Comparing Two Implementations of a Micromixing Model. Part I: Wall Shear-Layer Flow

A Lagrangian stochastic (LS) micromixing model is used for estimating concentration fluctuations in plumes of a passive, non-reactive tracer dispersing from elevated and ground-level compact sources into a neutral wall shear-layer flow. SPMMM (for sequential particle micromixing model) implements the familiar IECM (interaction by exchange with the conditional mean) micromixing scheme. The parametrization of the scalar micromixing time scale is identical to that proposed in a previously reported LS–IECM model (Cassiani et al., Atmos Environ 39:1457–1469, 2005a). However, while SPMMM is mathematically equivalent to the previously reported model, it differs in its numerical implementation: SPMMM releases N independent particles sequentially, whereas the previously reported model releases N independent particles simultaneously. In both implementations, the trajectories of the N particles are governed by single-point velocity statistics. The sequential particle implementation is computationally efficient, but cannot be applied to the case of reacting species. Results from both implementations are compared to experimental wind-tunnel dispersion data and to each other.     

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.     

First-Order Inconsistencies Caused by Rogue Trajectories

A theoretical requirement of the Interaction by Exchange with the Conditional Mean (IECM) micromixing model is that the mean concentration field produced by it must be consistent with the mean concentration field produced by a traditional Lagrangian stochastic (LS) marked particle model. We examine the violation of this requirement that occurs in a coupled LS–IECM model when unrealistically high particle velocities occur. No successful strategy was found to mitigate the effects of these rogue trajectories. It is our hope that this work will provide renewed impetus for investigation into rogue trajectories and methods to eliminate them from LS models.     

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.     

A Stochastic Single-Particle Lagrangian Model for the Concentration Fluctuations in a Plume Dispersing Inside an Urban Canopy

A new approach for estimating concentration fluctuations intensity in dense built-up environments using a Lagrangian stochastic (LS) particle model is described. Following past success in modelling the dynamics of concentration variance as a diffusion-advection process, the ensemble-averaged concentration variance is represented by particles that advect and diffuse throughout the computational domain. The calculation of the concentration variance is addressed by assuming an appropriate distribution of effective variance sources for a given mean concentration field. Dissipation is treated by allowing the variance carried by every particle to decay exponentially with a locally-estimated decay time. The approach has the benefit of easily handling complex boundary conditions. It can also be easily and naturally implemented as an extension to an existing LS model, which is used for mean concentration estimations. The method differs from existing two-particle methods that demand knowledge of the structure function of the flow. It is also more computationally efficient than micro-mixing approaches that involve maintaining high population levels of particles in every grid volume. The model is compared with high frequency concentration measurements, taken as part of the JU2003 (Joint Urban 2003) experiment that was carried out in Oklahoma City. Good agreement is observed.     

The Volumetric Particle Approach for Concentration Fluctuations and Chemical Reactions in Lagrangian Particle and Particle-grid Models

A new approach is proposed to predict concentration fluctuations in the framework of one-particle Lagrangian stochastic models. The approach is innovative since it allows the computation of concentration fluctuations in dispersing plumes using a Lagrangian one-particle model with micromixing but with no need for the simulating of background particles. The extension of the model for the treatment of chemically reactive plumes is also accomplished and allows the computation of plume-related chemical reactions in a Lagrangian one-particle framework separately from the background chemical reactions, accounting for the effect of concentration fluctuations on chemical reactions in a general, albeit approximate, manner. These characteristics should make the proposed approach an ideal tool for plume-in-grid calculations in chemistry transport models. The results are compared to the wind-tunnel experiments of Fackrell and Robins (J Fluid Mech, 117:1–26, 1982) for plume dispersion in a neutral boundary layer and to the measurements of Legg et al. (Boundary-Layer Meteorol, 35:277–302, 1986) for line source dispersion in and above a model canopy. Preliminary reacting plume simulations are also shown comparing the model with the experimental results of Brown and Bilger (J Fluid Mech, 312:373–407, 1996; Atmos Environ, 32:611–628, 1998) to demonstrate the feasibility of computing chemical reactions in the proposed framework.     

Dispersion of a Point-Source Release of a Passive Scalar Through an Urban-Like Array for Different Wind Directions

The dispersion of a point-source release of a passive scalar in a regular array of cubical, urban-like, obstacles is investigated by means of direct numerical simulations. The simulations are conducted under conditions of neutral stability and fully rough turbulent flow, at a roughness Reynolds number of Re _τ  = 500. The Navier–Stokes and scalar equations are integrated assuming a constant rate release from a point source close to the ground within the array. We focus on short-range dispersion, when most of the material is still within the building canopy. Mean and fluctuating concentrations are computed for three different pressure gradient directions (0°, 30°, 45°). The results agree well with available experimental data measured in a water channel for a flow angle of 0°. Profiles of mean concentration and the three-dimensional structure of the dispersion pattern are compared for the different forcing angles. A number of processes affecting the plume structure are identified and discussed, including: (i) advection or channelling of scalar down ‘streets’, (ii) lateral dispersion by turbulent fluctuations and topological dispersion induced by dividing streamlines around buildings, (iii) skewing of the plume due to flow turning with height, (iv) detrainment by turbulent dispersion or mean recirculation, (v) entrainment and release of scalar in building wakes, giving rise to ‘secondary sources’, (vi) plume meandering due to unsteady turbulent fluctuations. Finally, results on relative concentration fluctuations are presented and compared with the literature for point source dispersion over flat terrain and urban arrays.     

Effects of Fetch on Turbulent Flow and Pollutant Dispersion Within a Cubical Canopy

The effects of fetch on turbulent flow and pollutant dispersion within a canopy formed by regularly-spaced cubical objects is investigated using large-eddy simulation. Six tracer gases are simultaneously released from a ground-level continuous pollutant line source placed parallel to the spanwise axis at the first, second, third, fifth, seventh and tenth rows. Beyond the seventh row, the standard deviations of the fluctuations in the velocity components and the Reynolds shear stresses reach nearly equivalent states. Low-frequency turbulent flow is generated near the bottom surface around the first row and develops as the fetch increases. The turbulent flow eventually passes through the canopy at a near-constant interval. The mean concentration within the canopy reaches a near-constant value beyond the seventh row. In the first and second rows, narrow coherent structures frequently affect the pollutant escape from the top of the canopy. These structures increase in width as the fetch increases, and they mainly affect the removal of pollutants from the canopy.     

A Lagrangian Stochastic Model for Heavy Particle Dispersion in the Atmospheric Marine Boundary Layer

The dispersion of heavy particles and pollutants is often simulated with Lagrangian stochastic (LS) models. Although these models have been employed successfully over land, the free surface at the air-sea interface complicates the implementation of traditional LS models. We present an adaptation of traditional LS models to the atmospheric marine boundary layer (MBL), where the bottom boundary is represented by a realistic wavy surface that moves and deforms. In addition, the correlation function for the turbulent flow following a particle is extended to the anisotropic, unsteady case. Our new model reproduces behaviour for Lagrangian turbulence in a stratified air flow that departs only slightly from the expected behaviour in isotropic turbulence. When solving for the trajectory of a heavy particle in the air flow, the modelled turbulent forcing on the particle also behaves remarkably well. For example, the spectrum of the turbulence at the particle location follows that of a massless particle for time scales approximately larger than the Stokes’ particle response time. We anticipate that this model will prove especially useful in the context of sea-spray dispersion and its associated momentum, sensible and latent heat, and gas fluxes between spray droplets and the atmosphere.     

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.     

On Heavy Particle Dispersion in Turbulent Shear Flows: 3-D Analysis of the Effects of Crossing Trajectories

In the approaches used to predict the dispersion of discrete particles moving in a turbulent flow, the effects of crossing trajectories due to gravity (or any other external force field) are generally accounted for by modifying the integral time scales according to the well-known analysis of Csanady (J Atmos Sci 20:201–208, 1963). Here, an alternative theoretical analysis of the time correlation of the fluid velocity fluctuations along a particle trajectory is presented and applied in a turbulent shear flow. The study is carried out in the frame of three-dimensional Langevin-type stochastic models, where the main unknowns are the drift tensor components rather than the conventional integral time scales of the fluid seen by the particles. Starting from a model for the space-time velocity covariance tensor of the turbulence under the assumption of homogeneous shear flow, the various components of the time correlation tensor of the fluid seen are expressed in the asymptotic case of large mean relative velocity (between the particles and the flow) compared to the particle velocity fluctuations. In order to provide comparison with the generally used expressions arising from isotropic turbulence assumption, we examine also the conventional integral time scales of the fluid seen in the directions parallel and perpendicular to the mean relative velocity. The most prominent deviations from isotropic turbulence are observed when the external force field is in the direction of the mean velocity gradient: in this case the loss of correlation in the mean flow direction is significantly lower than expected in a uniform flow, an observation that is in qualitative agreement with the few available data.     

Large-Eddy Simulation of the Wind Field and Plume Dispersion Within Different Obstacle Arrays Using a Dynamic Mixing Length Subgrid-Scale Model

A novel dynamic mixing length (DML) subgrid-scale (SGS) model is proposed to improve the large-eddy simulations of the wind field and contaminant dispersion around a group of buildings. Wind field and contaminant dispersion in two kinds of building array geometries are simulated using the model, with wind-tunnel experimental data used to validate the model. The relative errors in the lateral profiles of the streamwise mean velocities behind the sixth row of the buildings of the staggered obstacle array and the aligned obstacle array at the half height of the building are 15 and 9%, respectively. The DML velocity fluctuations in the staggered and aligned obstacle arrays are in agreement with those of the experiment. The results indicate that the DML model can make a more accurate prediction of the mean velocity and velocity fluctuations. The DML model is highly suitable for the simulation of multi-scale turbulent flow in urban canyons, of high Reynolds number turbulent flow and of complex turbulent flow.     

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

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

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.     

Large-eddy Simulations of Flow Over Forested Ridges

Large-eddy simulations (LES) of flow over a series of small forested ridges are performed, and compared with numerical simulations using a one-and-a-half order mixing length closure scheme. The qualitative and quantitative similarity between these results provides some confidence in the results of recent analytical and numerical studies of flow over forested hills using first-order mixing length schemes. Time series of model velocities at various locations within the canopy allow the application of various experimental techniques to study the turbulence in the LES. The application of conditional analysis shows that the structure of the turbulence over a forested hill is broadly similar to that over flat ground, with sweeps and ejections dominating. Differences are seen across the hill, particularly associated with regions of mean flow separation and recirculation near the summit and in the lee of the hill. Detailed comparison of derived mixing lengths from the LES with the assumed values used in mixing-length closure schemes show that the mixing length varies with location across the hill and with height in the canopy. This is consistent with previous wind-tunnel measurements, and demonstrates that a constant mixing-length assumption is not strictly valid within the canopy. Despite this, the first-order mixing-length schemes do give similar results both for the mean flow and the turbulence in such situations.     

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.     

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.     

Measurements and Computations of Flow in an Urban Street System

We present results from laboratory and computational experiments on the turbulent flow over an array of rectangular blocks modelling a typical, asymmetric urban canopy at various orientations to the approach flow. The work forms part of a larger study on dispersion within such arrays (project DIPLOS) and concentrates on the nature of the mean flow and turbulence fields within the canopy region, recognising that unless the flow field is adequately represented in computational models there is no reason to expect realistic simulations of the nature of the dispersion of pollutants emitted within the canopy. Comparisons between the experimental data and those obtained from both large-eddy simulation (LES) and direct numerical simulation (DNS) are shown and it is concluded that careful use of LES can produce generally excellent agreement with laboratory and DNS results, lending further confidence in the use of LES for such situations. Various crucial issues are discussed and advice offered to both experimentalists and those seeking to compute canopy flows with turbulence resolving models.     

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.     

Large-Eddy Simulation Comparison of Neutral Flow Over a Canopy: Sensitivities to Physical and Numerical Conditions,and Similarity to Other Representations

The representation of a neutral atmospheric flow over roughness elements simulating a vegetation canopy is compared between two large-eddy simulation models, wind-tunnel data and recently updated empirical flux-gradient relationships. Special attention is devoted to the dynamics in the roughness sublayer above the canopy layer, where turbulence is most intense. By demonstrating that the flow properties are consistent across these different approaches, confidence in the individual independent representations is bolstered. Systematic sensitivity analyses with the Dutch Atmospheric Large-Eddy Simulation model show that the transition in the one-sided plant-area density from the canopy layer to unobstructed air potentially alters the flow in the canopy and roughness sublayer. Anomalously induced fluctuations can be fully suppressed by spreading the transition over four steps. Finer vertical resolutions only serve to reduce the magnitude of these fluctuations, but do not prevent them. To capture the general dynamics of the flow, a resolution of 10 % of the canopy height is found to suffice, while a finer resolution still improves the representation of the turbulent kinetic energy. Finally, quadrant analyses indicate that momentum transport is dominated by the mean velocity components within each quadrant. Consequently, a mass-flux approach can be applied to represent the momentum flux.