Dispersion in sheared Gaussian homogeneous turbulence

By integrating the Fokker-Planck equation corresponding to a Lagrangian stochastic trajectory model, which is consitent with the selection criterion of Thomson (1987), an analytical solution is given for the joint probability density functionp(x_i, u_i, t) for the position (x _i) and velocity (u _i) at timet of a neutral particle released into linearly-sheared, homogeneous turbulence. The solution is compared with dispersion experiments conforming to the restrictions of the model and with a shortrange experiment performed in highly inhomogeneous turbulence within and above a model crop canopy. When the turbulence intensity, wind shear and covariance are strong, the present solution is better than simpler solutions (Taylor, 1921; Durbin, 1983) and as good as any numerical Lagrangian stochastic model yet reported.     

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.     

Comprehensive Parametrization of Surface-Layer Transfer Coefficients for Use in Atmospheric Numerical Models

A new non-iterative bulk parametrization for surface-layer transfer coefficients for momentum and heat is presented. It is applicable for a wide range of aerodynamic and thermal roughness lengths, and includes the effect of the roughness sublayer. As a consequence, the non-iterative method is suitable for every surface type, especially for urban surfaces for which existing non-iterative parametrizations fail. The analytical approximation compares very well with an iterative approach. Our method can be easily implemented in atmospheric numerical models that already employ a non-iterative approach.     

An Improved Approach for Parameterizing Surface-Layer Turbulent Transfer Coefficients in Numerical Models

Based on classic iterative computation results, new equations to calculate the surface turbulent transfer coefficients are proposed, which allow for large ratios of the momentum and heat roughness lengths. Compared to the Launiainen scheme, our proposed scheme generates results closer to classical iterative computations. Under unstable stratification, the relative error in the Launiainen scheme increases linearly with increasing instability, even exceeding 15%, while the relative error of the present scheme is always less than 8.5%. Under stable stratification, the Launiainen scheme uses two equations, one for 0 < Ri _B ≤ 0.08 and another for 0.08 < Ri _B ≤ 0.2, and does not consider the condition that Ri _B > 0.2, while its relative errors in the region 0 < Ri _B ≤ 0.2 exceed 31 and 24% for momentum and heat transfer coefficients, respectively. In contrast, the present scheme uses only one equation for 0 < Ri _B ≤ 0.2 and another equation for Ri _B > 0.2, and the relative error of the present scheme is always less than 14%.     

Validation of a New Turbulent Parameterization for Dispersion Models in Convective Conditions

A new parameterization for turbulentdispersion in a convective boundary layer isproposed. The model is based on turbulentkinetic energy spectra and Taylor's diffusiontheory. The formulation, included in an advanceddispersion model, has been tested and comparedwith vertical and lateral dispersion schemesreported in the literature, using data from fieldexperiments. The application of a statisticalevaluation shows that the proposedparameterization has the best overall fit to the data.     

Performance of Steady-State Dispersion Models Under Low Wind-Speed Conditions

We examine the performance of two steady-state models, a numerical solution of the advection-diffusion equation and the Gaussian plume-model-based AERMOD (the American Meteorological Society/Environmental Protection Agency Regulatory Model), to predict dispersion for surface releases under low wind-speed conditions. A comparison of model estimates with observations from two tracer studies, the Prairie Grass experiment and the Idaho Falls experiment indicates that about 50% of the concentration estimates are within a factor of two of the observations, but the scatter is large: the 95% confidence interval of the ratio of the observed to estimated concentrations is about 4. The model based on the numerical solution of the diffusion equation in combination with the model of Eckman (1994, Atmos Environ 28:265–272) for horizontal spread performs better than AERMOD in explaining the observations. Accounting for meandering of the wind reduces some of the overestimation of concentrations at low wind speeds. The results deteriorate when routine one-level observations are used to construct model inputs. An empirical modification to the similarity estimate of the surface friction velocity reduces the underestimation at low wind speeds.     

Some Simple Statistical Models For Relative And Absolute Dispersion

Observations of the dispersion of a contaminant plume in the atmospheric boundary layer, obtained using a Lidar, are analysed in the coordinate frame relative to the instantaneous centre of mass of the plume, as well as the absolute (or fixed) coordinate frame. The study extends the work presented in a previous article, which analysed the structure of the probability density function (pdf) of concentration within the relative coordinate frame. Firstly, the plume displacement component, or plume meander, is analysed and a simple parametric form for the pdf of the plume centreline position is suggested. This is then used to analyse the accuracy and applicability of absolute framework statistical quantities obtained by a convolution of the relative frame statistical quantity with the plume centreline pdf.     

On Trajectory Curvature as a Selection Criterion for Valid Lagrangian Stochastic Dispersion Models

Recently Wilson and Flesch (Boundary-Layer Meteorology, 84, 411-426, 1997) suggested that the average increment d z to the orientation = arctan(w/u) of the Lagrangian velocity-fluctuation vector can be used to distinguish the better Lagrangian stochastic models within the well-mixed class. Here it is demonstrated that the specification of d z constitutes neither a sufficient or universally applicable criterion to distinguish the better Lagrangian stochastic models within the well-mixed class. The hypothesis made by Wilson and Flesch that Lagrangian stochastic models with /P_E irrotational are zero-spin models, having d z=0, is proven     

An Advanced Puff Model Based On A Mixed Eulerian/Lagrangian Approach For Turbulent Dispersion In The Convective Boundary Layer

An advanced model aimed at describing the problem of dispersion in theconvective boundary layer is proposed. The pollutant particles are groupedin clusters and modelled as Gaussian puffs. The expansion of each puff ismodelled according to the concept of relative dispersion and expressed interms of the spectral properties of the energy containing eddies of the turbulent field. The centre of mass of each puff is moved along a stochastic trajectory, obtained using a Lagrangian stochastic model and filtering the velocity with a recursive Kalman filter. At any instant, a filtering procedure, depending both on travel time and on puff size, acts to select spectral components involved in the expansion and in the meandering of the puff. Such an approach requires only a moderate number of puff releases, so that the proposed model is faster to run than a standard Lagrangian model. On the other hand, unlike the traditional puff model, it allows us to simulate both expansion and meandering of the puff. Therefore, it is well suited to simulate dispersion when the turbulent structures are larger thanthe plume dimensions, as for example in convective conditions. Being based onspectral formulations in both Eulerian and Lagrangian parts, the model is consistent in all the turbulent parameterizations utilised. Comparisons with a standard Lagrangian particle model as well as with a classical convective experimental dataset show good performance of the proposed model.     

Rotation Of Trajectories In Lagrangian Stochastic Models Of Turbulent Dispersion

We present a new measure for the rotation of Lagrangian trajectories in turbulence that simplifies and generalises that suggested by Wilson and Flesch ( Boundary-Layer Meteorol. 84, 411–426). The new measure is the cross product of the velocity and acceleration and is directly related to the area, rather than the angle, swept out by the velocity vector. It makes it possible to derive a simple but exact kinematic expression for the mean rotation of the velocity vector and to partition this expression into terms that are closed in terms of Eulerian velocity moments up to second order and unclosed terms. The unclosed terms arise from the interaction of the fluctuating part of the velocity and the rate of change of the fluctuating velocity.We examine the mean rotation of a class of Lagrangian stochastic models that are quadratic in velocity for Gaussian inhomogeneous turbulence. For some of these models, including that of Thomson ( J. Fluid Mech. 180, 113–153), the unclosed part of the mean rotation vanishes identically, while for other models it is non-zero. Thus the mean rotation criterion clearly separates the class of models into two sets, but still does not provide a criterion for choosing a single model.We also show that models for which = 0 are independent of whether the model is derived on the assumption that total Lagrangian velocity is Markovian or whether the fluctuating part is Markovian.     

Lagrangian Stochastic Models For Turbulent Dispersion In The Atmospheric Boundary Layer

A one-particle three-dimensional stochastic Lagrangian model fortransport of particles in a horizontally-homogeneous atmosphericsurface layer with arbitrary one-point probability density functionof Eulerian velocity fluctuations is suggested. A uniquely definedLagrangian stochastic model in the class of well-mixed models isconstructed from physically plausible assumptions. These assumptionsare: (i) in the neutrally stratified horizontally homogeneous surface layer, the vertical motion is mainly controlled by eddies whose size is of order of the current height; and (ii), the streamwise drift term is independent of the crosswind velocity. Numerical simulations for neutral stratification have shown a good agreement of our model with the well-known Thomson's model, with Flesch and Wilson's model, and with experimental measurements as well. However there is a discrepancy of these results with the results obtained by Reynolds' model.     

Trajectory Curvature As A Selection Criterion For valid Lagrangian Stochastic Dispersion Models

Among well-mixed multi-dimensional Lagrangian stochastic (LS) dispersion models, we observe that those in poorest agreement with observations produce spiralling trajectories, with an associated reduction in dispersion. We therefore investigate statistics of increments d ' to the orientation '= arctan(W'/U') of the Lagrangian velocity-fluctuation vector – as a possible means to distinguish the better LS models within the well-mixed class. Zero-spin models, having d' = 0, are found to provide best agreement with observations. It is not clear however, whether imposition of the zero-spin property selects (in conjunction with the well-mixed condition) a unique model.     

公路和城市街渠机动车大气污染物扩散模式发展综述

随着城市机动车数量的增加，机动车尾气污染已经成为城市污染物的重要来源。研究机动车尾气扩散规律，可为公路建设，车流量控制，街道大气污染的监测、评价与防治提供科学依据。对公路机动车污染物扩散模型的发展进行了回顾，详细论述了高斯模式、数值模式、统计模式等模式的发展历程及其目前存在的问题，并比较了几种典型模式的性能优劣及其各种条件下的适用性。随后对城市街渠峡谷机动车污染物扩散模型进行专述，指出了街渠峡谷模式研究的难点在于街渠流场模拟，介绍了国外最新街渠流场研究方法。最后提出了当前机动车大气污染物扩散模型存在的主要困难，展望了其解决途径和发展的方向。     

On the Formulation of Lagrangian Stochastic Models of Scalar Dispersion Within Plant Canopies

Lagrangian stochastic models, quadratic in velocity and satisfying the well-mixed condition for two-dimensional Gaussian turbulence, are used to make predictions of scalar dispersion within a model plant canopy. The non-uniqueness associated with satisfaction of the well-mixed condition is shown to be non-trivial (i.e. different models produce different predictions for scalar dispersion). The best agreement between measured and predicted mean concentrations of scalars is shown to be obtained with a small sub-class of optimal models. This sub-class of optimal models includes Thomson's model (J. Fluid Mech. 180, 529–556, 1987), the simplest model that satisfies the well-mixed condition for Gaussian turbulence, but does not include two other models identified recently as being in optimal agreement with the measured spread of tracers in a neutral boundary layer. It is therefore demonstrated that such models are not universal, i.e. applicable to a wide range of flows without readjustment of model parameters. Predictions for scalar dispersion in the model plant canopy are also obtained using the model of Flesch and Wilson (Boundary-Layer Meteorol. 61, 349–374, 1992). It is shown that, when used with a Gaussian velocity distribution or a maximum-missing-information velocity distribution, which accounts for the measured skewness and kurtosis of velocity statistics, the agreement between predictions obtained using the model of Flesch and Wilson and measurements is as good as that obtained using Thomson's model.     

Numerical Considerations for Lagrangian Stochastic Dispersion Models: Eliminating Rogue Trajectories,and the Importance of Numerical Accuracy

When Lagrangian stochastic models for turbulent dispersion are applied to complex atmospheric flows, some type of ad hoc intervention is almost always necessary to eliminate unphysical behaviour in the numerical solution. Here we discuss numerical strategies for solving the non-linear Langevin-based particle velocity evolution equation that eliminate such unphysical behaviour in both Reynolds-averaged and large-eddy simulation applications. Extremely large or ‘rogue’ particle velocities are caused when the numerical integration scheme becomes unstable. Such instabilities can be eliminated by using a sufficiently small integration timestep, or in cases where the required timestep is unrealistically small, an unconditionally stable implicit integration scheme can be used. When the generalized anisotropic turbulence model is used, it is critical that the input velocity covariance tensor be realizable, otherwise unphysical behaviour can become problematic regardless of the integration scheme or size of the timestep. A method is presented to ensure realizability, and thus eliminate such behaviour. It was also found that the numerical accuracy of the integration scheme determined the degree to which the second law of thermodynamics or ‘well-mixed condition’ was satisfied. Perhaps more importantly, it also determined the degree to which modelled Eulerian particle velocity statistics matched the specified Eulerian distributions (which is the ultimate goal of the numerical solution). It is recommended that future models be verified by not only checking the well-mixed condition, but perhaps more importantly by checking that computed Eulerian statistics match the Eulerian statistics specified as inputs.     

多烟团模式在环境风险评价中的应用

应用多烟团模式,以硫化氢泄漏对大气影响为研究对象,模拟一起典型的突发性环境风险事故。并结合风对硫化氢的影响作用,预测出给定稳定度时,少量硫化氢泄漏所达到的最大落地浓度以及最大落地浓度点的下风向距离。分析表明,在同样的稳定度条件下,风速的不同会导致硫化氢扩散存在很大差异。并且在模拟过程中,少量的危险性气体硫化氢在大气中的扩散没有出现致死浓度,但存在一定的危害范围。因此,相关部门应当给予足够的重视,并对其周边环境以及居民做出相应的应急防范措施。     

A New Scheme for the Simulation of Microscale Flow and Dispersion in Urban Areas by Coupling Large-Eddy Simulation with Mesoscale Models

A coupling scheme is proposed for the simulation of microscale flow and dispersion in which both the mesoscale field and small-scale turbulence are specified at the boundary of a microscale model. The small-scale turbulence is obtained individually in the inner and outer layers by the transformation of pre-computed databases, and then combined in a weighted sum. Validation of the results of a flow over a cluster of model buildings shows that the inner- and outer-layer transition height should be located in the roughness sublayer. Both the new scheme and the previous scheme are applied in the simulation of the flow over the central business district of Oklahoma City (a point source during intensive observation period 3 of the Joint Urban 2003 experimental campaign), with results showing that the wind speed is well predicted in the canopy layer. Compared with the previous scheme, the new scheme improves the prediction of the wind direction and turbulent kinetic energy (TKE) in the canopy layer. The flow field influences the scalar plume in two ways, i.e. the averaged flow field determines the advective flux and the TKE field determines the turbulent flux. Thus, the mean, root-mean-square and maximum of the concentration agree better with the observations with the new scheme. These results indicate that the new scheme is an effective means of simulating the complex flow and dispersion in urban canopies.     

Measurements of Turbulence and Dispersion in Three Idealized Urban Canopies with Different Aspect Ratios and Comparisons with a Gaussian Plume Model

Water-tunnel measurements of velocity, turbulence and scalar concentration for three model urban canopies with aspect ratios A _r of building height-to-width of 0.25, 1 and 3 are presented. The measurements for the canopies with A _r = 1 and 3 are new, while the measurements for A _r = 0.25 were previously published. A passive scalar was continuously released from a near-ground point source, and the concentration was measured at several distances from the source and at different heights above the ground. Plume spreads, concentration and distance from the source were non-dimensionalized using length, time and velocity scales reflecting the geometry of the buildings. The scaling collapses the data for all aspect ratios and is valid when the vertical extent of the plume is smaller than the canopy height. The observed plume spreads are compared with analytical relations, which predict linear growth in both transverse and vertical directions. The observed mean concentration is compared with a Gaussian dispersion model that predicts a ?2 power-law decay with distance from the source.     

Lagrangian Particle Dispersion Models in the Grey Zone of Turbulence: Adaptations to FLEXPART-COSMO for Simulations at 1 km Grid Resolution

Boundary-Layer Meteorology - Lagrangian particle dispersion models (LPDMs) are frequently used for regional-scale inversions of greenhouse gas emissions. However, the turbulence parameterizations...     

Fetch Limited Drag Coefficients

Measurements made at a tower located 2 km off the coast of Denmark inshallow water during the Risø Air Sea Experiment (RASEX) are analyzedto investigate the behaviour of the drag coefficient in the coastal zone.For a given wind speed, the drag coefficient is larger during conditions ofshort fetch (2-5 km) off-shore flow with younger growing waves than it isfor longer fetch (15-25 km) on-shore flow. For the strongest on-shorewinds, wave breaking enhances the drag coefficient. Variation of the neutral drag coefficient in RASEX is dominated byvariation of wave age, frequency bandwidth of the wave spectra and windspeed. The frequency bandwidth is proportional to the broadness of the waveheight spectra and is largest during conditions of light wind speeds. Usingthe RASEX data, simple models of the drag coefficient and roughness length are developed in terms of wind speed, wave age and bandwidth. An off-shoreflow model of the drag coefficient in terms of nondimensional fetch isdeveloped for situations when the wave state is not known.