Direct Numerical Simulation of Evaporative Cooling at the Lateral Boundary of Shallow Cumulus Clouds

Abstract

Abstract This study investigates the dynamics of the subsiding shell at the lateral boundary of cumulus clouds, focusing on the role of evaporative cooling. Since the size of this shell is well below what large-eddy simulations can resolve, the authors have performed direct numerical simulations of an idealized subsiding shell. The system develops a self-similar, Reynolds number–independent flow that allows for the determination of explicit scaling laws relating the characteristic length, time, and velocity scales of the shell. It is found that the shell width grows quadratically in time, linearly with the traveled distance. The magnitude of these growth rates shows that evaporative cooling, in its most idealized form, is capable of producing a fast-growing shell with numbers that are consistent with observations of the subsiding shell around real shallow cumulus clouds: for typical thermodynamic conditions in cumulus clouds, a velocity on the order of 1 m s−1 and a thickness on the order of 10 m are established in about 2 min. This fits well within the typical cloud lifetime, suggesting that this idealization is an adequate framework for the analysis of relevant aspects in the subsiding shell associated with buoyancy reversal. It also indicates that the scaling laws derived here can be used to estimate the potential strength of a subsiding shell and the mean lateral entrainment associated with it, once an estimate of the local thermodynamical state of the cloud boundary is provided. It is shown that the dominant parameter of this system is the saturation buoyancy, whereas the effect of the saturation mixing fraction is minor.