Numerical Experiments on the Dynamics of the Cloud–Environment Interface: Small Cumulus in a Shear-Free Environment

Abstract

We report herein high resolution two-dimensional numerical experiments on the dynamics of the mixing between the environment and a small cumulus cloud in the absence of shear. The current paper extends the work of Klaassen and Clark. Serious numerical errors associated with the finite-difference approximations to the conservation laws for the thermodynamic variables were identified. These errors led to an unrealistic supersaturation field (or condensation rate field) new cloud edges. To avoid these numerical artifacts, the prognostic conservation equation for the water vapor mixing ratio was replaced by the appropriate prognostic equation for the supersaturation (which lead to a diagnostic treatment for the water vapor) and refined numerical techniques were used. The experiments reported in this paper were performed using both prognostic and diagnostic approaches for water vapor. Each of these was used with bulk and detailed microphysics. Model results showed a consistent picture of the entrainment into a small cumulus cloud in the absence of environmental shear: the development and further evolution of nodes near lateral cloud boundaries generated an entraining region between the undiluted core and the environment. As in Klaassen and Clark, the driving mechanism for the entrainment process in then two-dimensional simulations was the generation of vorticity by horizontal buoyancy gradients across the cloud-environment interface. In contrast to their results, formation of nodes near the cloud top was not observed and downdrafts did not form. The evolution of cloud boundary instabilities was not affected by replacing the bulk microphysics with the detailed microphysics up to the finest scales resolved (2 meters). For the assumed maritime type of cloud condensation nuclei, the supersaturation field in the entraining eddies was characterized by maximum values substantially higher than those present inside the undiluted core far from the cloud-base primary nucleation region. These results are discussed in the context of the recent observational and theoretical studies of the entrainment processes in convective clouds.