Does small-scale turbulence matter for ice growth in mixed-phase clouds?

TL;DR

This work investigates whether small-scale turbulence materially affects ice growth via the Wegener-Bergeron-Findeisen process in mixed-phase clouds. By building a DNS-validated statistical model grounded in mapping-closure theory and Gaussian Lagrangian supersaturation, the authors connect microphysical growth laws to turbulent transport and condensation dynamics. They show that, for the studied CTGC and Pi-chamber parameter regimes, turbulence largely leaves the mean radii and glaciation timing unchanged, while increasing droplet-size dispersion and potentially shifting glaciation transitions under certain conditions. The approach offers a pathway to parameterize turbulence–microphysics coupling in larger-scale cloud models, addressing a key gap in representing mixed-phase cloud glaciation and its radiative impact.

Abstract

Representing the glaciation of mixed-phase clouds in terms of the Wegener-Bergeron-Findeisen process is a challenge for many weather and climate models, which tend to overestimate this process because cloud dynamics and microphysics are not accurately represented. As turbulence is essential for the transport of water vapour from evaporating liquid droplets to ice crystals, we developed a statistical model using established closures to assess the role of small-scale turbulence. The model successfully captures results of direct numerical simulations, and we use it to assess the role of small-scale turbulence. We find that small-scale turbulence broadens the droplet-size distribution somewhat, but it does not significantly affect the glaciation time on submetre scales. However, our analysis indicates that turbulence on larger spatial scales is likely to affect ice growth. While the model must be amended to describe larger scales, the present work facilitates a path forward to understanding the role of turbulence in the Wegener-Bergeron-Findeisen process.

Figures (5)

• Figure 1: Model results for ice growth in cloud-top generating cells chen2023mixed. Shown are the DNS results of chen2023mixed (solid lines) for the mean droplet radius ( a), liquid-water content LWC ( b), the mean ice-particle radius ( c) and the ice mass ( d) as functions of time. In each panel, curves for four parameter sets are shown, these parameter sets are given in Table \ref{['tab:parameters_fig1']}. Only ice particles with $r_\text{i} > \qty{0.001}{\mu \text{m}}$ are included in the statistics chen2023mixed. Also shown are simulations of the statistical model (dashed lines), and of its deterministic limit (dash-dotted lines). The deterministic limit is so close to the full statistical-model results that the lines are hard to distinguish.
• Figure 2: Model results for ice growth in the core of the Pi chamber chen2024pi. Shown are the DNS results (Section \ref{['sec:dns']}) (solid lines) for the mean droplet radius ( a), the liquid-water content LWC ( b), the mean ice-particle radius ( c), the ice mass ( d), water droplet concentration ( e) and ice particle concentration ( f) as functions of time. In each panel, curves for five different ice-particle injection rates [cm$^{-3}$${\rm min}^{-1}$] are shown, the parameter values are given in the insets. Also shown are simulations of the statistical model (dashed lines), and of its deterministic limit (dash-dotted lines). In most but not all cases, the deterministic limit is so close to the full statistical-model results that the lines are hard to distinguish.
• Figure 3: (a) Relative dispersion of droplet radii for ice growth in cloud-top generating cells chen2023mixed. Shown are the DNS results of chen2023mixed (solid lines), simulations of the statistical model (dashed lines). (b) Statistical-model results for the Damköhler number $\text{Da}_{r_\text{w}}$ versus time for the same cases as shown in panel ( a).
• Figure 4: Relative dispersion of droplet radii for the Pi chamber chen2024pi, for different ice-particle injection rates [cm$^{-3}$${\rm min}^{-1}$]. Shown are the DNS results (Section \ref{['sec:dns']}, solid lines), simulations of the statistical model (dashed lines), and of its deterministic limit (dash-dotted lines).
• Figure 5: Final probability distributions of particle radii for the Pi chamber chen2024pi, for different ice-particle injection rates [cm$^{-3}$${\rm min}^{-1}$]. Shown are statistical-model results (solid lines), and from its deterministic limit (dashed). ( a) water droplets, ( b) ice particles.