Abstract

The paper presents an extended theoretical background for applied modeling of the atmospheric convective boundary layer within the so-called zero-order jump approach, which implies vertical homogeneity of meteorological fields in the bulk of convective boundary layer (CBL) and zero-order discontinuities of variables at the interface of the layer.

The zero-order jump model equations for the most typical cases of CBL are derived. The models of nonsteady, horizontally homogeneous CBL with and without shear, extensively studied in the past with the aid of zero-order jump models, are shown to be particular cases of the general zero-order jump theoretical framework. The integral budgets of momentum and heat are considered for different types of dry CBL. The profiles of vertical turbulent fluxes are presented and analyzed. The general version of the equation of CBL depth growth rate (entrainment rate equation) is obtained by the integration of the turbulence kinetic energy balance equation, invoking basic assumptions of the zero-order parameterizations of the CBL vertical structure. The problems of parameterizing the turbulence vertical structure and closure of the entrainment rate equation for specific cases of CBL are discussed. A parameterization scheme for the horizontal turbulent exchange in zero-order jump models of CBL is proposed. The developed theory is generalized for the case of CBL over irregular terrain.

Abstract

A model of the atmospheric convective boundary layer (CBL) is realized in the thermally stratified wind tunnel of the Institute of Hydrology and Water Resources, University of Karlsruhe. Further experimental results from this model are presented. The wind tunnel with a test section 10 m long, 1.5 m wide, and 1.5 m high allows one to generate a quasi-stationary, horizontally evolving CBL, characterized by convective Richardson numbers Ri_ΔT up to 10 and Ri _N up to 20, with the bottom shear/buoyancy dynamic ratio u _*/w _* in the range of 0.2 to 0.5. The convective regime in the tunnel is dominated by bottom-up forcings. Effects of entrainment in the simulated CBL play a secondary role.

The spectra of turbulence in the wind tunnel flow are calculated from high-resolution velocity component and temperature time series, simultaneously measured using laser Doppler and resistance-wire technique, respectively. The spectra from the mixed core of the CBL and in the entrainment zone display pronounced inertial subranges. The ratio of vertical to horizontal velocity spectra in these subranges is within the interval from 1.3 to 2, which is slightly larger than could be expected for purely isotropic turbulence. Different maxima in the production ranges of the spectra are related to dominant turbulence scales in the wind tunnel flow. The energy-containing ranges of the wind tunnel spectra exhibit plateaulike shapes resulting from modification of the turbulence production by the flow shear. The comparison with atmospheric spectra and spectral data from water tank and large eddy simulation studies of the CBL suggests that the turbulence spectral regime in the tunnel flow has much in common with its atmospheric prototype.

The turbulence kinetic energy dissipation rate and the destruction rate of temperature fluctuations are evaluated based on the relationships resulting from the Kolmogorov theory for the inertial-subrange spectra. The dissipation rates obtained are within the scatter ranges of data from atmospheric measurements and model studies of convection. High dissipation values in the lower portion of the simulated CBL are indicative of the shear enhancement of turbulence production in the wind tunnel convective flow.

Abstract

A set of first-order model (FOM) equations, describing the sheared convective boundary layer (CBL) evolution, is derived. The model output is compared with predictions of the zero-order bulk model (ZOM) for the same CBL type. Large eddy simulation (LES) data are employed to test both models. The results show an advantage of the FOM over the ZOM in the prediction of entrainment, but in many CBL cases, the predictions by the two models are fairly close. Despite its relative simplicity, the ZOM is able to quantify the effects of shear production and dissipation in an integral sense—as long as the constants describing the integral dissipation of shear- and buoyancy-produced turbulence kinetic energy (TKE) are prescribed appropriately and the shear is weak enough that the denominator of the ZOM entrainment equation does not approach zero, causing a numerical instability in the solutions. Overall, the FOM better predicts the entrainment rate due to its ability to avoid this instability. Also, the FOM in a more physically consistent manner reproduces the sheared CBL entrainment zone, whose depth is controlled by a balance among shear generation, buoyancy consumption, and dissipation of TKE. Such balance is manifested by nearly constant values of Richardson numbers observed in the entrainment zone of simulated sheared CBLs. Conducted model tests support the conclusion that the surface shear generation of TKE and its corresponding dissipation, as well as the nonstationary terms, can be omitted from the integral TKE balance equation.

Abstract

Results are presented from a combined numerical and observational study of the convective boundary layer (CBL) diurnal evolution on a day of the International H₂O Project (IHOP_2002) experiment that was marked by the passage of a dryline across part of the Oklahoma and Texas Panhandles. The initial numerical setup was based on observational data obtained from IHOP_2002 measurement platforms and supplementary datasets from surrounding locations. The initial goals of the study were as follows: (i) numerical investigation of the structure and evolution of the relatively shallow and homogeneous CBL east of the dryline by means of large-eddy simulation (LES), (ii) evaluation of LES predictions of the sheared CBL growth against lidar observations of the CBL depth evolution, and (iii) comparison of the simulated turbulence structures with those observed by lidar and vertically pointing radar during the CBL evolution. In the process of meeting these goals, complications associated with comparisons between LES predictions and atmospheric observations of sheared CBLs were encountered, adding an additional purpose to this study, namely, to convey and analyze these issues.

For a period during mid- to late morning, the simulated CBL evolution was found to be in fair agreement with atmospheric lidar and radar observations, and the simulated entrainment dynamics were consistent with those from previous studies. However, CBL depths, determined from lidar data, increased at a faster rate than in the simulations during the afternoon, and the wind direction veered in the simulations more than in the observations. The CBL depth discrepancy can be explained by a dryline solenoidal circulation reported in other studies of the 22 May 2002 case. The discrepancy in winds can be explained by time variation of the large-scale pressure gradient, which was not included in LES.

Abstract

As computing capabilities expand, operational and research environments are moving toward the use of finescale atmospheric numerical models. These models are attractive for users who seek an accurate description of small-scale turbulent motions. One such numerical tool is the Weather Research and Forecasting (WRF) model, which has been extensively used in synoptic-scale and mesoscale studies. As finer-resolution simulations become more desirable, it remains a question whether the model features originally designed for the simulation of larger-scale atmospheric flows will translate to adequate reproductions of small-scale motions. In this study, turbulent flow in the dry atmospheric convective boundary layer (CBL) is simulated using a conventional large-eddy-simulation (LES) code and the WRF model applied in an LES mode. The two simulation configurations use almost identical numerical grids and are initialized with the same idealized vertical profiles of wind velocity, temperature, and moisture. The respective CBL forcings are set equal and held constant. The effects of the CBL wind shear and of the varying grid spacings are investigated. Horizontal slices of velocity fields are analyzed to enable a comparison of CBL flow patterns obtained with each simulation method. Two-dimensional velocity spectra are used to characterize the planar turbulence structure. One-dimensional velocity spectra are also calculated. Results show that the WRF model tends to attribute slightly more energy to larger-scale flow structures as compared with the CBL structures reproduced by the conventional LES. Consequently, the WRF model reproduces relatively less spatial variability of the velocity fields. Spectra from the WRF model also feature narrower inertial spectral subranges and indicate enhanced damping of turbulence on small scales.

Abstract

The reported study examines the dynamics of entrainment and its effects on the evolution of the dry atmospheric convective boundary layer (CBL) when wind shear is present. The sheared CBL can be studied by means of direct measurements in the atmosphere, laboratory studies, and numerical techniques. The advantages and disadvantages of each technique are discussed in the present paper, which also describes the methodological background for studying the dynamics of entrainment in sheared CBLs. For the reported study, large-eddy simulation (LES) was chosen as the primary method of convective entrainment investigation. Twenty-four LES runs were conducted for CBLs growing under varying conditions of surface buoyancy flux, free-atmospheric stratification, and wind shear. The simulations were divided into three categories: CBL with no mean wind (NS), CBL with a height-constant geostrophic wind of 20 m s⁻¹ (GC), and CBL with geostrophic wind shear (GS). In the simulated cases, the sheared CBLs grew fastest, relative to the NS CBLs, when the surface buoyancy flux was weak and the atmospheric stratification was moderate or weak.

Three fundamental findings resulted from the investigated CBL cases: (i) the entrainment zone shear is much more important than the surface shear in enhancing CBL entrainment, although entrainment zone shear is indirectly affected by surface shear; (ii) the sheared entrainment zone features a sublayer of nearly constant flux Richardson number, which points to a balance between shear production and buoyancy consumption of turbulence kinetic energy (TKE) that regulates entrainment; and (iii) the fraction of entrainment zone shear-generated TKE spent on the entrainment is lower than suggested by earlier studies.

Abstract

Several bulk model–based entrainment parameterizations for the atmospheric convective boundary layer (CBL) with wind shear are reviewed and tested against large-eddy simulation (LES) data to evaluate their ability to model one of the basic integral parameters of convective entrainment—the entrainment flux ratio. Test results indicate that many of these parameterizations fail to correctly reproduce entrainment flux in the presence of strong shear because they underestimate the dissipation of turbulence kinetic energy (TKE) produced by shear in the entrainment zone. It is also found that surface shear generation of TKE may be neglected in the entrainment parameterization because it is largely balanced by dissipation. However, the surface friction has an indirect effect on the entrainment through the modification of momentum distribution in the mixed layer and regulation of shear across the entrainment zone. Because of this effect, parameterizations that take into account the surface friction velocity but exclude entrainment zone shear may sufficiently describe entrainment when wind shear in the free atmosphere above the CBL is small. In this case, the surface shear acts as a proxy for the entrainment zone shear. Such parameterizations can be most useful if applied in situations where atmospheric data are insufficient for calculating entrainment zone shear. The importance of modeling a Richardson-number-limited, finite-depth entrainment zone is evidenced by the relatively accurate entrainment flux predictions by models that explicitly account for effects of entrainment zone shear, but predictions by these models are often adversely affected by the underestimation of TKE dissipation in the entrainment zone.

Abstract

A theory is presented for the Great Plains low-level jet in which the jet emerges in the sloping atmospheric boundary layer as the nocturnal phase of an oscillation arising from diurnal variations in turbulent diffusivity (Blackadar mechanism) and surface buoyancy (Holton mechanism). The governing equations are the equations of motion, mass conservation, and thermal energy for a stably stratified fluid in the Boussinesq approximation. Attention is restricted to remote (far above slope) geostrophic winds that blow along the terrain isoheights (southerly for the Great Plains). Diurnally periodic solutions are obtained analytically with diffusivities that vary as piecewise constant functions of time and slope buoyancies that vary as piecewise linear functions of time. The solution is controlled by 11 parameters: slope angle, Coriolis parameter, free-atmosphere Brunt–Väisälä frequency, free-atmosphere geostrophic wind, radiative damping parameter, day and night diffusivities, maximum and minimum surface buoyancies, and times of maximum surface buoyancy and sunset. The Holton mechanism, by itself, results in relatively weak wind maxima but produces strong jets when paired with the Blackadar mechanism. Jets with both Blackadar and Holton mechanisms operating are shown to be broadly consistent with observations and climatological analyses. Jets strengthen with increasing geostrophic wind, maximum surface buoyancy, and day-to-night ratio of the diffusivities and weaken with increasing Brunt–Väisälä frequency and magnitude of minimum slope buoyancy (greater nighttime cooling). Peak winds are maximized for slope angles characteristic of the Great Plains.

Abstract

Relationships between parameters of convective entrainment into a shear-free, linearly stratified atmosphere predicted by the zero-order jump and general-structure bulk models of entrainment are reexamined using data from large eddy simulations (LESs). Relevant data from other numerical simulations, water tank experiments, and atmospheric measurements are also incorporated in the analysis. Simulations have been performed for 10 values of the buoyancy gradient in the free atmosphere covering a typical atmospheric stability range. The entrainment parameters derived from LES and relationships between them are found to be sensitive to the model framework employed for their interpretation. Methods of determining bulk model entrainment parameters from the LES output are proposed and discussed.

Within the range of investigated free-atmosphere stratifications, the LES predictions of the inversion height and buoyancy increment across the inversion are found to be close to the analytical solutions for the equilibrium entrainment regime, which is realized when the rate of time change of the CBL-mean turbulence kinetic energy and the energy drain from the CBL top are both negligibly small. The zero-order model entrainment ratio of about 0.2 for this regime is generally supported by the LES data. However, the zero-order parameterization of the entrainment layer thickness is found insufficient. A set of relationships between the general-structure entrainment parameters for typical atmospheric stability conditions is retrieved from the LES. Dimensionless constants in these relationships are estimated from the LES and laboratory data. Power-law approximations for relationships between the entrainment parameters in the zero-order jump and general-structure bulk models are evaluated based on the conducted LES. In the regime of equilibrium entrainment, the stratification parameter of the entrainment layer, which is the ratio of the buoyancy gradient in the free atmosphere to the overall buoyancy gradient across the entrainment layer, appears to be a constant of about 1.2.

Abstract

The turbulence temperature spectrum and structure parameter are related through a widely adopted proportionality coefficient. We formally derive this expression, and present further evidence, to demonstrate that this coefficient is too large by a factor of 2.