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

Mark Pinsky,Alexander Khain,Alexei Korolev

doi:10.5194/acp-16-9273-2016

Mark Pinsky, Alexander Khain + Show 1 more

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https://doi.org/10.5194/acp-16-9273-2016

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Abstract

Abstract. An idealized diffusion–evaporation model of time-dependent mixing between a cloud volume and a droplet-free volume is analyzed. The initial droplet size distribution (DSD) in the cloud volume is assumed to be monodisperse. It is shown that evolution of the microphysical variables and the final equilibrium state are unambiguously determined by two non-dimensional parameters. The first one is the potential evaporation parameter R, proportional to the ratio of the saturation deficit to the liquid water content in the cloud volume, that determines whether the equilibrium state is reached at 100 % relative humidity, or is characterized by a complete evaporation of cloud droplets. The second parameter Da is the Damkölher number equal to the ratio of the characteristic mixing time to the phase relaxation time. Parameters R and Da determine the type of mixing.The results are analyzed within a wide range of values of R and Da. It is shown that there is no pure homogeneous mixing, since the first mixing stage is always inhomogeneous. The mixing type can change during the mixing process. Any mixing type leads to formation of a tail of small droplets in DSD and, therefore, to DSD broadening that depends on Da. At large Da, the final DSD dispersion can be as large as 0.2. The total duration of mixing varies from several to 100 phase relaxation time periods, depending on R and Da.The definitions of homogeneous and inhomogeneous types of mixing are reconsidered and clarified, enabling a more precise delimitation between them. The paper also compares the results obtained with those based on the classic mixing concepts. >

Highlights

Cloud physics typically investigates two types of turbulent mixing: homogeneous and extremely inhomogeneous (e.g., Burnet and Brenguier, 2007; Andrejczuk et al, 2009; Devenish et al, 2012; Kumar et al, 2012)
The mixing is simulated by solving a diffusion–evaporation equation written in the non-dimensional form
Analysis of the diffusion–evaporation equation shows that the time-dependent process of mixing and the final equilibrium state depend on two non-dimensional parameters

Summary

Introduction

Cloud physics typically investigates two types of turbulent mixing: homogeneous and extremely inhomogeneous (e.g., Burnet and Brenguier, 2007; Andrejczuk et al, 2009; Devenish et al, 2012; Kumar et al, 2012). The concept of extremely inhomogeneous mixing in clouds was introduced by Latham and Reed (1977), Baker and Latham (1979), Baker et al (1980) and Blyth et al (1980) 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 significance of the concepts of homogeneous and inhomogeneous mixing goes far beyond formation of large-sized droplets These concepts are closely related to the mechanisms involved in formation of droplet size distributions (DSD) in clouds and to the description of this formation in numerical cloud models. A detailed analysis of the classical concepts of homogeneous and extremely inhomogeneous mixing is given by Korolev et al (2016, hereafter Pt1)

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