Benchmarking Turbulence Models to Represent Cloud-Edge Mixing

TL;DR

The paper benchmarks four statistical turbulence models (LEM, EHM, RMM, MCM) against direct numerical simulations (DNS) to represent cloud-edge mixing, focusing on thermodynamics and microphysics. DNS serves as the ground truth, while the models differ in how they treat supersaturation fluctuations and droplet growth. All approaches capture thermodynamic evolution, but accurate microphysical predictions require representing spatial variability in supersaturation; LEM and MCM (and partially RMM) succeed, whereas EHM tends toward homogeneous mixing. The results guide the use of these models as subgrid-scale closures in LES, highlighting that MCM demands DNS-informed closures and that LEM/EHM have environment-dependent limitations, with DNS remaining essential for fidelity.

Abstract

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. 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). Implications of these results for using the presented models as subgrid-scale schemes are discussed.

Figures (9)

• Figure 1: Initial (a) $q_{\mathrm{v,i}}$, (b) $T_\text{i}$, (c) $S_i$, and (d) $q_{\mathrm{c,i}}$ profiles for different thermodynamics (denoted $n_0$-$n_3$, colored lines) or $r_\text{i}$ (gray lines). In (b), the reference temperature $T_0$ is shown (gray dashed-dotted line).
• Figure 2: For individual timesteps (blue to green), the development of the relative supersaturation (a), the $q_{\mathrm{c}}$ (b), the droplet concentration (c) and the conditional average of the droplet radius (d) are shown along the entrainment profile. $r_{\mathrm{m}}$ is calculated as an arithmetic mean of an ensemble of 1000 simulation runs, where only gridboxes that contain at least one particle are taken into account.
• Figure 3: Time evolution of the domain-averaged, that is, arithmetic mean of all grid boxes, (a) $q_\mathrm{v}$, (b) $T$, (c) $q_{\mathrm{c}}$ and (d) $S$, for four different energy dissipation rates (colors), and five models (pattern). Note that the DNS results are always in black to highlight them.
• Figure 4: Time evolution of the domain-averaged, that is, arithmetic mean of all grid boxes, (a) $N_\mathrm{c}$, (b) $r_{\mathrm{m}}$ for four different energy dissipation rates (colors), and five models (pattern). Note that the DNS results are always in black to highlight them.
• Figure 5: Time evolution of the domain-averaged, (a) $q_\mathrm{v}$, (b) $T$, (c) $q_{\mathrm{c}}$ and (d) $S$ for four different ambient humidities (colors), and five models (patterns). Note that the DNS results are always in black to highlight them. In (b) the reference temperature $T_0$ is shown (grey dashed-dotted line