Simulations of Rising Thermals Using a Lagrangian Stochastic Closure for the Subgrid Turbulent Fluxes

Turbulent clouds are challenging to model and simulate due to uncertainties in processes occurring at unresolved subgrid scales (SGS). These processes include the transport of cloud particles, supersaturation fluctuations, turbulent mixing, and the resulting stochastic droplet activation and growth by condensation. In this work, we use a stochastic Filtered Density Function (FDF) particle method to describe both temperature and the amount of water vapor distribution at unresolved scales in rising thermals. The particle method is solved in combination with an Eulerian scheme (here we use the CM1 model, Bryan and Fritsch 2002). In this hybrid implementation, the particle method plays two important roles: (a) it models the SGS variability of the environment where cloud particles would activate and grow by condensation, and (b) it provides the SGS unresolved fluxes that close the filtered equations underlying the Eulerian scheme, devoid of any approximation. The hybrid algorithm is tested in 2D and 3D simulations of dry and moist thermals against schemes that use standard subgrid models (such as Deardorff’s parametrization of the eddy viscosity). Our simulations suggest that FDF models may expand the ability of Large Eddy Simulations to represent cloud entrainment and associated microphysical details at the edge of cumulus clouds. Furthermore, the intrinsic character of this particle-based method is also useful to study generation and reorientation of vorticity around and within thunderstorm clouds.