Lagrangian Mixing Dynamics at the Cloudy–Clear Air Interface

Abstract

The entrainment of clear air and its subsequent mixing with a filament of cloudy air, as occurs at the edge of a cloud, is studied in three-dimensional direct numerical simulations that combine the Eulerian description of the turbulent velocity, temperature, and vapor fields with a Lagrangian cloud droplet ensemble. Forced and decaying turbulence is considered, such as when the dynamics around the filament is driven by larger-scale eddies or during the final period of the life cycle of a cloud. The microphysical response depicted in n d 2 hr 3 i space (where n d and r are droplet number density and radius, respectively) shows characteristics of both homogeneous and inhomogeneous mixing, depending on the Damk€ ohler number. The transition from inhomogeneous to homogeneous mixing leads to an offset of the homogeneous mixing curve to larger dilution fractions. The response of the system is governed by the smaller of the single droplet evaporation time scale and the bulk phase relaxation time scale. Variability within the n d 2 hr 3 i space increases with decreasing sample volume, especially during the mixing transients. All of these factors have implications for the interpretation of measurements in clouds. The qualitative mixing behavior changes for forced versus decaying turbulence, with the latter yielding remnant patches of unmixed cloud and stronger fluctuations. Buoyancy due to droplet evaporation is observed to play a minor role in the mixing for the present configuration. Finally, the mixing process leads to the transient formation of a pronounced nearly exponential tail of the probability density function of the Lagrangian supersaturation, and a similar tail emerges in the droplet size distribution under inhomogeneous conditions.

Scale Dependence of Cloud Microphysical Response to Turbulent Entrainment and Mixing

“…Contrary to expectations when the simulations were designed, there is no obvious change in the shape of the mixing trajectories as domain size varies. To be consistent with our prior work (Kumar et al, ), we also divide the cloud slab into four subdomains, as depicted in Figure c. Mixing trajectories for each subdomain are plotted in Figures d–h, progressing from the smallest to the largest domain.…”

“…It is thus possible that within the turbulence cascade, both D a > 1 and D a < 1 can exist at different spatial scales, so that one can also expect a different microphysical response at different scales (Andrejczuk et al, ; Beals et al, ; Korolev & Mazin, ; Lehmann et al, ; Lu et al, , ; Siebert et al, ). For example, some DNS results suggested that a transition from inhomogeneous to homogeneous mixing could lead to an inhomogeneous offset in the microphysical trajectory in a mixing diagram (Kumar et al, ). Driven in part by related questions of scale, computational efforts have pushed to reach steadily larger D a , within the capabilities of available computational resources.…”

Cloud droplets to drizzle: Contribution of transition drops to microphysical and optical properties of marine stratocumulus clouds

“…We consider whether such a mechanism could be operating here. The relevant microphysical time scale for this turbulence‐broadening effect [ Chandrakar et al ., ] is the phase relaxation time, given by , where is a modified water vapor diffusion coefficient and is the mean droplet diameter, and n is droplet concentration [ Kumar et al ., ]. The relevant turbulence time scale is the Lagrangian correlation time for the large‐scale mixing and can be roughly estimated from the Eulerian large‐eddy correlation time.…”

On Which Microphysical Time Scales to Use in Studies of Entrainment‐Mixing Mechanisms in Clouds

“…Turbulent entrainment‐mixing mechanisms have been studied for more than 50 years. Homogeneous/inhomogeneous entrainment‐mixing mechanisms are the most studied concepts (e.g., Endo et al,; Gerber et al, ; Kumar et al, ; Liu et al, ; Lu et al, ; Small et al, ; Yum et al, ). Mixing and droplet evaporation processes occur during entrainment‐mixing.…”