Entrainment in Cumulus Clouds: What Resolution is Cloud-Resolving?

Systematic numerical experiments were conducted to determine the spatial resolution required to resolve a moist thermal show convergence at a scale proportional to the smaller of the initial thermal diameter D-0 and a buoyancy length scale L-buoy. The buoyancy length scale L-buoy = Delta T-0/Delta Gamma (Delta T-0 is the initial buoyancy excess of the thermal and Delta Gamma is the ambient stratification) describes the maximum vertical displacement that can be induced against the stratification in the environment by buoyancy-driven pressure perturbations in the cloud and, thus, the maximum scale of eddies that cross the cloud boundary. For typical atmospheric conditions in which the cloud size D-0 is larger than L-buoy, numerical simulations of the mixing processes in cumulus clouds must resolve L-buoy.