A numerical investigation of cloud-top entrainment instability and related experiments

Abstract

Buoyancy reversal occurs between two homogeneous fluids when as a result of non-linear mixing the mixture becomes denser than either of the fluids. In 1980 both Randall and Deardorff suggested that such nonlinear mixing, which may occur across a stratocumulus cloud-top as a consequence of evaporative cooling. could create an entrainment instability; the ensuing rapid entrainment could lead to stratocumulus break-up. This break-up mechanism is known as cloud-top entrainment instability or CTEI. In 1990 Shy and Breidenthal investigated buoyancy reversal within a laboratory environment and proposed a model for turbulent entrainment, and conditions under which buoyancy reversal may lead to an entrainment instability. They found that an instability could occur only if D (the ratio of the density difference between the most cooled mixed parcel and the lower fluid to the density difference across the unmixed layers) was approximately one or larger. This restriction of a strong buoyancy reversal for an instability (hence SBRI) is more stringent than Randall's condition, D ≥ 0, and is almost never satisfied at the inversion topping a marine stratocumulus layer. We have used numerical simulations of a single eddy at an interface between two fluids to explore the entrainment model of Shy and Breidenthal. Consistent with SBRI. we find that in all cases a critical value of D, Dc, between 0.3 and 2.0 exists. For D Dc, kinetic energy is found to increase on the scale of the entraining eddy. We expand the domain to model the interaction of the multiple eddies with an entrainment interface. We find a similar Dc where unstable entrainment is exhibited, and a tendency for larger eddies to develop if Dc. > D. We explore the influence of the fluid and flow characteristics on Dc to bridge the gap between the laboratory and the atmosphere. We find that Dc is lower at Schmidt numbers of order unity, characteristic of the atmosphere, than for those equal to 103, typical of the laboratory fluid. In all cases Dc remains too large to be a factor in stratocumulus break-up.