Geometric Alignments of the Subgrid-Scale Force in the Atmospheric Boundary Layer

In recent years field experiments have been undertaken in the lower atmosphere to perform a priori tests of subgrid-scale (SGS) models for large-eddy simulations (LES). The experimental arrangements and data collected have facilitated studies of variables such as the filtered strain rate, SGS stress and dissipation, and the eddy viscosity coefficient. However, the experimental set-ups did not permit analysis of the divergence of the SGS stress (the SGS force vector), which is the term that enters directly in the LES momentum balance equations. Data from a field experiment (SGS2002) in the west desert of Utah, allows the calculation of the SGS force due to the unique 4 × 4 sonic anemometer array. The vector alignment of the SGS force is investigated under a range of atmospheric stabilities. The eddy viscosity model is likely aligned with the measured SGS force under near-neutral and unstable conditions, while its performance is unsatisfactory under stable conditions.     

Study of near-surface models for large-eddy simulations of a neutrally stratified atmospheric boundary layer

In large-eddy simulations (LES) of the atmospheric boundary layer (ABL), near-surface models are often used to supplement subgrid-scale (SGS) turbulent stresses when a major fraction of the energetic scales within the surface layer cannot be resolved with the temporal and spatial resolution at hand. In this study, we investigate the performance of both dynamic and non-dynamic eddy viscosity models coupled with near-surface models in simulations of a neutrally stratified ABL. Two near-surface models that are commonly used in LES of the atmospheric boundary layer are considered. Additionally, a hybrid Reynolds- averaged/LES eddy viscosity model is presented, which uses Prandtl’s mixing length model in the vicinity of the surface, and blends in with the dynamic Smagorinsky model away from the surface. Present simulations show that significant portions of the modelled turbulent stresses are generated by the near-surface models, and they play a dominant role in capturing the expected logarithmic wind profile. Visualizations of the instantaneous vorticity field reveal that flow structures in the vicinity of the surface depend on the choice of the near-surface model. Among the three near-surface models studied, the hybrid eddy viscosity model gives the closest agreement with the logarithmic wind profile in the surface layer. It is also observed that high levels of resolved turbulence stresses can be maintained with the so-called canopy stress model while producing good agreement with the logarithmic wind profile.     

涡旋相关法测定湍流通量偏低的研究

针对野外实验所发现的不同观测法测定地表能通量不平衡问题,进行了均匀加热大气边界层的大涡模拟实验.用模拟的湍流风、温度和湿度涨落的时间序列证实,对流边界层低频涡普遍存在,并经常以一簇一簇热泡的形式出现.风速较小时,有限时长的取样不足以捕捉低频涡的贡献,可造成涡旋相关法测量的统计量异常偏低.仿照涡旋相关法的步骤进行数据处理发现,经去除平均或趋势计算的温度和湿度通量偏低程度在边界层下部随观测高度的增高而显著,其中尤以湿度通量为甚.其结果在一定程度上可以解释低风速条件下地表能通量测量的不闭合问题,但是尚不能完全解释诸如青藏高原实验出现的严重不闭合.文中对此作了探讨性的讨论.     

The Baroclinic, Variable Eddy Viscosity Ekman Layer

The WKB method is used in conjunction with the variation of parameters technique to find an approximate analytical solution for Ekman layers with eddy viscosity and horizontal pressure gradient that are each variable with height from the surface. Behaviour of the solution is illustrated by comparing model output when several eddy viscosity and horizontal pressure gradient profiles are used. Cases where the pressure gradient decreases with height accentuate the super-geostrophic peak in the wind velocity profile, with decreasing eddy viscosity with height further enhancing this effect. Increasing pressure gradient with height reduces or eliminates the peak. The model output when using an eddy viscosity that has a low-level peak fits marine boundary-layer data taken during ASTEX better than the classic solution - the model giving greater low-level mixing which is seen in ASTEX data as well as in data from ERICA.     

A subgrid-scale model for large-eddy simulation of planetary boundary-layer flows

A long-standing problem in large-eddy simulations (LES) of the planetary boundary layer (PBL) is that the mean wind and temperature profiles differ from the Monin-Obukhov similarity forms in the surface layer. This shortcoming of LES has been attributed to poor grid resolution and inadequate sub-grid-scale (SGS) modeling. We study this deficiency in PBL LES solutions calculated over a range of shear and buoyancy forcing conditions. The discrepancy from similarity forms becomes larger with increasing shear and smaller buoyancy forcing, and persists even with substantial horizontal grid refinement. With strong buoyancy forcing, however, the error is negligible.In order to achieve better agreement between LES and similarity forms in the surface layer, a two-part SGS eddy-viscosity model is proposed. The model preserves the usual SGS turbulent kinetic energy formulation for the SGS eddy viscosity, but it explicitly includes a contribution from the mean flow and a reduction of the contributions from the turbulent fluctuations near the surface. Solutions with the new model yield increased fluctuation amplitudes near the surface and better correspondence with similarity forms out to a distance of 0.1–0.2 times the PBL depth, i.e., a typical surface-layer depth. These results are also found to be independent of grid anisotropy. The new model is simple to implement and computationally inexpensive.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

城市建筑动力学效应对对流边界层影响的敏感性试验

本文将大涡模拟应用于城市对流边界层(CBL)湍流结构和流场特征的研究,在大涡模式中,拖曳系数取与建筑物高度及建筑物高度标准差有关的表达式以考虑次网格建筑物对风速和湍流动能(TKE)的面积平均影响.模拟结果表明,由于城市建筑物对气流的拖曳作用,使建筑物冠层及整个CBL内风速大幅度减小,城市冠层内部风速减小尤为明显,在夹卷层内,风速有一明显的跃变.在边界层中部对流运动已经发展成为较强的热泡,城市建筑物的动力学效应使热泡的水平尺度增大,CBL内平均上升气流速度和下沉气流速度减小,同时使CBL中上升气流所占比例比平坦地面增大.城市建筑物使CBL低层热通量、动量通量、速度方差和位温方差明显增大,但对近地层高度以上的湍流量影响不大.     

一个对流边界层大涡模式的建立与调试

本文介绍一个适合于对流边界层的大涡模式的建立及其调试结果。该大涡模式建立过程中注重于计算的节省，同时也强调原理与方法的简单和合理性。模式的调试表明，对于平坦均一地形的情况，模拟可以获得合理的结果。调试同时显示了模式对较低水平分辨率的适用条件，以及模式应用于模拟较大水平范围问题的可能性。     

The diurnal wind variation in a variable eddy viscosity semi-geostrophic Ekman boundary-layer model: Analytical study

Summary ?A time-dependent semi-geostrophic Ekman boundary-layer model (SG), including slowly varying eddy diffusivity with height and inertial term effects, is developed to investigate the diurnal wind variation in the planetary boundary layer (PBL). An approximate analytical solution of this model is derived by using the WKB method, which extends the Tan and Farahani (1998)’s solution by including the vertical variable eddy viscosity. The features of the diurnal wind variation in the PBL mainly depend on three factors: the latitude, horizontal momentum advection and eddy viscosity. The vertical variable eddy viscosity has little influence on diurnal wind variation in the PBL at the low latitude, however its effect may be exacerbated in the mid- and high latitudes. In comparing with the constant eddy viscosity case, the decreasing (increasing) with height eddy viscosity produces a large (small) maximum wind speed (MWS) in the PBL, however, the eddy viscosity that has a mid-layer peak in the vertical gives rise to a higher height of occurrence of MWS. For the boundary-layer wind structure, there is a singular point when the modified SG inertial oscillation frequency η equals the forcing frequency ω. The isotachs of boundary-layer wind speed have almost no tilt to left or right relative to time evolution and the occurrence time of the MWS is the earliest at the singular point. The feature will be enhanced in the decreasing with height eddy viscosity case and weakened in the eddy viscosity initially increasing with height case. Received April 6, 2001; accepted December 27, 2001     

The partitioning of attached and detached eddy motion in the atmospheric surface layer using Lorentz wavelet filtering

Townsend's attached eddy hypothesis states that the turbulent structure in the constant stress layer can be decomposed into attached and detached eddy motion. This paper proposes and tests a methodology for separating the attached and detached eddy motion from time series measurements of velocity and temperature. The proposed methodology is based on the time-frequency localization and filtering capabilities of the orthonormal wavelet transforms. Using a relative entropy statistical measure, the optimal wavelet basis is identified first. The turbulence time series measurements are then transformed into the wavelet domain where the contribution of specific events in the time-frequency domain is identified. The filtering scheme utilizes a recently constructed Lorentz thresholding methodology that successfully eliminates all wavelet coefficients associated with the detached eddy motion. While this filtering scheme lacks the compression efficiency of the classical Donoho and Johnstone's universal thresholding model, it conserves the higher-order statistics and important turbulence interactions related to the Reynolds stresses. Following the filtering scheme, the attached eddy motion time series is re-constructed by an inverse wavelet transform of the non-zero wavelet coefficients. The proposed partitioning methodology for attached and detached eddy motion is tested using 56 Hz triaxial sonic anemometer velocity and temperature measurements above a uniform dry lake bed in Owens valley, California, for a wide range of atmospheric stability conditions. Validation that the wavelet filtered time series represents the attached eddy motion is also discussed in the context of conservation of turbulence energy and surface fluxes.     

Measurements Of Thermal Updraft Intensity Over Complex Terrain Using American White Pelicans And A Simple Boundary-Layer Forecast Model

An examination of boundary-layer meteorological and avian aerodynamic theories suggests that soaring birds can be used to measure the magnitude of vertical air motions within the boundary layer. These theories are applied to obtain mixed-layer normalized thermal updraft intensity over both flat and complex terrain from the climb rates of soaring American white pelicans and from diagnostic boundary-layer model-produced estimates of the boundary-layer depth z_i and the convective velocity scale w_*. Comparison of the flatland data with the profiles of normalized updraft velocity obtained from previous studies reveals that the pelican-derived measurements of thermal updraft intensity are in close agreement with those obtained using traditional research aircraft and large eddy simulation (LES) in the height range of 0.2 to 0.8 z_i. Given the success of this method, the profiles of thermal vertical velocity over the flatland and the nearby mountains are compared. This comparison shows that these profiles are statistically indistinguishable over this height range, indicating that the profile for thermal updraft intensity varies little over this sample of complex terrain. These observations support the findings of a recent LES study that explored the turbulent structure of the boundary layer using a range of terrain specifications. For terrain similar in scale to that encountered in this study, results of the LES suggest that the terrain caused less than an 11% variation in the standard deviation of vertical velocity.     

Simulation of a Stably Stratified Atmospheric Boundary Layer Using One-Dimensional Turbulence

One-dimensional turbulence (ODT) is a single-column simulation in which vertical motions are represented by an unsteady advective process, rather than their customary representation by a diffusive process. No space or time averaging of mesh-resolved motions is invoked. Molecular-transport scales can be resolved in ODT simulations of laboratory-scale flows, but this resolution of these scales is prohibitively expensive in ODT simulations of the atmospheric boundary layer (ABL), except possibly in small subregions of a non-uniform mesh.Here, two methods for ODT simulation of the ABL on uniform meshes are described and applied to the GABLS (GEWEX Atmospheric Boundary Layer Study; GEWEX is the Global Energy and Water Cycle Experiment) stable boundary-layer intercomparison case. One method involves resolution of the roughness scale using a fixed eddy viscosity to represent subgrid motions. The other method, which is implemented at lower spatial resolution, involves a variable eddy viscosity determined by the local mesh-resolved flow, as in multi-dimensional large-eddy simulation (LES). When run at typical LES resolution, it reproduces some of the key high-resolution results, but its fidelity is lower in some important respects. It is concluded that a more elaborate empirically based representation of the subgrid physics, closely analogous to closures currently employed in LES of the ABL, might improve its performance substantially, yielding a cost-effective ABL simulation tool. Prospects for further application of ODT to the ABL, including possible use of ODT as a near-surface subgrid closure framework for general circulation modeling, are assessed.     

Improvement of the K-profile Model for the Planetary Boundary Layer based on Large Eddy Simulation Data

Modifications of the widely used K-profile model of the planetary boundary layer (PBL), reported by Troen and Mahrt (TM) in 1986, are proposed and their effects examined by comparison with large eddy simulation (LES) data. The modifications involve three parts. First, the heat flux from the entrainment at the inversion layer is incorporated into the heat and momentum profiles, and it is used to predict the growth of the PBL directly. Second, profiles of the velocity scale and the Prandtl number in the PBL are proposed, in contrast to the constant values used in the TM model. Finally, non-local mixing of momentum was included. The results from the new PBL model and the original TM model are compared with LES data. The TM model was found to give too high PBL heights in the PBL with strong shear, and too low heights for the convection-dominated PBL, which causes unrealistic heat flux profiles. The new PBL model improves the predictability of the PBL height and produces profiles that are more realistic. Moreover, the new PBL model produces more realistic profiles of potential temperature and velocity. We also investigated how each of these three modifications affects the results, and found that explicit representation of the entrainment rate is the most critical.     

The Distribution and Uncertainty Quantification of Wind Profile in the Stochastic General Ekman Momentum Approximation Model

The general Ekman momentum approximation boundary-layer model(GEM) can be effectively used to describe the physical processes of the boundary layer. However, eddy viscosity, which is an approximated value, can lead to uncertainty in the solutions. In this paper, stochastic eddy viscosity is taken into consideration in the GEM, and generalized polynomial chaos is used to quantify the uncertainty. The goal of uncertainty quantification is to investigate the effects of uncertainty in the eddy viscosity on the model and to subsequently provide reliable distribution of simulation results. The performances of the stochastic eddy viscosity and generalized polynomial chaos method are validated based on three different types of eddy viscosities, and the results are compared based on the Monte Carlo method. The results indicate that the generalized polynomial chaos method can be accurately and efficiently used in uncertainty quantification for the GEM with stochastic eddy viscosity.     

Numerical studies on flow fields around buildings in an Urban street canyon and cross-road

The questions on how vortices are constructed and on the relationship between the flow patterns and concentration distributions in real street canyons are the most pressing questions in pollution control studies. In this paper, the very large eddy simulation (VLES) and large eddy simulation (LES) are applied to calculate the flow and pollutant concentration fields in an urban street canyon and a cross-road respectively. It is found that the flow separations are not only related to the canyon aspect ratios, but also with the flow velocities and wall temperatures. And the turbulent dispersions are so strongly affected by the flow fields that the pollutant concentration distributions can be distinguished from the different aspect ratios, flow velocities and wall temperatures.     

Spatial representativeness of single tower measurements and the imbalance problem with eddy-covariance fluxes: results of a large-eddy simulation study

A large-eddy simulation (LES) study is presented that investigates the spatial variability of temporal eddy covariance fluxes and the systematic underestimation of representative fluxes linked to them. It extends a prior numerical study by performing high resolution simulations that allow for virtual measurements down to 20 m in a convective boundary layer, so that conditions for small tower measurement sites can be analysed. It accounts for different convective regimes as the wind speed and the near-surface heat flux are varied. Moreover, it is the first LES imbalance study that extends to the stable boundary layer. It reveals shortcomings of single site measurements and the necessity of using horizontally-distributed observation networks. The imbalances in the convective case are attributed to a locally non-vanishing mean vertical advection due to turbulent organised structures (TOS). The strength of the TOS and thus the imbalance magnitude depends on height, the horizontal mean wind and the convection type. Contrary to the results of a prior study, TOS cannot generally be responsible for large energy imbalances: at low observation heights (corresponding to small towers and near-surface energy balance stations) the TOS related imbalances are generally about one order of magnitude smaller than those in field experiments. However, TOS may cause large imbalances at large towers not only in the case of cellular convection and low wind speeds, as found in the previous study, but also in the case of roll convection at large wind speeds. In the stably stratified boundary layer for all observation heights neither TOS nor significant imbalances are observed. Attempting to reduce imbalances in convective situations by applying the conventional linear detrending method increases the systematic flux underestimation. Thus, a new filter method is proposed.     

Passive scalar diffusion from surface sources in the convective boundary layer

We examine vertical and horizontal diffusion of a passive scalar puff from a surface point source in a convective boundary layer (CBL). Numerical results are presented from a large-eddy simulation (LES) with embedded subgrid Lagrangian particle simulation (LPS). There is good agreement in most respects with previous laboratory and numerical studies. Analytical approximations for the concentration, horizontal flux and vertical flux are found to work reasonably well; they are based on the assumption that the concentration follows a Gaussian function in the horizontal and vertical, and that the dimensionless width and height scales of the puff follow simple functions of time. Fluxes and concentration gradients are related through a continuity relationship, without the need for an eddy diffusivity assumption. The instantaneous, point-source fields can be integrated for any source geometry. We compare predictions from the LES/LPS model for a sinusoidal surface flux with previous results from an LES with sinusoidal buoyancy flux and confirm that the buoyancy perturbations diffuse like a passive scalar. We also consider a continuous point source and derive footprint functions for vertical flux measurements above the surface layer.     

对流边界层大涡模式的改进及对夹卷速度的研究

对已建的对流边界层(CBL)大涡模式进行了改进，将次网格闭合方案改为次网格能量闭合，并考虑了水汽的源汇项和水汽相变潜热的作用。通过对均匀下垫面上由热扰动发展的对流边界层的模拟及与实验结果的比较表明，模式较好地模拟了对流边界层的主要物理结构，较好地反映了各物理量之间的对应关系。本文在一定的对流理查森数(Ri*)范围内给出了一些算例，对无量纲夹卷速度(We/W*)进行了研究。结果表明，无量纲夹卷速度随地表热通量(Qs)的增大而增大，随对流边界层上部温度递减率（γ)的增大而减小。当9.06≤Ri*≤45.29时，无量纲夹卷速度We/W*可以拟合成A(Ri*)-1的形式，其中A=0.226。并且与我们的对流槽实验结果，Sullivan等人的大涡模拟结果以及Deardorff等人的对流槽实验结果作了比较，四者吻合较好。     

The Impact of Land-Surface Parameter Properties and Resolution on the Simulated Cloud-Topped Atmospheric Boundary Layer

A method to simulate characteristics of wind speed in the boundary layer of tropical cyclones in an idealized manner is developed and evaluated. The method can be used in a single-column modelling set-up with a planetary boundary-layer parametrization, or within large-eddy simulations (LES). The key step is to include terms in the horizontal velocity equations representing advection and centrifugal acceleration in tropical cyclones that occurs on scales larger than the domain size. Compared to other recently developed methods, which require two input parameters (a reference wind speed, and radius from the centre of a tropical cyclone) this new method also requires a third input parameter: the radial gradient of reference wind speed. With the new method, simulated wind profiles are similar to composite profiles from dropsonde observations; in contrast, a classic Ekman-type method tends to overpredict inflow-layer depth and magnitude, and two recently developed methods for tropical cyclone environments tend to overpredict near-surface wind speed. When used in LES, the new technique produces vertical profiles of total turbulent stress and estimated eddy viscosity that are similar to values determined from low-level aircraft flights in tropical cyclones. Temporal spectra from LES produce an inertial subrange for frequencies \(\gtrsim \)0.1 Hz, but only when the horizontal grid spacing \(\lesssim \)20 m.