A Homogeneous Langevin Equation Model, Part i: Simulation of Particle Trajectories in Turbulence with a Skewed Velocity Distribution

A Lagrangian stochastic model for the time evolution of the velocity of a fluid particle is presented. This model is based on a one-dimensional generalized Langevin equation, and assumes the velocity probability distribution of the turbulent fluid is skewed and spatially homogeneous. This has been shown to be an effective approach to simulating vertical dispersion in the convective boundary layer. We use a form of the Langevin equation that has a linear (in velocity) deterministic acceleration and a random acceleration that is a non-Gaussian, skewed process. For the case of homogeneous fluid velocity statistics, this 'linear-skewed' Langevin equation can be integrated explicitly, resulting in an efficient numerical simulation method. Model simulations were tested using cases for which exact, analytic statistical properties of particle velocity are known. Results of these tests show that, for homogeneous turbulence, a linear-skewed Langevin equation model can overcome the difficulties encountered in applying a Langevin equation with a skewed random acceleration. The linear-skewed Langevin equation model results are compared to results of a 'nonlinear-Gaussian' Langevin equation model, and show that the linear-skewed model is significantly more efficient.     

对流边界层中的一个双高斯型PDF扩散模式

对流边界层（ＣＢＬ）中的污染扩散是非高斯型的。本文在下列三个假设下建立了双高斯型几率分布函数（ＰＤＦ）模式：１．对流边界层任一确定高度铅直速度Ｗ的几率分布函数ｐｗ由两个高斯分布迭加而成；２．从污染源释放的粒子具有源高的铅直速度几率分布，且其轨迹是线性的；３．粒子在地面的反射为全反射，在混合层高度Ｚｉ为全反射或有部分吸收。然后分析了三个高度上铅直速度Ｗ的一些统计特征量，比较了由ＰＤＦ模式计算的横风向积分浓度和Ｌａｍｂ的数值模拟［１－３］，Ｄｅａｒｄｏｒｆｆ的水槽模拟［４－６］结果，并用美国ＣＯＮＤＯＲＳ计划的外场试验资料［７］对ＰＤＦ模式进行了验证，结果均相当一致。     

A Large-Eddy Simulation and Lagrangian Stochastic Study of Heavy Particle Dispersion in the Convective Boundary Layer

Large-eddy simulation and Lagrangian stochastic dispersion models were used to study heavy particle dispersion in the convective boundary layer (CBL). The effects of various geostrophic winds, particle diameters, and subgrid-scale (SGS) turbulence were investigated. Results showed an obvious depression in the vertical dispersion of heavy particles in the CBL and major vertical stratification in the distribution of particle concentrations, relative to the passive dispersion. Stronger geostrophic winds tended to increase the dispersion of heavy particles in the lower CBL. The SGS turbulence, particularly near the surface, markedly influenced the dispersion of heavy particles in the CBL. For reference, simulations using passive particles were also conducted; these simulation results agreed well with results from previous convective tank experiments and numerical simulations.     

热浮升烟流扩散的拉格朗日粒子模拟

本文建立了一个处理对流边界层热浮升烟流扩散的拉格朗日粒子模式。模式既考虑了对流边界层的特殊气流结构，并作了均匀湍流参数化的简化；同时提出了在拉格朗日模式中合理计入热浮升烟流抬升影响的近似方法。模拟计算结果表明:烟流热浮力的影响使得地面最大浓度值远比被动烟流的低，而且出现位置离源更远。模式计算与外场试验结果合理地一致。模式物理概念明确合理，输入参数少，计算量小，具有简单实用的优点，适合日常环境应用需要。     

风切变对边界层对流影响的大涡模拟研究

利用"西北干旱区陆-气相互作用野外观测实验"加密观测期间在敦煌站的观测资料以及大涡模式,模拟了对流边界层的发展,以及示踪物从混合层向残留层传输的时空变化。模拟的对流边界层的结构及演变特征与实测结果基本一致。进一步通过有风切变和无风切变的敏感性数值试验,研究了风切变对垂直速度、位温和示踪物浓度的水平分布以及示踪物传输高度的影响。研究结果表明,在有风切变的试验中(甚至风切变仅存在于近地层中),对流边界层的增长加强,而且示踪物被传输的高度也较高。与浮力驱动的对流边界层相比,由浮力和风切变共同驱动的边界层中上升气流较弱而下沉气流较强,但前者的上升气流与下沉气流的分布在垂直方向上更为倾斜。由于夹卷作用的增强,浮力和风切变共同驱动的对流边界层较浮力驱动的对流边界层暖。在夹卷层,浮力和风切变共同驱动的边界层对流的上升气流和下沉气流都比浮力驱动的边界层对流中的强,而且垂直速度的概率密度函数分布也较对称,其位温和示踪物浓度的概率密度函数分布也比浮力驱动的边界层中的平直。对湍流动能收支的分析也表明风切变对湍流动能有重要影响,尤其对夹卷层中的湍流动能切变产生项影响较大。示踪物浓度的概率密度函数垂直分布显示,浮力驱动的边界层中示踪物浓度随高度变化较小,而浮力和风切变共同驱动的边界层中示踪物浓度随高度递减,但是示踪物传输的高度比较高。     

ON THE PDF MODELS FOR ATMOSPHERIC DIFFUSION IN BOUNDARY LAYER

In this paper, taking its turbulent exchange coefficient as a function of the Lagrangian timescale and standard variance of the turbulence in atmosphere, the atmospheric dispersion PDFmodels are obtained on the basis of atmospheric diffusion K-theory. In the model the statistics ofwind speed are directly used as its parameters instead of classic dispersion parameters. The bi-Gaussian PDF is derived in convective boundary layer (CBL), from the statistics of verticalvelocity in both of the downdraft and updraft regions that are investigated theoretically in the otherpart of this paper. Giving the driven parameters of the CBL (including the convective velocity scalew* and the mixing depth h_i) and the time-averaged wind speed at release level, the PDF model isable to simulate the distribution of concentration released at any levels in the CBL. The PDF'ssimulations are fairly consistent with the measurements in CONDORS experiment or the resultsbrought out by some numerical simulations.     

实验速度场测量技术及对流边界层特征研究

在对流槽中对对流边界层(CBL)温度场实验研究的基础上,进一步尝试通过实验技术测量速度场并分析研究CBL中的速度场特征。在应用PIV测量技术时选用铝粉作示踪粒子。实验证明了在混合层中速度分布明显具有对流边界层热泡特性;混合层顶部的速度分布很好地反应出夹卷层的结构特征;湍流速度特征量的垂直分布合理,与野外实测结果和类似的对流槽实验结果接近;误差分析表明示踪粒子的跟随性良好,粒子速度的测量结果能真实地反应流体的运动特征,从而得证了分析结果的可靠性。     

A Three-Dimensional Correlation/Spectral Model for Turbulent Velocities in a Convective Boundary Layer

A three-dimensional model for correlation functions and spectra in theatmospheric, convective boundary layer (CBL) is presented. The modelincludes vertical inhomogeneities introduced by eddy-blocking at the ground.By assuming the disturbance to the turbulent flow resulting from the groundblocking is irrotational, an equation is developed which allows one to writethe inhomogeneous, two-dimensional (2D) cross spectra for the blocked flowin terms of the 2D cross spectra for a homogeneous flow. VonKármán's energy spectrum then is used to determine thehomogeneous, 2D cross spectra. Although there are only two adjustableparameters in the model, the variance and a length scale, the model is shownto agree quite well with a diversity of previous results for the CBL.     

A laboratory study of the turbulent velocity characteristics in the convective boundary layer

Based on the measurement of the velocity field in the convective boundary layer （CBL） in a convection water tank with the particle image velocimetry （PIV） technique, this paper studies the characteristics of the CBL turbulent velocity in a modified convection tank. The experiment results show that the velocity distribution in the mixed layer clearly possesses the characteristics of the CBL thermals, and the turbulent eddies can be seen obviously. The comparison of the vertical distribution of the turbulent velocity variables indicates that the modeling in the new tank is better than in the old one. The experiment data show that the thermal＇s motion in the entrainment zone sometimes fluctuates obviously due to the intermittence of turbulence. Analyses show that this fluctuation can influence the agreement of the measurement data with the parameterization scheme, in which the convective Richardson number is used to characterize the entrainment zone depth. The normalized square velocity wi^2/w＊^2. at the top of the mixed layer seems to be time-dependent, and has a decreasing trend during the experiments. This implies that the vertical turbulent velocity at the top of the mixed layer may not be proportional to the convective velocity （w＊）.     

A Density Correction for Lagrangian Particle Dispersion Models

Current Lagrangian particle dispersion models, used to simulate the dispersion of passive tracers in the turbulent planetary boundary layer (PBL), assume that the density is constant within the PBL. In deep PBLs, where the density at the boundary-layer top may be lower by more than 20% than at the surface, this assumption leads to errors in the tracer concentrations on the order of 10%. In the presence of a vertical wind shear, this also leads to inaccurate calculations of the horizontal tracer transport. To remove this deficiency, a Langevin equation is presented that contains a density correction term. The effect of the density correction is studied using data from a large-scale tracer experiment. It is found that for this experiment, the main effect of the density correction is an increase in the surface tracer concentrations, whereas the horizontal tracer transport patterns remain largely unaffected.     

A Comparison Of Aerosol-Layer And Convective Boundary-Layer Structure Over A Mountain Range During Staaarte '97

The temporal evolution and spatial structure of the aerosol layer (AL) height as observed with an airborne downlooking lidar over the Swiss Alps were investigated with a three-dimensional mesoscale numerical model and a particle dispersion model. Convective boundary-layer (CBL) heights were derived from the mesoscale model output, and the behaviour of surface-released particles was investigated with the particle dispersion model. While a previous investigation, using data from the same field study, equated the observed AL height with the CBL height, the results of the current investigation indicate that there is a considerable difference between AL and CBL heights caused by mixing and transport processes between the CBL and the free atmosphere. CBL heights show a more terrain-following behaviour and are lower than AL heights. We argue that processes causing the difference between AL and CBL heights are common over mountainous terrain and that the AL height is a length scale that needs to be considered in air pollution studies in mountainous terrain.     

论边界层中的大气扩散PDF模式

基于大气扩散Ｋ理论，用作为风速脉动均方差和拉氏时间尺度函数的湍流交换系数，得到了直接利用风速脉动几率密度而不用扩散参数的大气扩散ＰＤＦ模式。分别研究了对流边界层上升气流区与下降区垂直速度的统计特征，求得双正态ＰＤＦ模式。在给定ＣＢＬ自身参数如对流特征速度ｗ＊，顶高ｈｉ和源高度上的平均风速时，该模式计算出的无量纲浓度分布与室内外测试结果一致。     

Turbulent velocity distributions and implied trajectory models

Well-mixed, first-order Lagrangian stochastic (LS) particle trajectory models are derived from several idealized (“toy”) turbulent velocity distributions, and their performance is compared against the observations of Project Prairie Grass, i.e., the case of a continuous point source of tracer near the ground, in the horizontally homogeneous and neutrally stratified surface layer. Although in a context of limited information a Gaussian distribution is the preferred choice, and although the Gaussian corresponds to the simplest of this set of LS models (namely, the Langevin equation), models stemming from other velocity distributions give similar, albeit distinguishable, predictions.     

Forward-in-time and Backward-in-time Dispersion in the Convective Boundary Layer: the Concentration Footprint

The turbulence field obtained using a large-eddy simulation model is used to simulate particle dispersion in the convective boundary layer with both forward-in-time and backward-in-time modes. A Lagrangian stochastic model is used to treat subgrid-scale turbulence. Results of forward dispersion match both laboratory experiments and previous numerical studies for different release heights in the convective boundary layer. Results obtained from backward dispersion show obvious asymmetry when directly compared to results from forward dispersion. However, a direct comparison of forward and backward dispersion has no apparent physical meaning and might be misleading. Results of backward dispersion can be interpreted as three-dimensional or generalized concentration footprints, which indicate that sources in the entire boundary layer, not only sources at the surface, may influence a concentration measurement at a point. Footprints at four source heights in the convective boundary layer corresponding to four receptors are derived using forward and backward dispersion methods. The agreement among footprints derived with forward and backward methods illustrates the equivalence between both approaches. The paper shows explicitly that Lagrangian simulations can yield identical footprints using forward and backward methods in horizontally homogeneous turbulence.     

Coherence and Scale of Vertical Velocity in the Convective Boundary Layer from a Doppler Lidar

We utilized a Doppler lidar to measure integral scale and coherence of vertical velocity w in the daytime convective boundary layer (CBL). The high resolution 2 μm wavelength Doppler lidar developed by the NOAA Environmental Technology Laboratory was used to detect the mean radial velocity of aerosol particles. It operated continuously in the zenith-pointing mode for several days in the summer 1996 during the “Lidars in Flat Terrain” experiment over level farmland in central Illinois. We calculated profiles of w integral scales in both the alongwind and vertical directions from about 390 m height to the CBL top. In the middle of the mixed layer we found, from the ratio of the w integral scale in the vertical to that in the horizontal direction, that the w eddies are squashed by a factor of about 0.65 as compared to what would be the case for isotropic turbulence. Furthermore, there is a significant decrease of the vertical integral scale with height. The integral scale profiles and vertical coherence show that vertical velocity fluctuations in the CBL have a predictable anisotropic structure. We found no significant tilt of the thermal structures with height in the middle part of the CBL.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Dispersion of passive tracer in the atmospheric convective boundary layer with wind shears: a review of laboratory and numerical model studies

Summary Paper reviews recent laboratory and numerical model studies of passive gaseous tracer dispersion in the atmospheric convective boundary layer (CBL) with surface and elevated wind shears. Atmospheric measurement data used for validation of these two model techniques are briefly discussed as well. A historical overview is given of laboratory studies of dispersion in the atmospheric CBL. Model studies of tracer dispersion in two CBL types, the (i) non-steady, horizontally homogeneous CBL and (ii) quasi-stationary, horizontally heterogeneous CBL, are reviewed. The discussion is focused on the dispersion of non-buoyant plume emitted from a point source located at different elevations within the CBL. Approaches towards CBL modeling employed in different laboratory facilities (water tanks and wind tunnels) are described. The reviewed numerical techniques include Large Eddy Simulation (LES) and Lagrangian modeling. Numerical data on dispersion in the sheared CBL is analyzed in conjunction with experimental results from wind-tunnel CBLs.     

A Variable Mesh Spacing for Large-Eddy Simulation Models in the Convective Boundary Layer

A variable vertical mesh spacing for large-eddy simulation (LES) models in a convective boundary layer (CBL) is proposed. The argument is based on the fact that in the vertical direction the turbulence near the surface in a CBL is inhomogeneous and therefore the subfilter-scale effects depend on the relative location between the spectral peak of the vertical velocity and the filter cut-off wavelength. From the physical point of view, this lack of homogeneity makes the vertical mesh spacing the principal length scale and, as a consequence, the LES filter cut-off wavenumber is expressed in terms of this characteristic length scale. Assuming that the inertial subrange initial frequency is equal to the LES filter cut-off frequency and employing fitting expressions that describe the observed convective turbulent energy one-dimensional spectra, it is feasible to derive a relation to calculate the variable vertical mesh spacing. The incorporation of this variable vertical grid within a LES model shows that both the mean quantities (and their gradients) and the turbulent statistics quantities are well described near to the ground level, where the LES predictions are known to be a challenging task.     

一种粒子——烟团扩散模型的应用研究

本文运用随机游动模拟方法改进建立一种粒子—烟团模式，成功地模拟了对流边界层条件下污染物扩散，粒子—烟团模式的模拟结果与水槽试验的结果吻合较好。数值模拟试验结果表明粒子—烟团模式能在施放粒子数较少，从而运行时间很短的情况下，得到优于一般随机游动模式的模拟性能。用KNRC的资料对模式的模拟性能作一验证，表明模式也能很好地模拟实际大气中不同稳定度情况下的扩散。     

Footprints in Homogeneously and Heterogeneously Driven Boundary Layers Derived from a Lagrangian Stochastic Particle Model Embedded into Large-Eddy Simulation

A Lagrangian stochastic (LS) model, which is embedded into a parallelised large-eddy simulation (LES) model, is used for dispersion and footprint evaluations. For the first time an online coupling between LES and LS models is applied. The new model reproduces concentration patterns, which were obtained in prior studies, provided that subgrid-scale turbulence is included in the LS model. Comparisons with prior studies show that the model evaluates footprints successfully. Streamwise dispersion leads to footprint maxima that are situated less far upstream than previously reported. Negative flux footprints are detected in the convective boundary layer (CBL). The wide range of applicability of the model is shown by applying it under neutral and stable stratification. It is pointed out that the turning of the wind direction with height leads to a considerable dependency of source areas on height. First results of an application to a heterogeneously heated CBL are presented, which emphasize that footprints are severely affected by the inhomogeneity.     

一个对流边界层中的随机扩散模式

通过对对流边界层(CBL)湍流结构的分析,首次提出用两种不同尺度的湍流模拟CBL中的铅直扩散.在此基础上发展了一个随机扩散模式,并用它模拟了典型对流条件下两种高架连续点源的扩散.与Willis水槽模拟和Lamb等人数值模拟以及CONDORS计划外场试验的结果的比较表明,本模式能成功地模拟CBL中的横向积分浓度.与其它数值模式相比,还具有输入参数少、计算量极小和更加简单实用的优点.