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.     

Scaling Properties of Biologically Active Scalar Concentration Fluctuations in the Atmospheric Surface Layer over a Managed Peatland

The higher-order scalar concentration fluctuation properties are examined in the context of Monin–Obukhov similarity theory for a variety of greenhouse gases that have distinct and separate source/sink locations along an otherwise ideal micrometeorological field site. Air temperature and concentrations of water vapour, carbon dioxide and methane were measured at high frequency (10 Hz) above a flat and extensive peat-land soil in the San Joaquin–Sacramento Delta (California, USA) area, subjected to year-round grazing by beef cattle. Because of the heterogeneous distribution of the sources and sinks of CO₂ and especially CH₄ emitted by cattle, the scaling behaviour of the higher-order statistical properties diverged from predictions based on a balance between their production and dissipation rate terms, which can obtained for temperature and H₂O during stationary conditions. We identify and label these departures as ‘exogenous’ because they depend on heterogeneities and non-stationarities induced by boundary conditions on the flow. Spectral analysis revealed that the exogenous effects show their signatures in regions with frequencies lower than those associated with scalar vertical transport by turbulence, though the two regions may partially overlap in some cases. Cospectra of vertical fluxes appear less influenced by these exogenous effects because of the modulating role of the vertical velocity at low frequencies. Finally, under certain conditions, the presence of such exogenous factors in higher-order scalar fluctuation statistics may be ‘fingerprinted’ by a large storage term in the mean scalar budget.     

Joint PDF Modelling of Turbulent Flow and Dispersion in an Urban Street Canyon

The joint probability density function (PDF) of turbulent velocity and concentration of a passive scalar in an urban street canyon is computed using a newly developed particle-in-cell Monte Carlo method. Compared to moment closures, the PDF methodology provides the full one-point one-time PDF of the underlying fields containing all higher moments and correlations. The small-scale mixing of the scalar released from a concentrated source at the street level is modelled by the interaction by exchange with the conditional mean (IECM) model, with a micro-mixing time scale designed for geometrically complex settings. The boundary layer along no-slip walls (building sides and tops) is fully resolved using an elliptic relaxation technique, which captures the high anisotropy and inhomogeneity of the Reynolds stress tensor in these regions. A less computationally intensive technique based on wall functions to represent the boundary layers and its effect on the solution are also explored. The calculated statistics are compared to experimental data and large-eddy simulation. The present work can be considered as the first example of computation of the full joint PDF of velocity and a transported passive scalar in an urban setting. The methodology proves successful in providing high level statistical information on the turbulence and pollutant concentration fields in complex urban scenarios.     

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.     

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.     

Experimental Measurements of Expected Mass Fraction in a Contaminant Plume

The sudden release of a quantity of gas into the atmospheric boundary layer produces a contaminant cloud. The expected mass fraction function provides a relatively simple measure of the contaminant concentration values found within the cloud and represents the ensemble-averaged fraction of the conserved release mass found at the different contaminant concentration intervals as the cloud evolves. The plume generated by a line source in grid turbulence is used to investigate the expected mass fraction function as it applies to scalar concentration values found on a typical line normal to the plume axis. Simultaneous particle image velocimetry and planar laser induced fluorescence are used to measure velocity and concentration fields, respectively. The measured expected mass fraction functions are observed to be approximately self-similar when concentration values are normalized by the centreline mean concentration. The moments of the expected mass fraction function are observed to be simply related to the centreline moments of the probability density function of scalar concentration. Arguments based on a source fluid, non-source fluid decomposition of the scalar probability density function are used to explain these observations. The results are compared with the theoretical and experimental results established for a line source of scalar in grid turbulence.     

A Semi-analytical Model for Short-Range Near-Ground Continuous Dispersion

We present a semi-analytical model for the dispersion of passive scalars from continuous ground sources up to distances of a few hundred metres. We attempt to cope with problems typical of analytical models, such as the correct representation of the near-ground concentration and lateral dispersion, while avoiding the use of any empirical parameters. A previous analysis of Prairie Grass Project (PGP) data has shown that the near-ground, cross-wind integrated concentration decreases as some power of the distance from the source that is, itself, distance dependent. As the conventional power-law model is incapable of reproducing this behaviour, we propose a model in which the vertical diffusivity depends on both the height as a power law, and on the distance from the source. For this equation, we construct an infinite-series formal solution, with the first term used as an approximation. A set of equations based on this approximation and on Monin–Obukhov similarity theory is proposed for the the vertical diffusivity, from which the cross-wind integrated concentration is derived analytically. We further construct a simple empirical model for the distance-dependent vertical diffusivity. For the plume lateral width, a Langevin stochastic model depending on the plume height is proposed, whose formal analytical solution is used to derive a set of equations for the cloud width, which are easily solved numerically, with the results validated against PGP data. We apply four statistical measures to evaluate the performance of the model, including the computation of the 95% confidence intervals, for which we find very good agreement. Implementation of this model is extremely simple and computationally efficient.     

The Effect of the Vertical Source Distribution on Scalar Statistics within and above a Forest Canopy

Little is known about in-canopy processes that may alter forest–atmosphere exchanges of trace gases and aerosols. To improve our understanding of in-canopy mixing, we use large-eddy simulation to study the effect of scalar source/sink distributions on scalar concentration moments, fluxes, and correlation coefficients within and above an ideal forest canopy. Scalars are emitted from: (1) the ground, (2) the canopy, and (3) both the ground and the canopy; a scalar is also deposited onto the canopy. All scalar concentration moments, fluxes, and correlation coefficients are affected by the source location/distribution, as is the scalar segregation intensity. We conclude that vertical source/sink distribution has a profound impact on scalar concentration profiles, fluxes, correlation coefficient, and scalar segregation.     

A Velocity–Dissipation Lagrangian Stochastic Model for Turbulent Dispersion in Atmospheric Boundary-Layer and Canopy Flows

An extended Lagrangian stochastic dispersion model that includes time variations of the turbulent kinetic energy dissipation rate is proposed. The instantaneous dissipation rate is described by a log-normal distribution to account for rare and intense bursts of dissipation occurring over short durations. This behaviour of the instantaneous dissipation rate is consistent with field measurements inside a pine forest and with published dissipation rate measurements in the atmospheric surface layer. The extended model is also shown to satisfy the well-mixed condition even for the highly inhomogeneous case of canopy flow. Application of this model to atmospheric boundary-layer and canopy flows reveals two types of motion that cannot be predicted by conventional dispersion models: a strong sweeping motion of particles towards the ground, and strong intermittent ejections of particles from the surface or canopy layer, which allows these particles to escape low-velocity regions to a high-velocity zone in the free air above. This ejective phenomenon increases the probability of marked fluid particles to reach far regions, creating a heavy tail in the mean concentration far from the scalar source.     

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.     

Dispersion of a Passive Scalar Fluctuating Plume in a Turbulent Boundary Layer. Part III: Stochastic Modelling

We analyze the reliability of the Lagrangian stochastic micromixing method in predicting higher-order statistics of the passive scalar concentration induced by an elevated source (of varying diameter) placed in a turbulent boundary layer. To that purpose we analyze two different modelling approaches by testing their results against the wind-tunnel measurements discussed in Part I (Nironi et al., Boundary-Layer Meteorology, 2015, Vol. 156, 415–446). The first is a probability density function (PDF) micromixing model that simulates the effects of the molecular diffusivity on the concentration fluctuations by taking into account the background particles. The second is a new model, named VP\(\varGamma \), conceived in order to minimize the computational costs. This is based on the volumetric particle approach providing estimates of the first two concentration moments with no need for the simulation of the background particles. In this second approach, higher-order moments are computed based on the estimates of these two moments and under the assumption that the concentration PDF is a Gamma distribution. The comparisons concern the spatial distribution of the first four moments of the concentration and the evolution of the PDF along the plume centreline. The novelty of this work is twofold: (i) we perform a systematic comparison of the results of micro-mixing Lagrangian models against experiments providing profiles of the first four moments of the concentration within an inhomogeneous and anisotropic turbulent flow, and (ii) we show the reliability of the VP\(\varGamma \) model as an operational tool for the prediction of the PDF of the concentration.     

Comparison of Wind-tunnel and Water-channel Simulations of Plume Dispersion through a Large Array of Obstacles with a Scaled Field Experiment

We report on measurements of the near-field dispersion of contaminant plumes in a large array of building-like obstacles at three scales; namely, at full-scale in a field experiment, at 1:50 scale in a wind-tunnel simulation, and at 1:205 scale in a water-channel simulation. Plume concentration statistics extracted from the physical modelling in the wind-tunnel and water-channel simulations are compared to those obtained from a field experiment. The modification of the detailed structure of the plume as it interacts with the obstacles is investigated. To this purpose, measurements of the evolution of the mean concentration, concentration fluctuation intensity, concentration probability density function, and integral time scale of concentration fluctuations in the array plume obtained from the field experiment and the scaled wind-tunnel and water-channel experiments are reported and compared, as well as measurements of upwind and within-array velocity spectra. Generally, the wind-tunnel and water-channel results on the modification of the detailed plume structure by the obstacles were qualitatively similar to those observed in the field experiments. However, with the appropriate scaling, the water-channel simulations were able to reproduce quantitatively the results of the full-scale field experiments better than the wind-tunnel simulations.     

Three-Dimensional Scalar Microfront Systems in a Large-Eddy Simulation of Vegetation Canopy Flow

Large-eddy simulation is used to reproduce neutrallystratified airflow inside and immediately above a vegetation canopy. A passive scalaris released from the canopy and the evolution of scalar concentration above the canopyis studied. The most significant characteristic of the scalar concentration is the repeatedformation and dissipation of scalar microfronts, a phenomenon that has been observedin nature. These scalar microfronts consist of downstream-tilted regions of highscalar concentration gradients. Computer visualization tools and a conditional samplingand compositing technique are utilized to analyze these microfronts. Peaks in positivepressure perturbation exceeding an experimental threshold are found to be effectiveindicators of scalar microfronts. Convergence of the streamwise velocity componentand divergence of the cross-stream velocity component are observed in the immediatevicinity of scalar microfronts, which helps explain their relatively longlifetimes. Many of these three-dimensional features have been observedin previous field studies of canopy flow.     

Relationships between higher moments of concentration and of dose in turbulent dispersion

Chatwin and Sullivan (1990) proposed simple results for the relationships between moments of scalar fluctuations in self-similar turbulent shear flows. They showed these relationships to be well satisfied by observations from a range of experiments. Here their theory is extended to the skewness, kurtosis and higher order equivalents. It is shown that the relationships between these normalised moments are parameter-free, and are identical to those for zero molecular diffusion. Experimental observations are presented which show a remarkable degree of collapse when these normalised moments are plotted against each other. The agreement with the theoretical results is reasonably good, and better than for some other standard statistical distributions which are commonly applied to such observations. This is true not only for the concentration, but also for generalised doses. It is concluded that the simple theory provides a satisfactory basis for a model of both the concentration and of dose. Furthermore, the results suggest that the concentration and the dose can be modelled through a perturbation to a two-state model.     

Convective scaling of the average dissipation rate of temperature variance in the atmospheric surface layer

The flux of sensible heat from the land surface is related to the average rate of dissipation of temperature fluctuations in the atmospheric surface layer through the temperature variance budget equation. In many cases it is desirable to estimate the heat flux from measurement or inference of the dissipation rate. Here we study how the dissipation rate scales with atmospheric stability, using three inertial range methods to calculate the dissipation rate: power spectra, second order structure functions, and third order structure functions. Experimental data are analyzed from a pair of field experiments, during which turbulent fluctuations of velocity and temperature were measured over a broad range of neutral and unstable atmospheric flows. It is shown that the temperature dissipation rate scales with a single convective power law continuously from near-neutral to strongly unstable stratification. The dissipation scaling is found to nearly match production in the near-neutral region, but to be consistently lower than production in the more convective regimes. The convective scaling is shown to offer a simplified means of computing sensible heat flux from the dissipation rate of temperature variance.Also at Johns Hopkins University, Baltimore, MarylandAlso at Los Alamos National Laboratory, Los Alamos, New Mexico.     

An Analytical Model for the Two-Scalar Covariance Budget Inside a Uniform Dense Canopy

The two-scalar covariance budget is significant within the canopy sublayer (CSL) given its role in modelling scalar flux budgets using higher-order closure principles and in estimating the segregation ratio for chemically reactive species. Despite its importance, an explicit expression describing how the two-scalar covariance is modified by inhomogeneity in the flow statistics and in the vertical variation in scalar emission or uptake rates within the canopy volume remains elusive even for passive scalars. To progress on a narrower version of this problem, an analytical solution to the two-scalar covariance budget in the CSL is proposed for the most idealized flow conditions: a stationary and planar homogeneous flow inside a uniform and dense canopy with a constant leaf area density distribution. The foliage emission (or uptake) source strengths are assumed to vary exponentially with depth while the forest floor emission is represented as a scalar flux. The analytical solution is a superposition of a homogeneous part that describes how the two-scalar covariance at the canopy top is transported and dissipated within the canopy volume, and an inhomogeneous part governed by local production mechanisms of the two-scalar covariance. The homogeneous part is primarily described by the canopy adjustment length scale, and the attenuation coefficients of the turbulent kinetic energy and the mean velocity. Conditions for which the vertical variation of the two-scalar covariance is controlled by the rapid attenuation in the mean velocity and turbulent kinetic energy profiles, vis-à-vis the vertical variation of the scalar source strength, are explicitly established. This model also demonstrates how dissimilarity in the emissions from the ground, even for the extreme binary case with one scalar turned ‘on’ and the other scalar turned ‘off’, modifies the vertical variation of the two-scalar covariance within the CSL. To assess its applicability to field conditions, the analytical model predictions were compared with observations made at two different forest types—a sparse pine forest at the Hyytiälä SMEAR II-station (in Finland) and a dense alpine hardwood forest at Lavarone (in Italy). While the model assumptions do not represent the precise canopy morphology, attenuation properties of the turbulent kinetic energy and the mean velocity, observed mixing length, and scalar source attenuation properties for these two forest types, good agreement was found between measured and modelled two scalar covariances for multiple scalars and for the triple moments at the Hyytiälä site.     

A lagrangian random-walk model for simulating water vapor,CO2 and sensible heat flux densities and scalar profiles over and within a soybean canopy

An integrated canopy micrometeorological model is described for calculating CO₂, water vapor and sensible heat exchange rates and scalar concentration profiles over and within a crop canopy. The integrated model employs a Lagrangian random walk algorithm to calculate turbulent diffusion. The integrated model extends previous Lagrangian modelling efforts by employing biochemical, physiological and micrometeorological principles to evaluate vegetative sources and sinks. Model simulations of water vapor, CO₂ and sensible heat flux densities are tested against measurements made over a soybean canopy, while calculations of scalar profiles are tested against measurements made above and within the canopy. The model simulates energy and mass fluxes and scalar profiles above the canopy successfully. On the other hand, model calculations of scalar profiles inside the canopy do not match measurements.The tested Lagrangian model is also used to evaluate simpler modelling schemes, as needed for regional and global applications. Simple, half-order closure modelling schemes (which assume a constant scalar profile in the canopy) do not yield large errors in the computation of latent heat (LE) and CO₂ (F _c ) flux densities. Small errors occur because the source-sink formulation of LE andF _c are relatively insensitive to changes in scalar concentrations and the scalar gradients are small. On the other hand, complicated modelling frames may be needed to calculate sensible heat flux densities; the source-sink formulation of sensible heat is closely coupled to the within-canopy air temperature profile.     

A Stochastic Time Series Model for Threshold Crossing Statistics of Concentration Fluctuations in non-Intermittent Plumes

A numerical stochastic model is developed for the upcrossing rate across a specified threshold concentration. The model assumes that the concentration time series at a given spatial point within a dispersing plume can be approximated as a first-order Markovian process designed to be consistent with a given time-invariant concentration probability density function (pdf). The model requires only the specification of a concentration pdf with a given mean and variance and a concentration fluctuation integral time scale. Predicted upcrossing rates are compared with atmospheric plume concentration data obtained from a point source near the ground. For this data set, a log-normal pdf is found to give better estimates of the threshold crossing rate than a gamma pdf.     

Micromixing modelling of concentration fluctuations in inhomogeneous turbulence in the convective boundary layer

The micromixing technique, widely used in engineering calculations of mixing and chemical reaction, is extended to atmospheric boundary-layer flows. In particular, a model based on the interaction-by-exchange-with-the-conditional-mean (IECM) micromixing approach is formulated to calculate concentration fluctuation statistics for a line source and a point source in inhomogeneous and non-Gaussian turbulence in the convective boundary layer. The mixing time scale is parameterised as a linear function of time with the intercept value determined by the source size at small times. Good agreement with laboratory data for the intensity of concentration fluctuations is obtained with a value of 0.9 for the coefficient of the linear term in the time-scale parameterisation for a line source, and a value of 0.6 for a point source. Calculation of higher-order moments of the concentration field for a line source shows that non-Gaussian effects persist into the vertically well-mixed region. The cumulative distribution function predicted by the model for a point source agrees reasonably well with laboratory data, especially in the far field. In the limit of zero mixing time scale, the model reduces to a meandering plume model, thus enabling the concentration variance to be partitioned into meandering and relative components. The meandering component is shown to be more persistent for a point source than for a line source.