Mixing driven by radiative and evaporative cooling at the stratocumulus top

The stratocumulus-top mixing process is investigated using direct numerical simulations of a shear-free cloud-top mixing layer driven by evaporative and radiative cooling. An extension of previous linear formulations allows for quantifying radiative cooling, evaporative cooling, and the diffusive effects that artificially enhance mixing and evaporative cooling in high-viscosity direct numerical simulations (DNS) and many atmospheric simulations. The diffusive cooling accounts for 20% of the total evaporative cooling for the highest resolution (grid spacing ~14 cm), but this can be much larger (~100%) for lower resolutions that are commonly used in large-eddy simulations (grid spacing ~5 m). This result implies that the κ scaling for cloud cover might be strongly influenced by diffusive effects. Furthermore, the definition of the inversion point as the point of neutral buoyancy allows the derivation of two scaling laws. The in-cloud scaling law relates the velocity and buoyancy integral scales to a buoyancy flux defined by the inversion point. The entrainment-zone scaling law provides a relationship between the entrainment velocity and the liquid evaporation rate. By using this inversion point, it is shown that the radiative-cooling contribution to the entrainment velocity decouples from the evaporative-cooling contribution and behaves very similarly as in the smoke cloud. Finally, evaporative and radiative cooling have similar strengths, when this strength is measured by the integrated buoyancy source. This result partially explains why current entrainment parameterizations are not accurate enough, given that most of them implicitly assume that only one of the two mechanisms rules the entrainment