Linear Eddy Modeling of Entrainment and Mixing in Stratus Clouds

Abstract

Mixing of entrained air in stratus clouds is an important but poorly understood process. It is a crucial ingredient of cloud-top entrainment instability (CEI). CEI has been proposed as a breakup mechanism for stratus clouds. A recently developed model called the linear eddy model was used to simulate mixing of air entrained into stratus clouds. The linear eddy approach involves stochastic simulation on a one-dimensional domain with sufficient resolution to include all physically relevant length scales. In each realization, molecular diffusion is implemented explicitly, while a sequence of statistically independent “rearrangement events” represents the effect of turbulent eddies. Inertial range scaling is incorporated. The linear eddy model was used to simulate the mixing of one or more wisps of entrained air with a specified volume of cloud-topped boundary layer (CTBL) air. The volume was idealized to be a horizontal slab of fluid that travels from the top of the CTBL down to the surface in the descending branch of a large convective eddy. The probability density function of the mixing fraction of entrained air was determined from linear eddy model simulations as a function of time for a mean mixing fraction of 0.05 and three wisp sizes. The effect of the mixing on the mean buoyancy of the downdraft could then be calculated given a specification of the buoyancy as a function of mixing fraction. In the simulations, the entrained air did not completely mix with cloudy air just below the CTBL top, nor was uniform saturation maintained. Furthermore, when buoyancy functions typical of observed CTBLs were used, the mean downdraft buoyancy due to entrainment and mixing integrated over the cloud layer remained positive. This suggests that CEI is unlikely in stratocumulus. An additional conclusion is that using reduced spatial resolutions typical of published large-eddy simulations (LES) of CTBLs in mixing simulations significantly underestimates the buoyancy in the cloud layer near cloud top. This may explain why low-resolution LFS simulations have exhibited CEI under conditions for which CEI is not observed in the atmosphere.