Probability distributions of concentration fluctuations of a weakly diffusive passive plume in a turbulent boundary layer

Results are presented from an experimental investigation of turbulent dispersion of a saline plume of large Schmidt number (Sc=830) in a turbulent boundary-layer shear flow simulated in a laboratory water channel. The dispersion measurements are obtained in a neutrally buoyant plume from an elevated point source over a range of downstream distances, where both plume meandering and fine-structure variations in the instantaneous plume are important. High-resolution measurements of the scalar fluctuations in the plume are made with a rake of conductivity probes from which probability distributions of concentration at various points throught the plume are extracted from the time series.Seven candidate probability distributions were tested, namely, the exponential, lognormal, clipped normal, gamma, Weibull, conjugate beta, andK-distributions. Using the measured values of the conditional mean concentration, , and the conditional fluctuation intensity,i _p , the Weibull distribution provided the best match to the skewness and kurtosis over all downstream fetches. The skewness and kurtosis were always overpredicted by the lognormal probability density function (pdf), and underpredicted by the gamma pdf. The conjugate beta distribution for which the model parameters are determined using a method of moments based on the fluctuation intensity,i _p , and skewness,S _p , was capable of modeling the distribution of scalar concentration over a wide range of positions in the plume.     

大气边界层湍流标量场的概率分布及其特征分析

利用2004年11月在白洋淀地区和2005年1月在中国科学院大气物理研究所北京325 m气象塔的47 m高度由超声风温仪和水汽二氧化碳分析仪观测的湍流脉动资料,分析了大气边界层不同下垫面湍流标量场(温度、水汽和二氧化碳)的概率分布及其特征。标量场的概率分布通常不同于高斯分布,而且还会产生偏斜,可以用指数分布描述。因此,标量的偏斜度通常不为0,陡峭度也往往比3大。非0偏斜度的出现可能是由湍流时间序列中的相干结构和间歇性部分造成的。其中,相干结构的存在使概率分布偏斜,但是,它们对偏斜度的贡献相对较小,而与概率分布的长尾现象有关的间歇性则会使偏斜度大大增加。温度、水汽和二氧化碳的平均偏斜度和陡峭度反应了标量场与稳定度、下垫面、天气条件、源汇等因素之间的关系。在不同下垫面,温度和感热通量的偏斜度随稳定度变化比较一致;水汽通量的偏斜度在稳定和不稳定条件下都为正,而水汽本身在不稳定条件下可能出现负的偏斜度;二氧化碳和二氧化碳通量的偏斜度受下垫面影响很大,在不同下垫面,偏斜度与稳定度之间的关系并不一致;而3个标量的陡峭度随稳定度的变化不显著,它们与相应的偏斜度之间存在平方关系。     

Non-Gaussian Lagrangian Stochastic Model for Wind Field Simulation in the Surface Layer

Wind field simulation in the surface layer is often used to manage natural resources in terms of air quality,gene flow(through pollen drift),and plant disease transmission(spore dispersion).Although Lagrangian stochastic(LS)models describe stochastic wind behaviors,such models assume that wind velocities follow Gaussian distributions.However,measured surface-layer wind velocities show a strong skewness and kurtosis.This paper presents an improved model,a non-Gaussian LS model,which incorporates controllable non-Gaussian random variables to simulate the targeted non-Gaussian velocity distribution with more accurate skewness and kurtosis.Wind velocity statistics generated by the non-Gaussian model are evaluated by using the field data from the Cooperative Atmospheric Surface Exchange Study,October 1999 experimental dataset and comparing the data with statistics from the original Gaussian model.Results show that the non-Gaussian model improves the wind trajectory simulation by stably producing precise skewness and kurtosis in simulated wind velocities without sacrificing other features of the traditional Gaussian LS model,such as the accuracy in the mean and variance of simulated velocities.This improvement also leads to better accuracy in friction velocity(i.e.,a coupling of three-dimensional velocities).The model can also accommodate various non-Gaussian wind fields and a wide range of skewness–kurtosis combinations.Moreover,improved skewness and kurtosis in the simulated velocity will result in a significantly different dispersion for wind/particle simulations.Thus,the non-Gaussian model is worth applying to wind field simulation in the surface layer.     

The Relationship between Skewness and Kurtosis of A Diffusing Scalar

It has been demonstrated that in turbulent dispersion, there exists a quadratic relationship between the skewness (S) and kurtosis (K) statistics obtained from continuous, elevated sources of scalar contaminant released into both convective and stable atmospheric boundary layers. Specifically, one observes that where A and B are empirically fitted constants that depend on the flow. For two reasons, this is potentially useful information in regard to modelling the probability density function (PDF) of a diffusing scalar. First, since many PDFs have a signature relationship between their skewness and kurtosis, candidate models can immediately be either accepted or rejected depending upon whether they conform to the quadratic curve that is observed experimentally. Second, if one intends to model the PDF by inverting a limited number of moments, the task is reduced when there is a functional relationship between the standardized third and fourth moments. The aforementioned relationship has been corroborated by others who have examined data over a wide range of experimental configurations. However, from one flow to another, there appears to be a non-negligible variability in the two fitting constants of the quadratic curve. In this paper we put forth a framework to help explain this phenomenon, and we also attempt to predict how these parameters vary in space and/or time. Our point is illustrated with well-resolved data from a wind-tunnel, grid-turbulence, plume experiment.     

THE EFFECTS OF HIGHER EULERIAN VELOCITY MOMENTS ON THE MEAN CONCENTRATION DISTRIBUTION

In this paper, we present a well-mixed Lagrangian stochasticmodel for vertical dispersion, that can accommodate a Eulerianprobability density function of vertical velocity derived from themaximum missing information (or maximum entropy) principle. Withthis model, we study the effects of skewness (S) and kurtosis (K) ofvertical velocity on the spacial distribution of the mean concentrationdue to sources in the convective boundary layer. Model calculationsshow that the maximum ground-level concentration increases withincreasing S and decreasing K, but the downstream distance to thelocation of the maximum ground-level concentration is ratherinsensitive to S and K. Some earlier predictions of vertical dispersionfor short travel time are examined.     

Dispersion Moments of Fumigating Plumes – Lidar Estimates and Pdf Model Simulations

Near-instantaneous vertical scans ofpower plant plumes, sampled by a lidar over three days as part ofthe 1995 Kwinana Coastal Fumigation Study, are analysed to obtainhourly-averaged total dispersion moments up to fourth order, andalso the relative and meander spreads. Two distinct fumigationcases, termed as neutral and stable cases, are observed dependingon whether the plume transport prior to fumigation takes place ina neutral atmosphere, or in a stable region above the neutralatmosphere. Plumes in the stable case are observed to undergoslower fumigation. The mean spreads display contrasting behavioursfor the two fumigating cases, while the vertical skewness shows anegative peak value of about -1 for the neutral case and -2for the stable case in the fumigation zone. The lateral skewnessis positive with a peak value of about unity for both cases, andis attributed to wind directional shear within the thermalinternal boundary layer. The vertical kurtosis is greater than theGaussian value of 3 in the fumigation zone, while the lateralkurtosis is scattered about this value. A recently-developedskewed probability density function model with wind shear isapplied to describe the fumigation data. Overall, the modelsimulates the observed vertical and lateral statistics well up tothe fourth order, except for the lateral skewness and kurtosisvalues in the stable case, which is probably due to the lidar'srange and sensitivity constraints and an inadequate sample size.Although the lateral turbulent diffusion in the model is Gaussian(i.e., zero skewness), the inclusion of wind shear in the model ismanifested in the predicted lateral skewness being greater thanzero in the fumigation zone, and of similar magnitude to the lidardata in the neutral case.     

Concentration Fluctuations in Smoke Plumes Released Near the Ground

Near-ground artificial cloud releases in the turbulent atmospheric boundary layer were investigated experimentally by Lidar measurement techniques. Simple scaling relations between the average concentration and the lowest order moments are suggested by simple analytical models, and the experimental results are tested against these hypotheses. We find strong evidence for a simple scaling of the standard deviation, skewness and kurtosis with the average concentrations at the downwind distances observed in our experiments. Near-ground concentration fluctuations in fixed as well as moving frames of references are investigated. The scaling is supported by data from several experimental sites and different atmospheric stability conditions. One conclusion of the study is that relatively accurate estimates for the standard deviation, skewness and kurtosis can be obtained for the concentration fluctuations, given a reliable estimate of the space-time varying average concentration field.     

Autocorrelation properties of the sunshine number and sunshine stability number

Two new Boolean parameters are defined: the sunshine number (related to the state of the sky) and the sunshine stability number (which is as a measure of the fluctuation of the radiative regime). Elementary statistical and sequential properties of both parameters are presented in this paper. Actinometric and meteorological data measured at 15?s lag during 2009 in Timisoara (Romania, southeastern Europe) are used. The yearly series of daily averaged sunshine number has negative skewness and kurtosis. The series of daily averaged sunshine stability number has positive skewness and kurtosis. The series of daily averaged values of sunshine number are best described by an ARIMA(0,1,2) model. ARIMA(0,1,0) and ARIMA(0,2,0) models (associated with an appropriately defined white noise) may be used for synthesis of the sunshine number time series. The first model is to be preferred for practical reasons. The series of daily averaged values of sunshine stability number are best described by an ARIMA(2,2,1) model. The ARIMA(0,0,0) model is recommended to be used for generating time series of sunshine stability number. This model may be used for any particular day during the year and the only parameter depending on the day is the white noise standard deviation. A relationship between the white noise standard deviation and the daily averaged sunshine stability number is proposed.     

Boundedness of Turbulent Temperature Probability Distributions,and their Relation to the Vertical Profile in the Convective Boundary Layer

Higher-order moments, minima and maxima of turbulent temperature and water vapour mixing ratio probability density functions measured with an eddy-covariance system near the ground were related to each other and to vertical boundary-layer profiles of the same scalars obtained through airborne soundings. The dependence of kurtosis on squared skewness showed a kurtosis intercept below the Gaussian expectation, suggesting a compression of the probability density function by the presence of natural boundaries. This hypothesis was corroborated by comparing actual minima and maxima of turbulent fluctuations to estimates obtained from the first four sample moments by fitting a four-parameter beta distribution. The most sharply defined boundaries were found for the minima of temperature datasets during the day, indicating that negative temperature fluctuations at the sensor are limited by the availability of lower temperatures in the boundary layer. By comparison to vertical profiles, it could be verified that the turbulent minimum of temperature near the ground is close to the minimum of potential temperature in the boundary layer. The turbulent minimum of water vapour mixing ratio was found to be equal to the mixing ratio at a height above the minimum of the temperature profile. This height roughly agrees with the top of the non-local unstable domain according to bulk Richardson number profiles. We conclude that turbulence statistics measured near the surface cannot be solely explained by local effects, but contain information about the whole boundary layer including the entrainment zone.     

On the influence of non-Gaussianity on turbulent transport

Non-Gaussianity effects, first of all the influence of the third and fourth moments of the velocity probability density function, have to be assessed for higher-order closure models of turbulence and Lagrangian modelling of turbulent dispersion in complex flows. Whereas the role and the effects of the third moments are relatively well understood as essential for the explanation of specific observed features of the fully developed convective boundary layer, there are indications that the fourth moments may also be important, but little is known about these moments. Therefore, the effects of non-Gaussianity are considered for the turbulent motion of particles in non-neutral flows without fully developed convection, where the influence of the fourth moments may be expected to be particularly essential. The transport properties of these flows can be characterized by a diffusion coefficient which reflects these effects. It is shown, for different vertical velocity distributions, that the intensity of turbulent transport may be enhanced remarkably by non-Gaussianity. The diffusion coefficient is given as a modification of the Gaussian diffusivity, and this modifying factor is found to be determined to a very good approximation by the normalized fourth moment of the vertical velocity distribution function. This provides better insight into the effect of fourth moments and explains the varying importance of third and fourth moments in different flows.     

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.     

Random-walk model studies of the transport and diffusion of pollutants in katabatic flows

The flow and turbulence quantities governing dispersion in katabatic flows vary with both height and downslope distance. This variation cannot be accounted for in conventional plume dispersion models. In this study, three random-walk models of varying complexity are formulated to simulate dispersion in katabatic flows, and their strengths and weaknesses are discussed. The flow and turbulence parameters required by these models are determined from a high-resolution two-dimensional katabatic flow model based on a turbulent kinetic energy closure. Random-walk model calculations have been performed for several values of source height and slope angle to examine the influence of these parameters on dispersion. Finally, we simulated the perfluorocarbon and heavy methane tracer releases for Night 4 of the 1980 ASCOT field study over a nearly two-dimensional slope in Anderson Creek Valley, California. The observed peak concentrations are generally well-predicted. The effects of the pooling of the drainage air could not be taken into account in our katabatic flow model and, consequently, the predicted concentrations decay much more rapidly with time than the observed values.     

Turbulence in an almond orchard: Vertical variations in turbulent statistics

Three-dimensional wind velocity components were measured above and within a uniform almond orchard. Turbulent statistics associated with the turbulent flow inside the canopy are examined in detail. Turbulence in an almond orchard is characterized by relatively high turbulent intensities and large skewness and kurtosis values. These results indicate that the frequency distribution of wind velocity components is non-Gaussian. Conditional sampling of the turbulent measurements show that large, infrequent sweeps provide the predominant mechanism for tangential momentum stress in the canopy crown. Deep inside the canopy, a secondary wind maximum and small, but positive, tangential momentum stresses are observed.     

The Transport Time pdf for a Simple Turbulent Flow

In a turbulent fluid, the time a particle needs to travel from a point source to the observation point, can be considered as a random variable. It is shown that the probability density function (pdf) for this random variable is determined by the Lagrangian particle position pdf. The characteristics of the transport time pdf are discussed for the simple case of a turbulent fluid moving with a constant mean velocity.     

High-Order Statistics of Temperature Fluctuations in an Unstable Atmospheric Surface Layer over Grassland

Skewness(S) and kurtosis(K) of temperature in the surface layer over a grassland are investigated under unstable thermal stratifications. We find that both skewness and kurtosis generally obey Monin–Obukhov similarity theory and tend to be constant values(1.5 and 5.3, respectively) when the stability parameter z/L -2. Quantitative formulas of the similarity functions are proposed. The temperature probability density function(PDF) is close to Gaussian in near neutral stratification and non-Gaussian in unstable stratification. The influence of coherent motions on the PDF behavior is analyzed using the quadrant analysis technique. It shows that PDF behaviors are controlled by ejections and sweeps. The results also indicate that the PDF type of the ejections always follows a Gaussian distribution, while the PDF of the sweeps changes with stability.     

Modelling of concentration fluctuations in canopy turbulence

The knowledge of the concentration probability density function (pdf) is of importance in a number of practical applications, and a Lagrangian stochastic (LS) pdf model has been developed to predict statistics and concentration pdf generated by continuous releases of non-reactive and reactive substances in canopy generated turbulence. Turbulent dispersion is modelled using a LS model including the effects of wind shear and along-wind turbulence. The dissipation of concentration fluctuations associated with turbulence and molecular diffusivity is simulated by an Interaction by Exchange with the Conditional Mean (IECM) micromixing model. A general procedure to obtain the micromixing time scale needed in the IECM model useful in non-homogeneous conditions and for single and multiple scalar sources has been developed. An efficient algorithm based on a nested grid approach with particle splitting, merging techniques and time averaging has been used, thus allowing the calculation for cases of practical interest. The model has been tested against wind-tunnel experiments of single line and multiple line releases in a canopy layer. The approach accounted for chemical reactions in a straightforward manner with no closure assumptions, but here the validation is limited to non-reacting scalars.     

On the determination of the closure parameters in higher-order closure models

In higher-order closure models at least the pressure redistribution and the dissipation of the turbulent kinetic energy and the temperature variance have to be parameterized. Due to this, the introduction of proportionality coefficients — the so-called closure parameters — is forced, which have to be determined before the model is used. We compare a group of models which use the return-to-isotropy hypothesis (Rotta, 1951) to describe the pressure redistribution and assume local isotropy for the smallest eddies in order to parameterize the dissipation. Special concern is given to the method of Mellor and Yamada (1982). Some of the closure parameters are re-derived on the basis of sensitivity studies requiring that both shear production and buoyancy behave in a realistic way if pressure redistribution or dissipation is changed by varying the closure parameters. This set of parameters is compared with those obtained by fitting to experimental data, by use of the Monin-Obukhov similarity theory and by considering ratios of variances, covariances and mean flow gradients, respectively. It is shown that the various sets of closure parameters are at least of the same order. The differences give some insight into the advantages and disadvantages of the various determination procedures. However, the general accordance of the different parameter sets supports the assumption of universal constants.     

The perturbed structure of the neutral atmospheric boundary layer over irregular terrain

The differential equations for first-order (linear) response of the planetary boundary layer are formulated for flow over periodic terrain, for variations in both surface roughness and terrain elevation. A simple second-order closure model of the turbulence is used, and Coriolis forces are neglected. Flow over a periodic terrain produces corresponding periodic structure in all meteorological fields above the surface. The periodic structure consists of two components. The first is very nearly evanescent with height. It corresponds to the motion that would be observed were the atmosphere inviscid. The second component, introduced by turbulent viscosity, exhibits a phase variation with height in addition to a decay in amplitude. W.K.B. [Wentzel-Kramers-Brillouin] approximations for the two components are developed, and the coupling between the components is discussed. The formulation for calculating solutions by numerical integration is developed, including specification of appropriate boundary conditions. Calculations are presented in a companion paper.Wave Propagation Laboratory.Environmental Science Group.     

城市边界层动量和保守物通量的特征

利用2005年1-5月北京325 m气象塔47 m高度的湍流脉动资料(风速、温度、水汽和CO2),对城市边界层冠层内的湍流运动统计特征(相似关系、高阶矩、通量和谱等)进行了分析。其中,谱分析的结果表明,城市冠层内稳定度对湍流谱的影响比较小,而水平风速的影响比较大。因此,速度和温度的相似关系在夜间稳定条件下也成立。但是,由于水汽和CO2还受其他因素的影响,相似关系并不适用。更高阶矩的研究表明它们的陡峭度与偏斜度之间存在平方关系。而水汽和CO2之间也存在差异,它们的通量日变化特征明显不同,CO2通量的日变化更能体现人类活动的影响。同时,感热通量、潜热通量和CO2通量存在季节变化,尤其是潜热通量季节差异很大。     

On The Dynamical Content Of Lagrangian Stochastic Models In The Well-Mixed Class

It is shown how the correspondence between Lagrangian stochasticmodels and second-moment closures of the scalar-flux equation can be exploited to distinguishbetween Lagrangian stochastic models in the well-mixed class. It is found that physically realisticclosures of the scalar-flux equation correspond to Lagrangian stochastic models that have non-zero`spin' and so produce spiralling tracer-particle trajectories, whilst `zero-spin'models correspond to the isotropic-production model of scalar-fluxes.Lagrangian stochastic models consistent with rapid distortion theory and Speziale's transformation rule for the Reynolds stressequations in the extreme limit of two-dimensional turbulence are also shown to have non-zero spin.The residual non-uniqueness associated with satisfaction of thewell-mixed condition and the specification of mean spin is shown to be related to the helicity oftracer-particle trajectories. Investigations are also made of the influence upon turbulent dispersion oftime-dependent spin and of mean rotations of the fluctuating Lagrangian acceleration vector(i.e., second-order spin).