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Volume 16, issue 14
Atmos. Chem. Phys., 16, 9273–9297, 2016
https://doi.org/10.5194/acp-16-9273-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
Atmos. Chem. Phys., 16, 9273–9297, 2016
https://doi.org/10.5194/acp-16-9273-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 28 Jul 2016

Research article | 28 Jul 2016

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

Mark Pinsky1, Alexander Khain1, and Alexei Korolev2 Mark Pinsky et al.
  • 1Department of Atmospheric Sciences, The Hebrew University of Jerusalem, Jerusalem, Israel
  • 2Environment Canada, Cloud Physics and Severe Weather Section, Toronto, Canada

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. >

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Short summary
An idealized diffusion--evaporation model of time-dependent mixing between cloud and non-cloud volumes is analyzed. It is shown that the evolution of microphysical variables and the final equilibrium stage are unambiguously determined by two non-dimensional parameters. Delimitation between the types of mixing on the plane of these parameters is carried out. The definitions of homogeneous and inhomogeneous mixings are reconsidered and clarified. Results are compared with the classical concept.
An idealized diffusion--evaporation model of time-dependent mixing between cloud and non-cloud...
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