A diffusive model of the turbulent mixing of dry and cloudy air

Abstract

SUMMARYA model is presented of the turbulent mixing between a sphere of droplet-free air (saturated or undersaturated) and a spherical volume of cloud within which it is embedded. The rates of equalization of supersaturation, temperature and liquid water are examined as functions of the turbulent energy dissipation rate, the dimensions of the interacting volumes, the drop-size distribution in the cloud and other parameters. Spectral changes resulting from the mixing conform closely with those predicted by the recent inhomogeneous or dilution-only descriptions of mixing (Baker et ol. 1980; Telford and Chai 1980).It is shown that spectral changes observed during entrainment into shallow cumulus, stratocumulus and cap clouds are in good agreement with those predicted on the basis of this diffusive model.Calculations of mixing in the presence of an updraught yield size-distributions (including bimodal spectra) similar to those observed in natural clouds.Calculations of mixing during descent from cloud-top suggest that regions of substantial undersaturation may exist in the deep interiors of clouds which are entraining environmental air at their summits. Crude estimates of the degree of lateral spreading produced by turbulence as this descent proceeds indicates that significant horizontal structure in the water properties may exist throughout a substantial fraction of the cloud-depth.

Theoretical analysis of mixing in liquid clouds – Part 3: Inhomogeneous mixing

“…Note that time-dependent mixing was also considered in several studies (e.g., Baker et al, 1980;Baker and Latham, 1982;Jeffery and Reisner, 2006;Krueger et al, 1997;Kumar et al, 2012) using different approaches and numerical models. These studies, however, do not contain analysis on non-dimensional diffusionevaporation equation.…”

“…In this study, inhomogeneous mixing is investigated based on the analysis and solution of a 1-D diffusion-evaporation equation. To our knowledge, the idea of using a diffusive model of turbulent mixing to describe the mixing process was first proposed by Baker and Latham (1982). A diffusion-evaporation equation was also analyzed by Jeffery and Reisner (2006).…”

“…According to this concept, mixing of cloud air and sub-saturated air from cloud surrounding results in complete evaporation of a fraction of cloud droplets, whereas the size of other droplets remain unchanged. The studies of extremely inhomogeneous mixing were closely related to investigation of different mechanisms underlying enhanced growth of cloud droplets and warm precipitation formation (Baker et al, 1980;Baker and Latham, 1982). The concept of homogeneous mixing suggests that all the droplets partially evaporate, so the liquid water content decreases while the droplet concentration remains unchanged (Lehmann et al, 2009;Pt1).…”

Outlook for Research on Subtropical Marine Stratification Clouds

“…Liquid water fluxes are important (Randall, 1980a), and may be obtainable directly from aircraft measurements as well as remotely from millimeter-wavelength doppler radar. A related issue is the role of entrainment in determining the cloud droplet distribution (Baker and Latham, 1982). For this, microphysical measurements, in addition to dynamic and thermodynamic measurements, are needed.…”

Theoretical investigation of mixing in warm clouds – Part 2: Homogeneous mixing

“…Turbulent mixing at cloud edges and cloud tops accompanied by phase transitions has been the focus of numerous studies, beginning with the pioneering works of Baker and Latham (1979), Baker et al (1980), Blyth et al (1980) and Baker and Latham (1982). Laboratory experiments by Latham and Reed (1977) showed that after mixing with subsaturated air some droplets completely evaporate while others remain unchanged.…”