Subgrid Scale Modeling of Turbulence and Cloud Microphysics Interactions

Abstract

Clouds have a significant but uncertain impact on Earth's climatological and hydrological cycles. In particular, the warm rain process has considerable inconsistencies between current theories and observations. One hypothesis to explain this is the role of turbulence in broadening the droplet size distribution. The primary methods of studying these processes have been through laboratory studies, direct numerical simulations, and large eddy simulations. However, these processes are difficult to study as they occur on a broad range of scales. This makes large eddy simulations appealing as they remain computationally efficient by modeling the smallest, dissipative scales of motion. While past studies have made efforts to improve the subgrid-scale stress tensor and scalar flux vectors in large-eddy simulations, subgrid-scale terms related to cloud microphysics have received little attention. Specifically, subgrid-scale supersaturation variance is important when considering a Lagrangian microphysics approach as it arises from the Langevin equation, and both subgrid scale supersaturation and concentration covariance and subgrid scale concentration variance arise from the filtered evolution equation for droplet size distribution. It is these terms that were the focus of this study. This study computed the true subgrid-scale variance and covariance terms from data of direct numerical simulations of Rayleigh-Bénard convection in the Michigan Technological University Pi Chamber. Five cases of varying aerosol injection rates were considered, each with a Rayleigh number of 7.9x10^6. The true subgrid-scale terms were compared to two candidate models: the gradient model and the scale-similarity model. Statistical analysis consisting of probability density functions, joint probability density functions, and correlation coefficients was used to assess model performance. Results concluded that the gradient model had relatively poor agreement with the true subgrid-scale terms with joint probability density functions that did not follow the one-to-one line which would indicate good skill, and correlation coefficients between 0 - 0.4. In contrast, results from the similarity model indicated joint probability density functions that closely followed the one-to-one line, and correlation coefficients between 0.3 - 0.9 suggesting good agreement between the true and modeled subgrid-scale term. Altogether, the similarity model showed promise for modeling the subgrid-scale supersaturation variance, supersaturation and concentration covariance, and concentration variance. However, future investigation with higher Rayleigh numbers is warranted where larger scale separation exists between the large and small scales of turbulence.