is almost no difference between homogeneous and inhomogeneous mixing (except when n/n a is small). Lehmann et al (2009) argue that the classification of mixing in terms of a single Damköhler number may be ambiguous since there is no a priori reason to fix a mixing length scale and hence τ r . As turbulence consists of a spectrum of eddy sizes, in any given cloud the mixing could be inhomogeneous at some scales and homogeneous at other scales.…”

“…Since τ s 10 s, mixing at scales greater than several metres will be inhomogeneous but not necessarily at centimetre scales. A length scale, l c = ε 1/2 τ 3/2 s , can be defined (Baker et al, 1980;Lehmann et al, 2009) at which there is a transition from inhomogeneous to homogeneous mixing (i.e. Da = 1).…”