Characterization of wind-shear effects on entrainment in a convective boundary layer

Abstract

Direct numerical simulations are used to characterize wind-shear effects on entrainment in a barotropic convective boundary layer (CBL) that grows into a linearly stratified atmosphere. We consider weakly to strongly unstable conditions $-z_{enc}/L_{Ob}\gtrsim 4$, where $z_{enc}$ is the encroachment CBL depth and $L_{Ob}$ is the Obukhov length. Dimensional analysis allows us to characterize such a sheared CBL by a normalized CBL depth, a Froude number and a Reynolds number. The first two non-dimensional quantities embed the dependence of the system on time, on the surface buoyancy flux, and on the buoyancy stratification and wind velocity in the free atmosphere. We show that the dependence of entrainment-zone properties on these two non-dimensional quantities can be expressed in terms of just one independent variable, the ratio between a shear scale $(\unicode[STIX]{x0394}z_{i})_{s}\equiv \sqrt{1/3}\unicode[STIX]{x0394}u/N_{0}$ and a convective scale $(\unicode[STIX]{x0394}z_{i})_{c}\equiv 0.25z_{enc}$, where $\unicode[STIX]{x0394}u$ is the velocity increment across the entrainment zone, and $N_{0}$ is the buoyancy frequency of the free atmosphere. Here $(\unicode[STIX]{x0394}z_{i})_{s}$ and $(\unicode[STIX]{x0394}z_{i})_{c}$ represent the entrainment-zone thickness in the limits of weak convective instability (strong wind) and strong convective instability (weak wind), respectively. We derive scaling laws for the CBL depth, the entrainment-zone thickness, the mean entrainment velocity and the entrainment-flux ratio as functions of $(\unicode[STIX]{x0394}z_{i})_{s}/(\unicode[STIX]{x0394}z_{i})_{c}$. These scaling laws can also be expressed as functions of only a Richardson number $(N_{0}z_{enc}/\unicode[STIX]{x0394}u)^{2}$, but not in terms of only the stability parameter $-z_{enc}/L_{Ob}$.

Steady-State Large-Eddy Simulations of Convective and Stable Urban Boundary Layers

“…• a relatively uniform volumetric cooling (that shows agreement with the R profile obtained using method vi; shown in Fig. 8b) • a stabilizing velocity w s that sharply decreases over the entrainment zone with a lower peak than that obtained from method vi, which is partly due to the use of an entrainment ratio of −0.25 in method vi (varies under sheared-convective conditions; Liu et al 2018;Haghshenas and Mellado 2019) and partly due to the discussed limitations of the applied temporal averaging) • a linear decrease in both the parameters w s and R for z > h that forces the flow in the free atmosphere to the predefined lapse rate, Γ = − 0.003 K m −1 .…”

“…1) can be defined to produce a mean temperature profile with a predefined boundary-layer height and inversion strength a priori. However, this method is limited due to its employment of the entrainment ratio as this term changes under sheared-convective conditions (Liu et al 2018;Haghshenas and Mellado 2019) and because no such simplification and closure scheme exists in the stable case. Method vi was applied to reproduce the mean temperature profile of the convective reference state.…”

Evolution of Oceanic Near-Surface Stratification in Response to an Autumn Storm

“…Studies of entrainment in the sheared convective atmospheric boundary layer show that shear production of turbulence in the inversion can occur for gradient Richardson number significantly above 1/3 (Haghshenas and Mellado 2019), similar to the situation during the storm. Haghshenas and Mellado (2019) found that as the shear increases, the gradient Richardson number tends to a value of about 1/3, similar to the values in the LES (Grant and Belcher 2011). While the present situation is not directly comparable to entrainment in the atmospheric boundary layer, the interaction between the well-mixed layer and the transition layer through the transport of TKE may help explain why the results obtained with Eq.…”

Nonsingular Zero-Order Bulk Models of Sheared Convective Boundary Layers

“…This singularity arises when the entrainment parameterization is derived in the idealized framework of the bulk models and the CBL depth is used in the scaling of the shear production at the CBL top in the local TKE approach (see, e.g., Tennekes and Driedonks 1981), or is used in the scaling of the integral of the negative buoyancy flux in the integral TKE approach (see, e.g., Boers et al 1984). This is physically inconsistent with the observation that, under strong-wind-shear conditions, the entrainment zone, defined as the region of negative buoyancy flux at the boundary layer top, is characterized by a local length scale that is different from the CBL depth (Zeman and Tennekes 1977;Kim et al 2003;Pino and Vilà-Guerau De Arellano 2008;Haghshenas and Mellado 2019). Applying this local length scale in the integral analysis of the TKE budget, Haghshenas and Mellado (2019) derived nonsingular parameterizations for different CBL properties.…”

“…In this paper, we show that the infinitesimal transition-layer representation of the ZOM is sufficient to precisely reproduce bulk properties in the cloud-free sheared CBL, as long as the entrainment closure appropriately represents the local effects of wind shear on entrainment. If required, the actual finite thickness of the transition layer can be constructed a posteriori at the top of the predicted zero-order CBL depth using either the relationships between the zero-order CBL depth and various actual CBL depths provided in Haghshenas and Mellado (2019) or the transition-layer parameterizations proposed in previous work (Pino et al 2006;Kim et al 2006;Liu et al 2016). (By the term ''actual CBLs,'' we explicitly mean atmospheric CBLs or threedimensional simulations of them.…”