Bulk Scaling Model of Entrainment Zone Thickness in a Convective Boundary Layer, with a Shear Effect Promoted by Velocity Difference

Anran Li,Wenfeng Gao,Tao Liu

doi:10.3390/atmos11010063

Abstract

Studying the thickness of the convective boundary layer (CBL) is helpful for understanding atmospheric structure and the diffusion of air pollutants. When there is velocity shear in CBL, the flow field structure is very different from that of shear-free CBL, which makes the thickness model of the entrainment zone deviate. A large-eddy simulation (LES) approach is carried out for a horizontally homogeneous, atmospheric CBL, with a shear effect promoted by velocity difference to explore the bulk scaling model of the entrainment zone thickness. The post-processed data indicate that the existing bulk scaling models cannot synthetically represent the effects of shear and buoyancy on entrainment, resulting in reduced accuracy or limited applicability. Based on the fraction of turbulent kinetic energy (TKE) used for entrainment, a different form of the characteristic velocity scale, which includes the shear effect, is proposed, and a modified bulk scaling model that uses a potential temperature gradient to replace the potential temperature jump across the entrainment zone is constructed with the numerical results. The new model is found to provide an improved prediction of the entrainment zone thickness in a sheared CBL.

Highlights

Due to the compound influence of surface radiation, potential temperature gradient, wind shear, and other factors, the flow field in a sheared convective boundary layer (CBL) is complex; this is especially true in the entrainment zone formed by shear and buoyancy between the mixed zone and the free atmosphere, which restricts the exchange of matter and heat between the layers
Since horizontal averages may be taken as substitutes for the ensemble averages in the horizontally homogeneous CBL, the horizontally averaged flow statistics are assumed to converge to corresponding ensemble means
Model 2 uses the entrainment velocity we as the velocity scale, which implicitly reflects the influence of the CBL characteristic factors on entrainment

Summary

Introduction

Due to the compound influence of surface radiation, potential temperature gradient ( named inversion strength), wind shear, and other factors, the flow field in a sheared convective boundary layer (CBL) is complex; this is especially true in the entrainment zone formed by shear and buoyancy between the mixed zone and the free atmosphere, which restricts the exchange of matter and heat between the layers. The current bulk scaling models for the entrainment zone are primarily based on the CBL framework of a “zero-order model” (ZOM) [5] and a “first-order model” (FOM) [6]. The height of the entrainment zone, zi , as sketched, is defined by the level of the buoyancy flux minimum w0 θ0 i , and the upper limit of the entrainment zone, z2 , is the zero-crossing height of the buoyancy flux profile, using linear interpolation between discrete grid points. The height of the mixed zone, z1 , takes the corresponding level of zero buoyancy flux. Due to the large-scale turbulent eddies in the entrainment zone, it is difficult to accurately locate the height of zero buoyancy flux in the upper layer, and Fedorovich et al [7] and Conzemius and Fedorovich [3,4] adopted the height at which the Atmosphere 2020, 11, 63; doi:10.3390/atmos11010063 www.mdpi.com/journal/atmosphere

Methods

Results

Conclusion