The Stability of Cloud Top with Regard to Entrainment: Amendment of the Theory of Cloud-Top Entrainment Instability

Abstract

The stability of a uniformly saturated cloud layer separated from an overlying nonturbulent unsaturated layer by a thin inversion is considered. The stability of the interface can be described by entraining a parcel of air from above the inversion into the cloud layer below and by subsequently studying the effect of the mixing on the buoyancy of the parcel. From the relevant momentum equation for the parcel it is shown that the important quantity to consider is the total buoyancy (total mass of the parcel times the virtual potential temperature difference between parcel and environment) of the parcel per unit mass of entrained air. The total buoyancy is a more general and useful concept than all other parameters discussed in the literature.