A Fractal Interfacial Entrainment Model for Dry Convective Boundary Layers. Part II: Discussion of Model Behavior and Comparison with Other Models

Abstract

Details of the fractal interfacial entrainment (FIE) model recently presented by Kamada are compared to those of previous models, water tank results, and atmospheric data from the Wangara experiment. Effects of capping inversion resolution and anisotropy upon total, lateral and cloud top entrainment are discussed. Modeling of interfacial shear is also considered. The use of mean interfacial depth refines previous corrections for finite inversion depths. Analysis of the component TKE budgets shows that lateral entrainment dominates, but that this feature does not alter overall entrainment rates. The FIE schema support the indirect view of cloud top entrainment. Mixed layer height simulations for Wangara, day 33, agree roughly with previous estimates as they should. Ball ratios and entrainment rates among various models do, however, diverge at large and small overall Richardson numbers, respectively. As convective activity subsides, inversion level TKE may be maintained by increased shear production due to interfacial thinning. This would allow the mixed layer to remain inversion capped until total collapse. For episodic entrainment models of the Manins type with large interfacial shear, a unit valued, local, critical Froude or Richardson number is proposed. The oft assumed one-fourth value for the critical Richardson number does not apply here because converging plumes will enhance the scale of eddies which initiate the cascade. This implies larger buoyancy losses of TKE in the inversion than in the stable surface layer for the same degree of stratification and thus a larger critical Richardson number. These results also suggest that the minimum velocity for an entraining eddy is ≈2w*. We also describe an inversion length scale hierarchy which shows Reynolds and Richardson number similarity.