A Homogeneous Langevin Equation Model, Part ii: Simulation of Dispersion in the Convective Boundary Layer

We present a Lagrangian stochastic model of vertical dispersion in the convective boundary layer (CBL). This model is based on a generalized Langevin equation that uses the simplifying assumption that the skewed vertical velocity probability distribution is spatially homogeneous. This approach has been shown to account for two key properties of CBL turbulence associated with large-scale coherent turbulent structures: skewed vertical velocity distributions and long velocity correlation time. A 'linear-skewed' form of the generalized Langevin equation is used, which has a linear (in velocity) deterministic acceleration and a skewed random acceleration. 'Reflection' boundary conditions for selecting a new velocity for a particle that encounters a boundary were investigated, including alternatives to the standard assumption that the magnitudes of the particle incident and reflected velocities are positively correlated. Model simulations were tested using cases for which exact, analytic statistical properties of particle velocity and position are known, i.e., well-mixed spatial and velocity distributions. Simulations of laboratory experiments of CBL dispersion show that (1) the homogeneous linear-skewed Langevin equation model (as well as an alternative 'nonlinear-Gaussian' Langevin equation model) can simulate the important aspects of dispersion in the CBL, and (2) a negatively-correlated-speed reflection boundary condition simulates the observed dispersion of material near the surface in the CBL significantly better than alternative reflection boundary conditions. The homogeneous linear-skewed Langevin equation model has the advantage that it is computationally more efficient than the homogeneous nonlinear-Gaussian Langevin equation model, and considerably more efficient than inhomogeneous Langevin equation models.     

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.     

Lagrangian statistical simulation of the turbulent motion of heavy particles

A Lagrangian stochastic model for the motion of heavy particles has been developed by coupling a stochastic model for the motion of fluid elements to the Stokes equations of motion of a particle in a turbulent flow. The effects of crossing trajectories and continuity are incorporated by generalising Csanady's (1963) ideas developed for stationary homogeneous turbulence; effects of turbulence inhomogeneity and nonstationarity are embodied in the stochastic model for the fluid motion.The model has been used particularly to examine the effects of turbulence nonstationarity through simulations of the dispersion of heavy particles in the decaying homogeneous turbulence which is obtained by Taylor-transforming grid turbulence. Significant differences from the stationary case occur, mainly as a result of the growth of the turbulent time scale with time.The importance of the source location in influencing both passive scalar and particle dispersion in grid turbulence is highlighted by the model and can be simply accounted for by nondimensionalisation using the r.m.s. turbulence velocity at the source and the mean travel time from the grid to the source as velocity and time scales, respectively. Reconciliation of the three different experiments of Snyder and Lumley (1971), Wells and Stock (1983) and Ferguson (1986) reporting heavy particle flow and dispersion statistics in wind tunnel grid turbulence has been attempted using this nondimensionalisation. A good correspondence between the various data sets was not obtained because the source in the Wells and Stock, and Ferguson experiments was located at the grid where the self-similar development of the turbulence which underlies the scaling is not appropriate.The model matches the data for the heaviest particles used by Snyder and Lumley reasonably well. For very light particles, it correctly reverts to the passive scalar limit, while the experimental data in general do not properly approach this limit.     

Application of Dynamic Subgrid-scale Models for Large-eddy Simulation of the Daytime Convective Boundary Layer over Heterogeneous Surfaces

The sensitivity of large-eddy simulation (LES) to the representation of subgrid-scale (SGS) processes is explored for the case of the convective boundary layer (CBL) developing over surfaces with varying degrees of spatial heterogeneity. Three representations of SGS processes are explored: the traditional constant Smagorinsky–Lilly model and two other dynamic models with Lagrangian averaging approaches to calculate the Smagorinsky coefficient (C _S ) and SGS Prandtl number (Pr). With initial data based roughly on the observed meteorology, simulations of daytime CBL growth are performed over surfaces with characteristics (i.e. fluxes and roughness) ranging from homogeneous, to striped heterogeneity, to a realistic representation of heterogeneity as derived from a recent field study. In both idealized tests and the realistic case, SGS sensitivities are mostly manifest near the surface and entrainment zone. However, unlike simulations over complex domains or under neutral or stable conditions, these differences for the CBL simulation, where large eddies dominate, are not significant enough to distinguish the performance of the different SGS models, irrespective of surface heterogeneity.     

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。     

Laboratory and Numerical Studies of the Convective Boundary Layer Capped by a Strong Inversion

The convective boundary layer (CBL) with a wide range of stability is simulated experimentally using a thermally stratified wind tunnel, and numerically by direct numerical simulation (DNS). The turbulence structures and flow characteristics of various CBL flows, capped by a strong temperature inversion and affected by surface shear, are investigated. The various vertical profiles of turbulence statistics similar to those from the observed CBL in the field are successfully simulated in both the wind-tunnel experiment and in DNS. The comparison of the wind-tunnel data and DNS results with those of atmospheric observations and water-tank studies shows the crucial dependence of the turbulence statistics in the upper part of the layer on the strength of the inversion layer, as well as the modification of the CBL turbulence regime by the surface shear.     

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.     

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.     

Large-Eddy Simulations of Atmospheric Flows Over Complex Terrain Using the Immersed-Boundary Method in the Weather Research and Forecasting Model

Atmospheric flow over complex terrain, particularly recirculation flows, greatly influences wind-turbine siting, forest-fire behaviour, and trace-gas and pollutant dispersion. However, there is a large uncertainty in the simulation of flow over complex topography, which is attributable to the type of turbulence model, the subgrid-scale (SGS) turbulence parametrization, terrain-following coordinates, and numerical errors in finite-difference methods. Here, we upgrade the large-eddy simulation module within the Weather Research and Forecasting model by incorporating the immersed-boundary method into the module to improve simulations of the flow and recirculation over complex terrain. Simulations over the Bolund Hill indicate improved mean absolute speed-up errors with respect to previous studies, as well an improved simulation of the recirculation zone behind the escarpment of the hill. With regard to the SGS parametrization, the Lagrangian-averaged scale-dependent Smagorinsky model performs better than the classic Smagorinsky model in reproducing both velocity and turbulent kinetic energy. A finer grid resolution also improves the strength of the recirculation in flow simulations, with a higher horizontal grid resolution improving simulations just behind the escarpment, and a higher vertical grid resolution improving results on the lee side of the hill. Our modelling approach has broad applications for the simulation of atmospheric flows over complex topography.     

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。     

日间对流边界层中的非局地动量混合

日间对流边界层最显著的结构特征是在热力作用下所形成的组织化对流。与小尺度湍涡不同的是,组织化对流具有边界层尺度的垂直相干性,可实现垂直贯穿边界层的非局地物质和能量传输。本文针对对流边界层中的动量混合,探究组织化对流对动量输送的贡献。以高精度大涡模拟数据为研究资料,通过傅里叶变换、本征正交分解和经验模态分解3种滤波方法,分离组织化对流和背景湍涡,计算与两者相关的非局地和局地动量通量,发现与组织化对流相关的非局地动量通量是总通量的重要组成部分,并主导混合层中的垂直动量输送。而后,基于协谱和相位谱分析,探究组织化对流的空间结构对动量传输的影响,发现在热力主导的不稳定环境中,单体型环流结构对动量的传输效率较低。而在风切较强的近中性环境中,滚涡型组织化结构可使垂直和水平流向扰动速度的相位差减小,从而提升动量传输效率。研究结果表明,边界层方案需要包含非局地动量通量项,其参数化应考虑整体稳定度对传输效率的影响。     

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＊）.     

冀中南一次强对流暴雨的数值模拟

利用NCEP 1°×1°再分析资料和常规资料对2009年5月发生在河北中南部的强对流暴雨天气过程进行了数值模拟。低空700 hPa流场的中尺度扰动和涡度场的加强说明：发生在河北中南部的短时强对流暴雨与东北回流密切相关 ,低空东北风的辐合,使地转平衡遭到破坏,从而引发水平辐合和辐散及铅直运动,在地转适应过程中,700 hPa中尺度环流偶在河北中南部形成并加强,对应的正负涡度对也出现并增大,使辐合上升运动增强,强对流暴雨出现在辐合场和辐散场之间区域。高空急流中心右前侧辐合导致气流下沉,向南的一支引起低空北风加大。加强的东北回流与低空较强偏南气流在河北南部相遇,耦合上升。可见,垂直环流的形成及东北回流的加强是此次强对流暴雨产生的重要原因。     

On the Nature of the Transition Between Roll and Cellular Organization in the Convective Boundary Layer

Both observational and numerical studies of the convective boundary layer (CBL) have demonstrated that when surface heat fluxes are small and mean wind shear is strong, convective updrafts tend to organize into horizontal rolls aligned within 10–20\(^\circ \) of the geostrophic wind direction. However, under large surface heat fluxes and weak to negligible shear, convection tends to organize into open cells, similar to turbulent Rayleigh-Bénard convection. Using a suite of 14 large-eddy simulations (LES) spanning a range of \(-z_i/L\) between zero (neutral) and 1041 (highly convective), where \(z_i\) is the CBL depth and L is the Obukhov length, the transition between roll- and cellular-type convection is investigated systematically for the first time using LES. Mean vertical profiles including velocity variances and turbulent transport efficiencies, as well the “roll factor,” which characterizes the rotational symmetry of the vertical velocity field, indicate the transition occurs gradually over a range of \(-z_i/L\); however, the most significant changes in vertical profiles and CBL organization occur from near-neutral conditions up to about \(-z_i/L \approx \) 15–20. Turbulent transport efficiencies and quadrant analysis are used to characterize the turbulent transport of momentum and heat with increasing \(-z_i/L\). It is found that turbulence transports heat efficiently from weakly to highly convective conditions; however, turbulent momentum transport becomes increasingly inefficient as \(-z_i/L\) increases.     

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.     

DYNAMIC STUDY ON INFLUENCE OF INERTIAL GRAVITY WAVES INDUCED BY UNBALANCED FLOW ON MEIYU FRONT HEAVY RAIN*

The Meiyu front heavy rain process in 1-3 June 2000 is numerically simulated in this paper, and results are then analyzed to show the effects of geostrophic balance collapse,unbalanced flow occurrence,low level jet (LLJ) development,and gravity waves genesis and propagation on the rainstorm.Analyses indicate that the sudden northwest movement of subtropical high may destruct the local geostrophic balance,leading to an increase in the local pressure gradient and the occurrence of ageostrophic flow,and meanwhile the adjustment of circulation starts to build a new balance.During the process,an LLJ and gravity waves appear correspondingly.The dispersion of unbalanced energy through the divergence/convergence of the geostrophic departure winds, promotes the propagation of strong wind cores along the LLJ,and the dispersion direction is influenced by the steering flow and the moisture concentration area.The development of LLJ is one of important conditions,which induces the heavy rain especially in the left front part of the jet where the convergence and shear of winds occur.It is also found that the genesis of disturbance, meso-vortex,and meso-convective system provides a favorable condition for the rainstorm.The above results are clearly illustrated by the high spatial and temporal resolution simulation data from a mesoscale numerical model.     

Evaluation of the Diurnal Cycle in the Atmospheric Boundary Layer Over Land as Represented by a Variety of Single-Column Models: The Second GABLS Experiment

We present the main results from the second model intercomparison within the GEWEX (Global Energy and Water cycle EXperiment) Atmospheric Boundary Layer Study (GABLS). The target is to examine the diurnal cycle over land in today??s numerical weather prediction and climate models for operational and research purposes. The set-up of the case is based on observations taken during the Cooperative Atmosphere-Surface Exchange Study-1999 (CASES-99), which was held in Kansas, USA in the early autumn with a strong diurnal cycle with no clouds present. The models are forced with a constant geostrophic wind, prescribed surface temperature and large-scale divergence. Results from 30 different model simulations and one large-eddy simulation (LES) are analyzed and compared with observations. Even though the surface temperature is prescribed, the models give variable near-surface air temperatures. This, in turn, gives rise to differences in low-level stability affecting the turbulence and the turbulent heat fluxes. The increase in modelled upward sensible heat flux during the morning transition is typically too weak and the growth of the convective boundary layer before noon is too slow. This is related to weak modelled near-surface winds during the morning hours. The agreement between the models, the LES and observations is the best during the late afternoon. From this intercomparison study, we find that modelling the diurnal cycle is still a big challenge. For the convective part of the diurnal cycle, some of the first-order schemes perform somewhat better while the turbulent kinetic energy (TKE) schemes tend to be slightly better during nighttime conditions. Finer vertical resolution tends to improve results to some extent, but is certainly not the solution to all the deficiencies identified.     

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 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.