Considering turbulence is crucial to understanding clouds. However, covering all scales involved in the turbulent mixing of clouds with their environment is computationally challenging, urging the development of simpler models to represent some of the processes involved. By using full direct numerical simulations as a reference, this study compares several statistical approaches for representing small-scale turbulent mixing, while assessing their applicability as subgrid-scale models for large-eddy simulations. All models use a comparable Lagrangian representation of cloud microphysics and simulate the same cases of cloud-edge mixing, covering different ambient humidities and turbulence intensities. It is demonstrated that all statistical models represent the evolution of thermodynamics successfully, but not all models capture the changes in cloud microphysics (cloud droplet number concentration, droplet mean radius, and spectral width). Accurate microphysical evolution arises when the modeling framework represents spatially heterogeneous supersaturation and its time evolution along mixing interfaces, either by explicitly resolving turbulence or by evolving the full probability distribution of the scalar. Models that relax toward a space-dependent mean recover key features such as spatial asymmetry and partial broadening and, therefore, constitute a useful representation of mixing under carefully chosen circumstances. By comparison, models relying on a space-independent mean systematically compress the distribution. These results identify the representation of supersaturation variability and its history as the primary requirement for representing small-scale mixing in clouds.
Significance Statement
Although small-scale turbulence is crucial to the development of clouds, the representation of its effects is challenging. Direct numerical simulations accurately represent the underlying fluid dynamics and cloud microphysical processes on all relevant length and time scales but require enormous computational resources. Therefore, simplified models are used to parameterize the effects of small-scale turbulence on clouds. Here, we compare four approaches of different complexities to the results from direct numerical simulations. While simpler models successfully capture changes in thermodynamic quantities, the adequate consideration of spatial dependencies is shown to be necessary to represent the development of cloud droplets.
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