A Simple Model for Spatially-averaged Wind Profiles Within and Above an Urban Canopy

This paper deals with the modelling of the flow in the urban canopy layer. It critically reviews a well-known formula for the spatially-averaged wind profile, originally proposed by Cionco in 1965, and provides a new interpretation for it. This opens up a number of new applications for modelling mean wind flow over the neighbourhood scale. The model is based on a balance equation between the obstacle drag force and the local shear stress as proposed by Cionco for a vegetative canopy. The buildings within the canopy are represented as a canopy element drag formulated in terms of morphological parameters such as λ _f and λ _p (the ratios of plan area and frontal area of buildings to the lot area). These parameters can be obtained from the analysis of urban digital elevation models. The shear stress is parameterised using a mixing length approach. Spatially-averaged velocity profiles for different values of building packing density corresponding to different flow regimes are obtained and analysed. The computed solutions are compared with published data from wind-tunnel and water-tunnel experiments over arrays of cubes. The model is used to estimate the spatially-averaged velocity profile within and above neighbourhood areas of real cities by using vertical profiles of λ _f .     

Aerodynamic Parameters of Regular Arrays of Rectangular Blocks with Various Geometries

The aerodynamic effects of various configurations of an urban array were investigated in a wind-tunnel experiment. Three aerodynamic parameters characterising arrays—the drag coefficient (C _d ), roughness length (z _o) and displacement height (d)—are used for analysis. C _d is based on the direct measurement of the total surface shear using a floating element, and the other two parameters are estimated by logarithmic fitting of the measured wind profile and predetermined total drag force. The configurations of 63 arrays used for measurement were designed to estimate the effects of layout, wind direction and the height variability of the blocks on these parameters for various roughness packing densities. The results are summarised as follows: (1) The estimated C _d and z _o of the staggered arrays peak against the plan area index (λ _p ) and frontal area index (λ _f ), in contrast with values for the square arrays, which are less sensitive to λ _p and λ _f . In addition, the square arrays with a wind direction of 45° have a considerably larger C _d , and the wind direction increases z _o/H by up to a factor of 2. (2) The effect of the non-uniformity of roughness height on z _o is more remarkable when λ _f exceeds 20%, and the discrepancy in z _o is particularly remarkable and exceeds 200%. (3) The effect of the layout of tall blocks on C _d is stronger than that of short blocks. These results indicate that the effects of both wind direction and the non-uniformity of the heights of buildings on urban aerodynamic parameters vary greatly with λ _p and λ _f ; hence, these effects should be taken into account by considering the roughness packing density.     

Aerodynamic Parameters of Urban Building Arrays with Random Geometries

It is difficult to describe the flow characteristics within and above urban canopies using only geometrical parameters such as plan area index (λ _p ) and frontal area index (λ _f ) because urban surfaces comprise buildings with random layouts, shapes, and heights. Furthermore, two types of ‘randomness’ are associated with the geometry of building arrays: the randomness of element heights (vertical) and that of the rotation angles of each block (horizontal). In this study, wind-tunnel experiments were conducted on seven types of urban building arrays with various roughness packing densities to measure the bulk drag coefficient (C _d ) and mean wind profile; aerodynamic parameters such as roughness length (z _o ) and displacement height (d) were also estimated. The results are compared with previous results from regular arrays having neither ‘vertical’ nor ‘horizontal’ randomness. In vertical random arrays, the plot of C _d and z _o versus λ _f exhibited a monotonic increase, and z _o increased by a factor of almost two for λ _f = 48–70%. C _d was strongly influenced by the standard deviation of the height of blocks (σ) when λ _p ≥ 17%, whereas C _d was independent of σ when λ _p = 7%. In the case of horizontal random arrays, the plot of the estimated C _d against λ _f showed a peak. The effect of both vertical and horizontal randomness of the layout on aerodynamic parameters can be explained by the structure of the vortices around the blocks; the aspect ratio of the block is an appropriate index for the estimation of such features.     

Large-Eddy Simulations on the Effects of Surface Geometry of Building Arrays on Turbulent Organized Structures

Turbulent organized structures (TOS) above building arrays were investigated using a large-eddy simulation (LES) model for a city (LES-CITY). Square and staggered building arrays produced contrasting behaviour in terms of turbulence that roughly corresponded to the conventional classification of ‘D-type’ and ‘K-type’ roughness, respectively: (1) The drag coefficients (referred to the building height) for staggered arrays were sensitive to building area density, but those for square arrays were not. (2) The relative contributions of ejections to sweeps (S₂/S₄) at the building height for square arrays were sensitive to building area density and nearly equalled or exceeded 1.0 (ejection dominant), but those for staggered arrays were insensitive to building area density and were mostly below 1.0 (sweep dominant). (3) Streaky patterns of longitudinal low speed regions (i.e., low speed streaks) existed in all flows regardless of array type. Height variations of the buildings in the square array drastically increased the drag coefficient and modified the turbulent flow structures. The mechanism of D-type and K-type urban-like roughness flows and the difference from vegetation flows are discussed. Although urban-like roughness flows exhibited mixed properties of mixing layers and flat-wall boundary layers as far as S₂/S₄ was concerned, the turbulent organized structures of urban-like roughness flows resembled those of flat-wall boundary layers.     

Estimation of Roughness Parameters Within Sparse Urban-Like Obstacle Arrays

We conduct wind-tunnel experiments on three different uniform roughness arrays composed of sparsely distributed rectangular cylinders for the estimation of surface parameters. Roughness parameters such as the roughness length z ₀ and zero-plane displacement d are extracted using a best-fit approximation of the measured wind velocity. We also perform a large-eddy simulation (LES) to confirm that four sampling points are sufficient to surrogate a space average above the canopy layer of the sparse roughness arrays. We propose a new morphological model from a systematic analysis of experimental data on the arrays. The friction velocity predicted by the proposed model agrees well with the peak value of the measured Reynolds shear stress ${(-\left<\overline{u'w'}\right>)^{0.5}}${(-\left<\overline{u'w'}\right>)^{0.5}}. The proposed model is further validated in an additional wind-tunnel experiment conducted on a scaled configuration of a real urban area exposed to four wind directions. The proposed model is found to perform very well particularly in the estimation of the friction velocity, readily leading to a better estimation of turbulence, which is essential for an accurate prediction of pollutant dispersion.     

Wind-tunnel Modelling of Dispersion from a Scalar Area Source in Urban-Like Roughness

A wind-tunnel study was conducted to investigate ventilation of scalars from urban-like geometries at neighbourhood scale by exploring two different geometries a uniform height roughness and a non-uniform height roughness, both with an equal plan and frontal density of λ _p = λ _f = 25%. In both configurations a sub-unit of the idealized urban surface was coated with a thin layer of naphthalene to represent area sources. The naphthalene sublimation method was used to measure directly total area-averaged transport of scalars out of the complex geometries. At the same time, naphthalene vapour concentrations controlled by the turbulent fluxes were detected using a fast Flame Ionisation Detection (FID) technique. This paper describes the novel use of a naphthalene coated surface as an area source in dispersion studies. Particular emphasis was also given to testing whether the concentration measurements were independent of Reynolds number. For low wind speeds, transfer from the naphthalene surface is determined by a combination of forced and natural convection. Compared with a propane point source release, a 25% higher free stream velocity was needed for the naphthalene area source to yield Reynolds-number-independent concentration fields. Ventilation transfer coefficients w _T /U derived from the naphthalene sublimation method showed that, whilst there was enhanced vertical momentum exchange due to obstacle height variability, advection was reduced and dispersion from the source area was not enhanced. Thus, the height variability of a canopy is an important parameter when generalising urban dispersion. Fine resolution concentration measurements in the canopy showed the effect of height variability on dispersion at street scale. Rapid vertical transport in the wake of individual high-rise obstacles was found to generate elevated point-like sources. A Gaussian plume model was used to analyse differences in the downstream plumes. Intensified lateral and vertical plume spread and plume dilution with height was found for the non-uniform height roughness.     

Effects of Wall Heating on Flow Characteristics in a Street Canyon

We develop a large-eddy simulation (LES) model based on a meteorological numerical model for a real scale street-canyon flow with rough building facets heated by a given temperature. The model is applied to a canyon with the aspect ratio of unity for two idealized heating scenarios: (1) the roof and the entire upstream wall are heated, named as ‘assisting cases’, and (2) the roof and the entire downstream wall are heated, named as ‘opposing cases’. These facets were heated up to 15 K above the air temperature. A wall function for temperature is proposed for a rough facet with an assumption that the thermal roughness length, z _0T, is much smaller than the aerodynamic roughness length, z ₀. It is demonstrated that the sensible heat flux and canyon-air temperature are significantly influenced by the near-facet process that is parametrized by z _0T as the primary factor; other processes such as in-canyon mixing and roof-level exchange are secondary. This new finding strongly suggests that it is vital to choose an appropriate value of z _0T in a numerical simulation of street-canyon flows with the facet-air exchange processes of heat or any scalar. The finding also raises an awareness of the demand for carefully designed laboratory or field experiments of quantifying z _0T values for various urban surfaces. For the opposing cases, an unsteady penetrating narrow updraft zone appears occasionally along the heated wall and this feature is consistent field observations. The unique result indicates the superior capability of LES. The results of this study can be used to guide the parametrization of turbulent processes inside the urban canopy layer.     

Temperature–Humidity Dissimilarity and Heat-to-water-vapour Transport Efficiency Above and Within a Pine Forest Canopy: the Role of the Bowen Ratio

Over the past 15 years atmospheric surface-layer experiments over heterogeneous canopies have shown that the vertical transfer of sensible heat and water vapour exhibit a strong dissimilarity. In particular, the sensible-heat-to-water-vapour transport efficiencies generally exceed unity. One of the main consequences is that evaporation (latent heat flux) computed by the flux-variance method is overestimated, as persistently demonstrated by comparisons with evaporation obtained with the eddy-correlation method. Various authors proposed to take into account the temperature–humidity dissimilarity to extend the applicability of the flux-variance method in order to compute evaporation from non-uniform surfaces. They attempted to connect the sensible-heat-to-water-vapour transport efficiency (λ) to the correlation coefficient between temperature and humidity turbulent fluctuations (R _Tq ). This approach was found to be successful over ‘wet’ surfaces for which λ can be approximated by R _Tq and ‘dry’ surfaces for which λ can be approximated by 1/R _Tq . However, no solution has been proposed until now for intermediate hydrological conditions. We investigated this question using eddy-correlation measurements above and inside a pine forest canopy. For both levels, our data present a strong likeness with previously published results over heterogeneous surfaces. In particular, they confirm that λ is R _Tq in wet conditions and 1/R _Tq in dry conditions. Moreover, we defined the range of the Bowen ratio (Bo) values for which those two approximations are valid (below 0.1 and greater than 1, respectively) and established a relationship between λ, R _Tq and Bo for the intermediate range of Bo. We are confident that this new parameterization will enlarge the applicability of the flux-variance method to all kinds of heterogeneous surfaces in various hydrological conditions     

Momentum Absorption in Rough-Wall Boundary Layers with Sparse Roughness Elements in Random and Clustered Distributions

A wind-tunnel experiment has been used to investigate momentum absorption by rough surfaces with sparse random and clustered distributions of roughness elements. An unusual (though longstanding) method was used to measure the boundary-layer depth δ and friction velocity u _* and thence to infer the functional relationship z ₀/h = f(λ) between the normalised roughness length z ₀/ h and the roughness density λ (where z ₀ is the roughness length and h the mean height of the roughness elements). The method for finding u _* is based on fitting the velocity defect in the outer layer to a functional form for the dimensionless velocity-defect profile in a canonical zero-pressure-gradient boundary layer. For the conditions investigated here, involving boundary layers over sparse roughness with strong local heterogeneity, this velocity-defect-law method is found to be more robust than several alternative methods for finding u _* (uw covariance, momentum integral and slope of the logarithmic velocity profile).The experimental results show that, (1) there is general agreement in the relationship z ₀/h = f(λ) between the present experiment with random arrays and other wind-tunnel experiments with regular arrays; (2) the main effect of clustering is to increase the scatter in the z ₀/h = f(λ) relationship, through increased local horizontal heterogeneity; (3) this scatter obscures any trend in the z ₀/h = f(λ) relationship in response to clustering; and (4) the agreement between the body of wind-tunnel data (taken as a whole) and field data is good, though with scatter for which it is likely that a major contribution stems from local horizontal heterogeneity in the field.     

Aerodynamic Scaling for Estimating the Mean Height of Dense Canopies

We used an aerodynamic method to objectively determine a representative canopy height, using standard meteorological measurements. The canopy height may change if the tree height is used to represent the actual canopy, but little work to date has focused on creating a standard for determining the representative canopy height. Here we propose the ‘aerodynamic canopy height’ h _a as the most effective means of resolving the representative canopy height for all forests. We determined h _a by simple linear regression between zero-plane displacement d and roughness length z ₀, without the need for stand inventory data. The applicability of h _a was confirmed in five different forests, including a forest with a complex canopy structure. Comparison with stand inventory data showed that h _a was almost equivalent to the representative height of trees composing the crown surface if the forest had a simple structure, or to the representative height of taller trees composing the upper canopy in forests with a complex canopy structure. The linear relationship between d and z ₀ was explained by assuming that the logarithmic wind profile above the canopy and the exponential wind profile within the canopy were continuous and smooth at canopy height. This was supported by observations, which showed that h _a was essentially the same as the height defined by the inflection point of the vertical profile of wind speed. The applicability of h _a was also verified using data from several previous studies.     

Large-Eddy Simulation of Flow and Pollutant Transports in and Above Two-Dimensional Idealized Street Canyons

A large-eddy simulation (LES) model, using the one-equation subgrid-scale (SGS) parametrization, was developed to study the flow and pollutant transport in and above urban street canyons. Three identical two-dimensional (2D) street canyons of unity aspect ratio, each consisting of a ground-level area source of constant pollutant concentration, are evenly aligned in a cross-flow in the streamwise direction x. The flow falls into the skimming flow regime. A larger computational domain is adopted to accurately resolve the turbulence above roof level and its influence on the flow characteristics in the street canyons. The LES calculated statistics of wind and pollutant transports agree well with other field, laboratory and modelling results available in the literature. The maximum wind velocity standard deviations σ _i in the streamwise (σ _u ), spanwise (σ _v ) and vertical (σ _w ) directions are located near the roof-level windward corners. Moreover, a second σ _w peak is found at z ≈ 1.5h (h is the building height) over the street canyons. Normalizing σ _i by the local friction velocity u _*, it is found that σ _u /u _* ≈ 1.8, σ _v /u _* ≈ 1.3 and σ _w /u _* ≈ 1.25 exhibiting rather uniform values in the urban roughness sublayer. Quadrant analysis of the vertical momentum flux u′′w′′ shows that, while the inward and outward interactions are small, the sweeps and ejections dominate the momentum transport over the street canyons. In the x direction, the two-point correlations of velocity R _v,x and R _w,x drop to zero at a separation larger than h but R _u,x (= 0.2) persists even at a separation of half the domain size. Partitioning the convective transfer coefficient Ω _T of pollutant into its removal and re-entry components, an increasing pollutant re-entrainment from 26.3 to 43.3% in the x direction is revealed, suggesting the impact of background pollutant on the air quality in street canyons.     

Organised Motion in a Tall Spruce Canopy: Temporal Scales,Structure Spacing and Terrain Effects

This study investigates the organised motion near the canopy-atmosphere interface of a moderately dense spruce forest in heterogeneous, complex terrain. Wind direction is used to assess differences in topography and surface properties. Observations were obtained at several heights above and within the canopy using sonic anemometers and fast-response gas analysers over the course of several weeks. Analysed variables include the three-dimensional wind vector, the sonic temperature, and the concentration of carbon dioxide. Wavelet analysis was used to extract the organised motion from time series and to derive its temporal scales. Spectral Fourier analysis was deployed to compute power spectra and phase spectra. Profiles of temporal scales of ramp-like coherent structures in the vertical and longitudinal wind components showed a reversed variation with height and were of similar size within the canopy. Temporal scales of scalar fields were comparable to those of the longitudinal wind component suggesting that the lateral scalar transport dominates. The existence of a – 1 power law in the longitudinal power spectra was confirmed for a few cases only, with a majority showing a clear 5/3 decay. The variation of effective scales of organised motion in the longitudinal velocity and temperature were found to vary with atmospheric stability, suggesting that both Kelvin-Helmholtz instabilities and attached eddies dominate the flow with increasing convectional forcing. The canopy mixing-layer analogy was observed to be applicable for ramp-like coherent structures in the vertical wind component for selected wind directions only. Departures from the prediction of m = Λ _w L _s ⁻¹ = 8–10 (where Λ _w is the streamwise spacing of coherent structures in the vertical wind w and L _s is a canopy shear length scale) were caused by smaller shear length scales associated with large-scale changes in the terrain as well as the vertical structure of the canopy. The occurrence of linear gravity waves was related to a rise in local topography and can therefore be referred to as mountain-type gravity waves. Temporal scales of wave motion and ramp-like coherent structures were observed to be comparable.     

Spatio-Temporal Surface Shear-Stress Variability in Live Plant Canopies and Cube Arrays

This study presents spatiotemporally-resolved measurements of surface shear-stress τ _s in live plant canopies and rigid wooden cube arrays to identify the sheltering capability against sediment erosion of these different roughness elements. Live plants have highly irregular structures that can be extremely flexible and porous resulting in considerable changes to the drag and flow regimes relative to rigid imitations mainly used in other wind-tunnel studies. Mean velocity and kinematic Reynolds stress profiles show that well-developed natural boundary layers were generated above the 8 m long wind-tunnel test section covered with the roughness elements at four different roughness densities (λ = 0, 0.017, 0.08, 0.18). Speed-up around the cubes caused higher peak surface shear stress than in experiments with plants at all roughness densities, demonstrating the more effective sheltering ability of the plants. The sheltered areas in the lee of the plants are significantly narrower with higher surface shear stress than those found in the lee of the cubes, and are dependent on the wind speed due to the plants ability to streamline with the flow. This streamlining behaviour results in a decreasing sheltering effect at increasing wind speeds and in lower net turbulence production than in experiments with cubes. Turbulence intensity distributions suggest a suppression of horseshoe vortices in the plant case. Comparison of the surface shear-stress measurements with sediment erosion patterns shows that the fraction of time a threshold skin friction velocity is exceeded can be used to assess erosion of, and deposition on, that surface.     

珠海凤凰山森林下垫面干季和湿季气象要素的对比分析与动量和感热交换系数的参数化研究

利用珠海凤凰山陆气相互作用观测塔站2014年11月至2016年5月的观测数据,对比分析了干湿季森林下垫面能量通量和气象要素的变化特征,分析了在不同稳定度下3个风向范围（315°～45°、45°～135°和135°～225°）的动量和感热交换系数随冠层表面风速的变化特征,并对动量和感热交换系数进行了参数化研究。结果表明:干季感热和潜热通量值相当,湿季潜热远大于感热。干季和湿季的夜晚都出现负感热现象,感热从大气向森林输送。相对湿度的变化幅度大,与该地气象状况密切相关,相对湿度的垂直梯度夜晚较大,白天较小。干季的气温垂直梯度比湿季的明显。风速在冬季变化平缓,夏季变化剧烈,低层风速随高度变化梯度明显,高层较紊乱。各高度风向差异不大。中性和近中性状态下,在风向为315°～45°、45°～135°和135°～225°时,动量交换系数C_dn分别为0.05、0.0055和0.022,感热交换系数C_hn分别为0.0055、0.003和0.004。在稳定和不稳定状态下,动量交换系数C_d、感热交换系数C_h随冠层表面风速v明显发生变化,稳定条件下,C_d、C_h随v的增大而增大;不稳定条件下,C_d、C_h随v的增大而减小。分不同风向对森林冠层C_d、C_h在稳定和不稳定条件下与v的关系进行了拟合,得到了参数化公式。     

A Modelling Study of Flux Imbalance and the Influence of Entrainment in the Convective Boundary Layer

It is frequently observed in field experiments that the eddy covariance heat fluxes are systematically underestimated as compared to the available energy. The flux imbalance problem is investigated using the NCAR’s large-eddy simulation (LES) model imbedded with an online scheme to calculate Reynolds-averaged fluxes. A top–down and a bottom–up tracer are implemented into the LES model to quantify the influence of entrainment and bottom–up diffusion processes on flux imbalance. The results show that the flux imbalance follows a set of universal functions that capture the exponential decreasing dependence on u _*/w _*, where u _* and w _* are friction velocity and the convective velocity scale, respectively, and an elliptic relationship to z/z _i , where z _i is the mixing-layer height. The source location in the boundary layer is an important factor controlling the imbalance magnitude and its horizontal and vertical distributions. The flux imbalance of heat and the bottom–up tracer is tightly related to turbulent coherent structures, whereas for the top–down diffusion, such relations are weak to nonexistent. Our results are broadly consistent with previous studies on the flux imbalance problem, suggesting that the published results are robust and are not artefacts of numerical schemes.     

Flux-gradient profiles for momentum and heat over an urban surface

Summary In this paper, we evaluate the applicability of flux-gradient relationships for momentum and heat for urban boundary layers within the Monin-Obukhov similarity (MOS) theory framework. Although the theory is widely used for smooth wall boundary layers, it is not known how well the theory works for urban layers. To address this problem, we measured the vertical profiles of wind velocity, air temperature, and fluxes of heat and momentum over a residential area and compared the results to theory. The measurements were done above an urban canopy whose mean height z_h is 7.3 m. 3-D sonic anemometers and fine wire thermocouples were installed at 4 heights in the region 1.5z_h < z < 4z_h. We found the following: (1) The non-dimensional horizontal wind speed has good agreement with the stratified logarithmic profile predicted using the semi-empirical Monin-Obukov similarity (MOS) function, when it was scaled by the surface friction velocity that is derived from the shear stress extrapolated to the roof-top level. (2) The scaled gradient of horizontal wind speed followed a conventional semi-empirical function for a flat surface at a level (z/z_h = 2.9), whereas, in the vicinity of the canopy height was larger than the commonly-used empirical relationship. (3) The potential temperature profile above the canopy shows dependency on the atmospheric stability and the scaled gradient of temperature is in good agreement with a conventional shear function for heat. In the case of heat, the dependency on height was not found. (4) The flux-gradient relationship for momentum and heat in the region 1.5z_h < z < 4z_h was rather similar to that for flat surfaces than that for vegetated canopies.     

Variance Method to Determine Turbulent Fluxes of Momentum And Sensible Heat in The Stable Atmospheric Surface Layer

Evidence is presented that in the stable atmospheric surface layer turbulent fluxes of heat and momentum can be determined from the standard deviations of longitudinal wind velocity and temperature, σ _u and σ _T respectively, measured at a single level. An attractive aspect of this method is that it yields fluxes from measurements that can be obtained with two-dimensional sonic anemometers. These instruments are increasingly being used at official weather stations, where they replace the standard cup anemometer–wind vane system. With methods such as the one described in this note, a widespread, good quality, flux network can be established, which would greatly benefit the modelling community. It is shown that a ‘variance’ dimensionless height (ζ _σ) defined from σ _u and σ _T is highly related to the ‘conventional’ dimensionless stability parameter ζ=z/L, where z is height and L is the Obukhov length. Empirical functions for ζ _σ are proposed that allow direct calculation of heat and momentum fluxes from σ _u and σ _T. The method performs fairly well also during a night of intermittent turbulence.     

Along-wind dispersion of puffs released in a built-up urban area

The SF₆ gas tracer observations for puffs released near the ground during the Joint Urban 2003 (JU2003) urban dispersion experiment in Oklahoma City have been analysed. The JU2003 observations, at distances of about 100–1,100 m from the source, show that, at small times, when the puff is still within the built-up downtown domain, the standard deviation of the concentration time series, σ_t, is influenced by the initial puff spread due to buildings near the source and by hold-up in the wakes of large buildings at the sampler locations. This effect is parameterised by assuming an initial σ_to of about 42 s, leading to a comprehensive similarity formula: σ_t = 42 + 0.1t. The second term, 0.1t, is consistent with an earlier similarity relation, σ_t = 0.1t, derived from puff observations in many experiments over rural terrain. The along-wind dispersion coefficient, σ_x, is assumed to equal σ_t u, in which u is the puff speed calculated as the distance from the source to the sampler, x, divided by the time after the release that the maximum concentration is observed at the sampler. σ_x can be expressed as σ_x = σ_xo + 0.14x, with the initial σ_xo of 45 m. This initial σ_xo agrees with the suggestion of an initial plume spread of about 40 m, made by McElroy and Pooler from analysis of the 1960s’ St. Louis urban dispersion experiment. The puff speeds, u, are initially only about 20% of the observed wind speed, averaged over about 80 street-level and rooftop anemometers in the city, but approach the mean observed wind speed as the puffs grow vertically. The scatter in the σ_t data is about ± a factor of two or three at any given travel time. The maximum σ_t is about 250 s, and the maximum duration of the puff over the sampler, Dt, sometimes called the retention time, is about 1,100 s or 18 min for these puffs and distances.     

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.     

Subfilter-Scale Modelling Using Transport Equations: Large-Eddy Simulation of the Moderately Convective Atmospheric Boundary Layer

We perform large-eddy simulation (LES) of a moderately convective atmospheric boundary layer (ABL) using a prognostic subfilter-scale (SFS) model obtained by truncating the full conservation equations for the SFS stresses and fluxes. The truncated conservation equations contain production mechanisms that are absent in eddy-diffusivity closures and, thus, have the potential to better parametrize the SFS stresses and fluxes. To study the performance of the conservation-equation-based SFS closure, we compare LES results from the surface layer with observations from the Horizontal Array Turbulence Study (HATS) experiment. For comparison, we also show LES results obtained using an eddy-diffusivity closure. Following past studies, we plot various statistics versus the non-dimensional parameter, Λ _w /Δ, where Λ _w is the wavelength corresponding to the peak in the vertical velocity spectrum and Δ is the filter width. The LES runs are designed using different domain sizes, filter widths and surface fluxes, in order to replicate partly the conditions in the HATS experiment. Our results show that statistics from the different LES runs collapse reasonably and exhibit clear trends when plotted against Λ _w /Δ. The trends exhibited by the production terms in the modelled SFS conservation equations are qualitatively similar to those seen in the HATS data with the exception of SFS buoyant production, which is underpredicted. The dominant production terms in the modelled SFS stress and flux budgets obtained from LES are found to approach asymptotically constant values at low Λ _w /Δ. For the SFS stress budgets, we show that several of these asymptotes are in good agreement with their corresponding theoretical values in the limit Λ _w /Δ → 0. The modelled SFS conservation equations yield trends in the mean values and fluctuations of the SFS stresses and fluxes that agree better with the HATS data than do those obtained using an eddy-diffusivity closure. They, however, underpredict considerably the level of SFS anisotropy near the wall when compared to observations, which could be a consequence of the shortcomings in the model used for the pressure destruction terms. Finally, we address the computational cost incurred due to the use of additional prognostic equations.