Evaluating the Parameterization of Entrainment Process through the Large-Eddy Simulation

This study investigates the entrainment process at the top of sheared convective boundary layer (CBL) by means of the large-eddy simulation (LES). The case with geostrophic wind linearly increasing with height (GS) is considered. Simulations are conducted for CBLs growing under varying conditions of surface roughness, free-atmospheric stratification, and geostrophic wind shear. The data are collected in the period when the turbulence is in steady state. According to the simulated vertical distributions of potential temperature, velocity, and heat and momentum fluxes, the profiles of these variables are idealized in the framework of first-order jump model (FOM). By using the idealized profiles in CBL, the parameterization scheme of entrainment ratio, which is defined as the ratio of heat flux at the CBL top to the value at the surface, is derived from the turbulent kinetic energy (TKE) budget. As compared to the constant geostrophic wind (GC) case, an additional term, which represents the contribution of shear-produced TKE in the mixed layer, should be considered. A new turbulent velocity scale is proposed and used in the parameterization scheme of entrainment zone depth. The LES data are employed to test the parameterization schemes of entrainment flux ratio and entrainment zone depth. The results show that about 40% shear-produced TKE at the CBL top is contributed to the entrainment process. This value is much smaller than that proposed by Kim et al. (2006) and Pino et al. (2006), but slightly larger than that suggested by Sun and Xu (2009). The comparison indicates that the new parameterization of entrainment zone depth is slightly better than those proposed by Kim et al. (2006). The LES data also show that the contribution of shear-produced TKE in the surface layer to the entrainment process is negligibly small. The contribution of shear-produced TKE in the mixed layer to the entrainment process is also very small, but it increases during the CBL development. Thus it cannot be neglected for the well developed CBL, especially when the geostrophic wind shear is relatively large.