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.     

A numerical study of daily transitions in the convective boundary layer

We examine daily (morning–afternoon) transitions in the atmospheric boundary layer based on large-eddy simulations. Under consideration are the effects of the stratification at the top of the mixed layer and of the wind shear. The results describe the transitory behaviour of temperature and wind velocity, their second moments, the boundary-layer height Z _m (defined by the maximum of the potential temperature gradient) and its standard deviation σ _m , the mixed-layer height z _i (defined by the minimum of the potential temperature flux), entrainment velocity W _e, and the entrainment flux H _i . The entrainment flux and the entrainment velocity are found to lag slightly in time with respect to the surface temperature flux. The simulations imply that the atmospheric values of velocity variances, measured at various instants during the daytime, and normalized in terms of the actual convective scale w_*, are not expected to collapse to a single curve, but to produce a significant scatter of observational points. The measured values of the temperature variance, normalized in terms of the actual convective scale Θ_*, are expected to form a single curve in the mixed layer, and to exhibit a considerable scatter in the interfacial layer.     

The Fallacy of Drifting Snow

A common parametrization over snow-covered surfaces that are undergoing saltation is that the aerodynamic roughness length for wind speed (z ₀) scales as au_*²/g{\alpha u_\ast^2/g}, where u _* is the friction velocity, g is the acceleration of gravity, and α is an empirical constant. Data analyses seem to support this scaling: many published plots of z ₀ measured over snow demonstrate proportionality to u_*²{u_\ast^2 }. In fact, I show similar plots here that are based on two large eddy-covariance datasets: one collected over snow-covered Arctic sea ice; another collected over snow-covered Antarctic sea ice. But in these and in most such plots from the literature, the independent variable, u _*, was used to compute z ₀ in the first place; the plots thus suffer from fictitious correlation that causes z ₀ to unavoidably increase with u _* without any intervening physics. For these two datasets, when I plot z ₀ against u _* derived from a bulk flux algorithm—and thus minimize the fictitious correlation—z ₀ is independent of u _* in the drifting snow region, u _* ≥ 0.30 ms⁻¹. I conclude that the relation z₀ = au_*²/g{z_0 = \alpha u_\ast^2/g} when snow is drifting is a fallacy fostered by analyses that suffer from fictitious correlation.     

The Role of Shear in the Morning Transition Boundary Layer

We use large-eddy simulation (LES) to better define the early stages of the morning transition boundary layer. Previous LES studies relating to the morning transition boundary layer focus on the role of the entraining convective boundary layer (CBL). By using a combination of different domain sizes and grid lengths, the full evolution from the stable boundary layer (SBL) to the CBL is modelled here. In the early stages of the morning transition the boundary layer is shown to be a combination of a shallow mixed layer capped by a significant shear driven stable boundary layer (the so-called mixed CBL–SBL state). The mixed CBL–SBL state is the key to understanding the sensitivity to shear. Turbulent kinetic energy budgets also indicate that it is shear driven. The negative flux from the mixed CBL–SBL state extends much further above the minimum than is typically found for the CBL later in the day, and the depth of penetration scales as w _m /N _i , where w _m is the combined friction and convective velocity scale and N _i the static stability at the inversion top.     

A Simple Model for the Vertical Transport of Reactive Species in the Convective Atmospheric Boundary Layer

We have developed a simple, steady-state, one-dimensional second-order closure model to obtain continuous profiles of turbulent fluxes and mean concentrations of non-conserved scalars in a convective boundary layer without shear. As a basic tool we first set up a model for conserved species with standard parameterizations. This leads to formulations for profiles of the turbulent diffusivity and the ratio of temperature-scalar covariance to the flux of the passive scalar. The model is then extended to solving, in terms of profiles of mean concentrations and fluxes, the NO _x –O₃ triad problem. The chemical reactions involve one first-order reaction, the destruction of NO₂ with decay time τ, and one second-order reaction, the destruction of NO and O₃ with the reaction constant k. Since the fluxes of the sum concentrations of NO _x = NO + NO₂ and O₃ + NO₂ turn out to be constant throughout the boundary layer, the problem reduces to solving two differential equations for the concentration and the flux of NO₂. The boundary conditions are the three surface fluxes and the fluxes at the top of the boundary layer, the last obtained from the entrainment velocity, and the concentration differences between the free troposphere and the top of the boundary layer. The equations are solved in a dimensionless form by using 1/(kτ) as the concentration unit, the depth h of the boundary layer as the length unit, the convective velocity scale w _* as the velocity unit, and the surface temperature flux divided by w _* as the temperature unit. Special care has been devoted to the inclusion of the scalar–scalar covariance between the concentrations of O₃ and NO. Sample calculations show that the fluxes of the reactive species deviate significantly from those of non-reactive species. Further, the diffusivities, defined by minus the flux divided by the concentration gradient may become negative for reactive species in contrast to those of non-reactive species, which in the present model are never negative.     

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.     

On the Kinetic Energy Budget of the Unstable Atmospheric Surface Layer

We present a new account of the kinetic energy budget within an unstable atmospheric surface layer (ASL) beneath a convective outer layer. It is based on the structural model of turbulence introduced by McNaughton (Boundary-Layer Meteorology, 112: 199–221, 2004). In this model the turbulence is described as a self-organizing system with a highly organized structure that resists change by instability. This system is driven from above, with both the mean motion and the large-scale convective motions of the outer layer creating shear across the surface layer. The outer convective motions thus modulate the turbulence processes in the surface layer, causing variable downwards fluxes of momentum and kinetic energy. The variable components of the momentum flux sum to zero, but the associated energy divergence is cumulative, increasing both the average kinetic energy of the turbulence in the surface layer and the rate at which that energy is dissipated. The tendency of buoyancy to preferentially enhance the vertical motions is opposed by pressure reaction forces, so pressure production, which is the work done against these reaction forces, exactly equals buoyant production of kinetic energy. The pressure potential energy that is produced is then redistributed throughout the layer through many conversions, back and forth, between pressure potential and kinetic energy with zero sums. These exchanges generally increase the kinetic energy of the turbulence, the rate at which turbulence transfers momentum and the rate at which it dissipates energy, but does not alter its overall structure. In this model the velocity scale for turbulent transport processes in the surface layer is (kzɛ)^1/3 rather than the friction velocity, u_*. Here k is the von Kármán constant, z is observation height, ɛ is the dissipation rate. The model agrees very well with published experimental results, and provides the foundation for the new similarity model of the unstable ASL, replacing the older Monin–Obukhov similarity theory, whose assumptions are no longer tenable.     

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.     

Vertical Structure of Selected Turbulence Characteristics above an Urban Canopy

Summary In this paper the results of an urban measurement campaign are presented. The experiment took place from July 1995 to February 1996 in Basel, Switzerland. A total of more than 2000 undisturbed 30-minute runs of simultaneous measurements of the fluctuations of the wind vector u′, v′, w′ and the sonic temperature θ _s ′ at three different heights (z=36, 50 and 76 m a.g.l.) are analysed with respect to the integral statistics and their spectral behaviour. Estimates of the zero plane displacement height d calculated by the temperature variance method yield a value of 22 m for the two lower levels, which corresponds to 0.92 h (the mean height of the roughness elements). At all three measurement heights the dimensionless standard deviation σ _w /u _* is systematically smaller than the Monin-Obukhov similarity function for the inertial sublayer, however, deviations are smaller compared to other urban turbulence studies. The σ_θ/θ_* values follow the inertial sublayer prediction very close for the two lowest levels, while at the uppermost level significant deviations are observed. Profiles of normalized velocity and temperature variances show a clear dependence on stability. The profile of friction velocity u _* is similar to the profiles reported in other urban studies with a maximum around z/h=2.1. Spectral characteristics of the wind components in general show a clear dependence on stability and dimensionless measurement height z/h with a shift of the spectral peak to lower frequencies as thermal stability changes from stable to unstable conditions and as z/h decreases. Velocity spectra follow the −2/3 slope in the inertial subrange region and the ratios of spectral energy densities S _w (f)/S _u (f) approach the value of 4/3 required for local isotropy in the inertial subrange. Velocity spectra and spectral peaks fit best to the well established surface layer spectra from Kaimal et al. (1972) at the uppermost level at z/h=3.2. Received September 26, 1997 Revised February 15, 1998     

Variability of surface roughness and turbulence intensities at a coastal site in India

Surface-layer features with different prevailing wind directions for two distinct seasons (Southwest Monsoon and Northeast Monsoon) on the west coast of India are studied using data obtained from tower-based sensors at a site located about 500 m from the coast. Only daytime runs have been used for the present analysis. The surface boundary-layer fluxes have been estimated using the eddy correlation method. The surface roughnessz ₀ obtained using the stability-corrected wind profiles (Paulson, 1970) has been found to be low for the Southwest monsson season. For the other season,z ₀ is relatively high. The drag coefficientC _D varies with height in the NE monsoon season but not in the season with lowz ₀. This aspect is reflected in the wind profiles for the two seasons and is discussed in detail. The scaling behaviour of friction velocityu _* and the turbulence intensity of longitudinal, lateral and vertical winds _u, _v and _w, respectively) are further examined to study their dependence on fetch. Our study shows that for the non-dimensional case, _u/u_* and _v/u_* do not show any surface roughness dependence in either season. On the other hand, for _w/u_* for the season with lowz ₀, the values are seen to agree well with that of Panofskyet al. (1977) for homogeneous terrain whereas for the other season with highz ₀, the results seem to conform more to the values observed by Smedman and Högström (1983) for coastal terrain. The results are discussed in the light of observations by other investigators.     

Measurements of spray at an air-water interface

The spray content in the surface boundary layer above an air—water interface was determined by a series of measurements at various feteches and wind speeds in a laboratory facility. The droplet flux density N(z) can be described in terms of the scaling flux density N_* and von Karman constant K throguh the equation, N(z)/N_* = −(1/K) ln(z/z_0d) where z is height above the mean water level and z_0d is the droplet boundary layer thickness. N_* is given by a unique relationship in terms of the roughness Reynolds number u_*σ/ν where σ is the root-mean-square surface displacement. Spray inception occurred for u_* 0.3. The dominant mode of spray generation in the present and most other laboratory tests, as well as in available field data, appears to be bubble bursting.     

Monin–Obukhov Similarity Functions of the Structure Parameter of Temperature and Turbulent Kinetic Energy Dissipation Rate in the Stable Boundary Layer

The Monin–Obukhov similarity theory (MOST) functions f_ε and f_T, of the dissipation rate of turbulent kinetic energy (TKE). ε, and the structure parameter of temperature, C_T², were determined for the stable atmospheric surface layer using data gathered in the context of CASES-99. These data cover a relatively wide stability range, i.e. ζ=z/L of up to 10, where z is the height and L the Obukhov length. The best fits were given by f_ε = 0.8 + 2.5ζ and f_T= 4.7[ 1+1.6(ζ)^2/3], which differ somewhat from previously published functions. ε was obtained from spectra of the longitudinal wind velocity using a time series model (ARMA) method instead of the traditional Fourier transform. The neutral limit f_ε =0.8 implies that there is an imbalance between TKE production and dissipation in the simplified TKE budget equation. Similarly, we found a production-dissipation imbalance for the temperature fluctuation budget equation. Correcting for the production-dissipation imbalance, the ‘standard’ MOST functions for dimensionless wind speed and temperature gradients (φ_m and φ_m) were determined from f_ε and f_T and compared with the φ_m and φ_h formulations of Businger and others. We found good agreement with the Beljaars and Holtslag [J. Appl. Meteorol. 30, 327–341 (1991)] relations. Lastly, the flux and gradient Richardson numbers are discussed also in terms of f_ε and f_T.     

Turbulent Flow at 190 m Height Above London During 2006–2008: A Climatology and the Applicability of Similarity Theory

Flow and turbulence above urban terrain is more complex than above rural terrain, due to the different momentum and heat transfer characteristics that are affected by the presence of buildings (e.g. pressure variations around buildings). The applicability of similarity theory (as developed over rural terrain) is tested using observations of flow from a sonic anemometer located at 190.3 m height in London, U.K. using about 6500 h of data. Turbulence statistics—dimensionless wind speed and temperature, standard deviations and correlation coefficients for momentum and heat transfer—were analysed in three ways. First, turbulence statistics were plotted as a function only of a local stability parameter z/Λ (where Λ is the local Obukhov length and z is the height above ground); the σ _i /u _* values (i = u, v, w) for neutral conditions are 2.3, 1.85 and 1.35 respectively, similar to canonical values. Second, analysis of urban mixed-layer formulations during daytime convective conditions over London was undertaken, showing that atmospheric turbulence at high altitude over large cities might not behave dissimilarly from that over rural terrain. Third, correlation coefficients for heat and momentum were analyzed with respect to local stability. The results give confidence in using the framework of local similarity for turbulence measured over London, and perhaps other cities. However, the following caveats for our data are worth noting: (i) the terrain is reasonably flat, (ii) building heights vary little over a large area, and (iii) the sensor height is above the mean roughness sublayer depth.     

Effects of Topographical Slope Angle and Atmospheric Stratification on Surface-Layer Turbulence

The effect of topographical slope angle and atmospheric stratification on turbulence intensities in the unstably stratified surface layer have been parameterized using observations obtained from a three-dimensional sonic anemometer installed at 8 m height above the ground at the Seoul National University (SNU) campus site in Korea for the years 1999–2001. Winds obtained from the sonic anemometer are analyzed according to the mean wind direction, since the topographical slope angle changes significantly along the azimuthal direction. The effects of the topographical slope angle and atmospheric stratification on surface-layer turbulence intensity are examined with these data. It is found that both the friction velocity and the variance for each component of wind normalized by the mean wind speed decrease with increase of the topographical slope angle, having a maximum decreasing rate at very unstable stratification. The decreasing rate of the normalized friction velocity (u _* /U) is found to be much larger than that of the turbulence intensity of each wind component due to the reduction of wind shear with increase in slope angle under unstable stratification. The decreasing rate of the w component of turbulence intensity (σ _w /U) is the smallest over the downslope surface whereas that of the u component (σ _u /U) has a minimum over the upslope surface. Consequently, σ _w /u _* has a maximum increasing rate with increase in slope angle for the downslope wind, whereas σ _u /u _* has its maximum for the upslope wind. The sloping terrain is found to reduce both the friction velocity and turbulence intensity compared with those on a flat surface. However, the reduction of the friction velocity over the sloping terrain is larger than that of the turbulence intensity, thereby enhancing the turbulence intensity normalized by the friction velocity over sloping terrain compared with that over a flat surface.     

Flux Footprints in the Convective Boundary Layer: Large-Eddy Simulation and Lagrangian Stochastic Modelling

We investigated the flux footprints of receptors at different heights in the convective boundary layer (CBL). The footprints were derived using a forward Lagrangian stochastic (LS) method coupled with the turbulent fields from a large-eddy simulation model. Crosswind-integrated flux footprints shown as a function of upstream distances and sensor heights in the CBL were derived and compared using two LS particle simulation methods: an instantaneous area release and a crosswind linear continuous release. We found that for almost all sensor heights in the CBL, a major positive flux footprint zone was located close to the sensor upstream, while a weak negative footprint zone was located further upstream, with the transition band in non-dimensional upwind distances −X between approximately 1.5 and 2.0. Two-dimensional (2D) flux footprints for a point sensor were also simulated. For a sensor height of 0.158 z _i, where z _i is the CBL depth, we found that a major positive flux footprint zone followed a weak negative zone in the upstream direction. Two even weaker positive zones were also present on either side of the footprint axis, where the latter was rotated slightly from the geostrophic wind direction. Using CBL scaling, the 2D footprint result was normalized to show the source areas and was applied to real parameters obtained using aircraft-based measurements. With a mean wind speed in the CBL of U = 5.1 m s⁻¹, convective velocity of w _* = 1.37 m s⁻¹, CBL depth of z _i = 1,000 m, and flight track height of 159 m above the surface, the total flux footprint contribution zone was estimated to range from about 0.1 to 4.5 km upstream, in the case where the wind was perpendicular to the flight track. When the wind was parallel to the flight track, the total footprint contribution zone covered approximately 0.5 km on one side and 0.8 km on the other side of the flight track.     

The characteristics of turbulent velocity components in the surface layer under convective conditions

It is proposed that the ratios of the standard deviations of the horizontal velocity components to the friction velocity in the surface layer under convective conditions depend only onz _i /L wherez _i is the height of the lowest inversion andL is the Monin-Obukhov length. This hypothesis is tested by using observations from several data sets over uniform surfaces and appears to fit the data well. Empirical curves are fitted to the observations which have the property that at largez _i /-L, the standard deviations become proportional tow _*, the convective scaling velocity.Fluctuations of vertical velocity obtained from the same experiments scale withz/L, wherez is the height above the surface, in good agreement with Monin-Obukhov theory.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Effect of the Entrainment Flux Ratio on the Relationship between Entrainment Rate and Convective Richardson Number

The parameterization of the dimensionless entrainment rate (w _e /w _*) versus the convective Richardson number (Ri _δθ ) is discussed in the framework of a first-order jump model (FOM). A theoretical estimation for the proportionality coefficient in this parameterization, namely, the total entrainment flux ratio, is derived. This states that the total entrainment flux ratio in FOM can be estimated as the ratio of the entrainment zone thickness to the mixed-layer depth, a relationship that is supported by earlier tank experiments, and suggesting that the total entrainment flux ratio should be treated as a variable. Analyses show that the variability of the total entrainment flux ratio is actually the effect of stratification in the free atmosphere on the entrainment process, which should be taken into account in the parameterization. Further examination of data from tank experiments and large-eddy simulations demonstrate that the different power laws for w _e /w _* versus Ri _δθ can be interpreted as the variability of the total entrainment flux ratio. These results indicate that the dimensionless entrainment rate depends not only on the convective Richardson number but also upon the total entrainment flux ratio.     

An experimental investigation of a wind-generated suspension of particulate matter from a tailings disposal area

A wind tunnel investigation of the wind erosion of uranium mine-tailings material typical of a northern Ontario site has been carried out. The aim of the study was to measure the effects of various parameters, including mean and turbulent wind characteristics of the boundary layer and surface moisture content, upon the erosion process. The analysis of experimental data has yielded a mathematical model for predicting the net vertical mass fluxes. The results show that the dry vertical flux is proportional to u _* ^2.3and the wet flux to u _* ^5.0 Partical size analysis was also carried out.     

Standard deviation of vertical two-point longitudinal velocity differences in the atmospheric boundary layer

The standard deviation of vertical two-point longitudinal velocity fluctuation differences is analyzed experimentally with eleven sets of turbulence measurements obtained at the NASA 150-m ground-winds tower site at Cape Kennedy, Florida. It is concluded that /u _*0 is proportional to (fz/u _*0)^0.22, where the coefficient of proportionality is a function of fz/u _*0 and u _*0/fL ₀. The quantities f and L₀ denote the Coriolis parameter and the surface Monin-Obukhov stability length, respectively; u _*0 is the surface friction velocity; z is the vertical distance between the two points over which the velocity difference is calculated; and zz is the mean height of the mid-point of the interval z above natural grade. The results of the analysis are valid for 20<-u _*0/fL ₀<2000.