Numerical Modelling of the Turbulent Flow Developing Within and Over a 3-D Building Array, Part I: A High-Resolution Reynolds-Averaged Navier—Stokes Approach

A study of the neutrally-stratified flow within and over an array of three-dimensional buildings (cubes) was undertaken using simple Reynolds-averaged Navier—Stokes (RANS) flow models. These models consist of a general solution of the ensemble-averaged, steady-state, three-dimensional Navier—Stokes equations, where the k-ε turbulence model (k is turbulence kinetic energy and ε is viscous dissipation rate) has been used to close the system of equations. Two turbulence closure models were tested, namely, the standard and Kato—Launder k-ε models. The latter model is a modified k-ε model designed specifically to overcome the stagnation point anomaly in flows past a bluff body where the standard k-ε model overpredicts the production of turbulence kinetic energy near the stagnation point. Results of a detailed comparison between a wind-tunnel experiment and the RANS flow model predictions are presented. More specifically, vertical profiles of the predicted mean streamwise velocity, mean vertical velocity, and turbulence kinetic energy at a number of streamwise locations that extend from the impingement zone upstream of the array, through the array interior, to the exit region downstream of the array are presented and compared to those measured in the wind-tunnel experiment. Generally, the numerical predictions show good agreement for the mean flow velocities. The turbulence kinetic energy was underestimated by the two different closure models. After validation, the results of the high-resolution RANS flow model predictions were used to diagnose the dispersive stress, within and above the building array. The importance of dispersive stresses, which arise from point-to-point variations in the mean flow field, relative to the spatially-averaged Reynolds stresses are assessed for the building array.     

Wind Conditions in Idealized Building Clusters: Macroscopic Simulations Using a Porous Turbulence Model

Simulating turbulent flows in a city of many thousands of buildings using general high-resolution microscopic simulations requires a grid number that is beyond present computer resources. We thus regard a city as porous media and divide the whole hybrid domain into a porous city region and a clear fluid region, which are represented by a macroscopic k–e{\varepsilon} model. Some microscopic information is neglected by the volume-averaging technique in the porous city to reduce the calculation load. A single domain approach is used to account for the interface conditions. We investigated the turbulent airflow through aligned cube arrays (with 7, 14 or 21 rows). The building height H, the street width W, and the building width B are the same (0.15 m), and the fraction of the volume occupied by fluid (i.e. the porosity) is 0.75; the approaching flow is parallel to the main streets. There are both microscopic and macroscopic simulations, with microscopic simulations being well validated by experimental data. We analysed microscopic wind conditions and the ventilation capacity in such cube arrays, and then calculated macroscopic time-averaged properties to provide a comparison for macroscopic simulations. We found that the macroscopic k–e{\varepsilon} turbulence model predicted the macroscopic flow reduction through porous cube clusters relatively well, but under-predicted the macroscopic turbulent kinetic energy (TKE) near the windward edge of the porous region. For a sufficiently long porous cube array, macroscopic flow quantities maintain constant conditions in a fully developed region.     

CFD simulation of airflow over a regular array of cubes. Part II: analysis of spatial average properties

In the first part of this study, results of a computational fluid dynamics simulation over an array of cubes have been validated against a set of wind-tunnel measurements. In Part II, such numerical results are used to investigate spatially-averaged properties of the flow and passive tracer dispersion that are of interest for high resolution urban mesoscale modelling (e.g. non resolved obstacle approaches). The results show that vertical profiles of mean horizontal wind are linear within the canopy and logarithmic above. The drag coefficient, derived from the numerical results using the classical formula for the drag force, is height dependent (it decreases with height). However, a modification of the formula is proposed (accounting for subgrid velocity scales) that makes the drag coefficient constant with height. Results also show that the dispersive fluxes are similar in magnitude to the turbulent fluxes, and that they play a very important role within the canopy. Vertical profiles of turbulent length scales (to be used in k–l closure schemes, where k is the turbulent kinetic energy and l a turbulent length scale) are also derived. Finally the distribution of the values around the mean over the reference volumes are analysed for wind and tracer concentrations.     

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.     

Large-Eddy Simulation of Flow and Pollutant Transport in Urban Street Canyons with Ground Heating

Our study employed large-eddy simulation (LES) based on a one-equation subgrid-scale model to investigate the flow field and pollutant dispersion characteristics inside urban street canyons. Unstable thermal stratification was produced by heating the ground of the street canyon. Using the Boussinesq approximation, thermal buoyancy forces were taken into account in both the Navier–Stokes equations and the transport equation for subgrid-scale turbulent kinetic energy (TKE). The LESs were validated against experimental data obtained in wind-tunnel studies before the model was applied to study the detailed turbulence, temperature, and pollutant dispersion characteristics in the street canyon of aspect ratio 1. The effects of different Richardson numbers (Ri) were investigated. The ground heating significantly enhanced mean flow, turbulence, and pollutant flux inside the street canyon, but weakened the shear at the roof level. The mean flow was observed to be no longer isolated from the free stream and fresh air could be entrained into the street canyon at the roof-level leeward corner. Weighed against higher temperature, the ground heating facilitated pollutant removal from the street canyon.     

Numerical simulation of January 28 cold air outbreak during GALE Part I: The model and sensitivity tests of turbulence closures

A mesoscale planetary boundary layer (PBL) numerical model has been developed to study airflow over complex topography. Turbulence closures using the turbulent kinetic energy (TKE) and dissipation () equations are investigated in combination with the level 2.5 scheme of Mellor and Yamada (1982) to determine eddy diffusivities for momentum and heat. This modified E- closure is simpler than the level 3 one which requires more prognostic equations for moist turbulent transport.One-dimensional (1-D) model results show that the PBL mean flows under various stability conditions are not significantly sensitive to the modified Blackadar and Kolmogorov eddy mixing-length formulations used in this E- model, although the latter yields excessively large mixing lengths in the entrainment region of the upper PBL. Eddy mixing lengths in the Kolmogorov-type formulation can be better defined by introducing background dissipation. Using the same prognostic TKE equation, the 1-D model results are not significantly affected by different diagnostic formulations in the closures. The simulated results compare well with large-eddy simulations and those obtained using higher-order closure schemes including the level 3 one. The results are found to be insensitive to eddy Prandtl number, in contrast to the 2-D model results (see Part II).     

New Approaches in Two-equation Turbulence Modelling for Atmospheric Applications

The turbulence closure in atmospheric boundary-layer modelling utilizing Reynolds Averaged Navier–Stokes (RANS) equations at mesoscale as well as at local scale is lacking today a common approach. The standard kɛ model, although it has been successful for local scale problems especially in neutral conditions, is deficient for mesoscale flows without modifications. The k–ɛ model is re-examined and a new general approach in developing two-equation turbulence models is proposed with the aim of improving their reliability and consequently their range of applicability. This exercise has led to the replacement of the ɛ-transport equation by the transport equation for the turbulence inverse length scale (wavenumber). The present version of the model is restricted to neutrally stratified flows but applicable to both local scale and mesoscale flows. The model capabilities are demonstrated by application to a series of one-dimensional planetary boundary-layer problems and a two-dimensional flow over a square obstacle. For those applications, the present model gave considerably better results than the standard k–ɛ model.     

Evaluation of the Turbulent Kinetic Energy Dissipation Rate Inside Canopies by Zero- and Level-Crossing Density Methods

Inferring the vertical variation of the mean turbulent kinetic energy dissipation rate (ε) inside dense canopies remains a basic research problem to be confronted. Using detailed laser Doppler anemometry (LDA) measurements collected within a densely arrayed rod canopy, traditional and newly proposed methods to infer ε profiles are compared. The traditional methods for estimating ε at a given layer include isotropic relationships applied to the viscous dissipation scales that are resolved by LDA measurements, higher order structure function methods, and residuals of the turbulent kinetic energy budget in which production and transport terms are all independently inferred. The newly proposed method extends earlier approaches based on zero-crossing statistics, which were shown to be promising in a number of laboratory flows. The extension to account for an arbitrary threshold (hereafter referred to as the level-crossing method) instead of zero-crossing minimizes the effects of instrument noise on the inferred ε. While none of the ε methods employed here can be titled as ‘measured’, these methods differ in their underlying assumptions and simplifications. Above the canopy, where a balance between production and dissipation rate of turbulent kinetic energy is expected, the agreement among all the methods is reasonably good. In the lower-to-middle layers of the canopy, all the methods agree except for those based on a structure-function inference of ε. This departure can be attributed to the lack of a well-defined inertial subrange in these layers. In the upper canopy layers, the disagreements between the methods are largest. Even the higher order structure-function methods disagree with each other when ε is inferred from third- and fifth-order moments. However, for all layers within the canopy, the proposed zero- and threshold-crossing methods agree well with estimates of ε derived from the isotropic relationship applied to the viscous dissipation range. Finally, the advantages of introducing thresholds to minimize two types of instrument noises, additive and multiplicative, are briefly discussed.     

Computational Fluid Dynamics Modelling of the Diurnal Variation of Flow in a Street Canyon

Urban surface and radiation processes are incorporated into a computational fluid dynamics (CFD) model to investigate the diurnal variation of flow in a street canyon with an aspect ratio of 1. The developed CFD model predicts surface and substrate temperatures of the roof, walls, and road. One-day simulations are performed with various ambient wind speeds of 2, 3, 4, 5, and 6 ms⁻¹, with the ambient wind perpendicular to the north–south oriented canyon. During the day, the largest maximum surface temperature for all surfaces is found at the road surface for an ambient wind speed of 3 ms⁻¹ (56.0°C). Two flow regimes are identified by the vortex configuration in the street canyon. Flow regime I is characterized by a primary vortex. Flow regime II is characterized by two counter-rotating vortices, which appears in the presence of strong downwind building-wall heating. Air temperature is relatively low near the downwind building wall in flow regime I and inside the upper vortex in flow regime II. In flow regime II, the upper vortex expands with increasing ambient wind speed, thus enlarging the extent of cool air within the canyon. The canyon wind speed in flow regime II is proportional to the ambient wind speed, but that in flow regime I is not. For weak ambient winds, the dependency of surface sensible heat flux on the ambient wind speed is found to play an essential role in determining the relationship between canyon wind speed and ambient wind speed.     

Numerical simulations of pollutant dispersion in an idealized urban area,for different meteorological conditions

In order to estimate the impacts of buildings on air pollution dispersion, numerical simulations are performed over an idealized urban area, modelled as regular rows of large rectangular obstacles. The simulations are evaluated with the results of the Mock Urban Setting Test (MUST), which is a near full-scale experiment conducted in Utah’s West Desert area: it consists of releases of a neutral gas in a field of regularly spaced shipping containers. The numerical simulations are performed with the model Mercure_Saturne, which is a three-dimensional computational fluid dynamics code adapted to atmospheric flow and dispersion simulations. It resolves complex geometries and uses, in this study, a k–∈ closure for the turbulence model. Sensitivity studies focus on how to prescribe the inflow conditions for turbulent kinetic energy. Furthermore, different sets of coefficients available in the literature for the k–∈ closure model are tested. Twenty MUST trials with different meteorological conditions are simulated and detailed analyses are performed for both the dynamical variables and average concentration. Our results show overall good agreement according to statistical comparison parameters, with a fraction of predictions for average concentration within a factor of two of observations of 67.1%. The set of simulations offers several inflow wind directions and allows us to emphasize the impact of elongated buildings, which create a deflection of the plume centerline relative to the upstream wind direction.     

Simulation of Turbulent Flow in An Urban Forested Park Damaged by a Windstorm

The damage caused by windstorms to forest ecosystems is often very heterogeneous. In order to improve the stability of forested landscapes, it is of great importance to identify the factors responsible for this spatial variability. The structure of the landscape itself may play a role, through possible influences of canopy heterogeneities on the development of turbulence. For the purpose of investigating the role of landscape fragmentation on turbulence development, we used a numerical flow model with a k–ε turbulence scheme model, previously validated in simple cases with well-defined surface changes (roughness change and forest edge flow). A series of two- and three-dimensional simulations were performed over a heterogeneous urban forested park in Europe, which was severely damaged in various places by the Lothar windstorm in December 1999. The model shows the development of a region of strong turbulence, resulting from the generation of large wind shear at the top of the canopy. A sensitivity study shows how the location, extension and intensity of the region depend on canopy characteristics such as the leaf density, the nature of the edge or the presence of gaps and clearings. Simulations performed in conditions representative of the windstorm show that the location of the damaged areas corresponds very closely to the regions where the turbulent kinetic energy was above a certain threshold.     

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.     

利用LAP-3000型风廓线雷达资料对深圳地区湍流耗散率特征的研究

利用2010年1-2月深圳LAP3000型风廓线雷达资料, 对湍流耗散率进行了估算, 针对典型晴天条件下的湍流耗散率ε、折射率结构常数C₂ⁿ、水平风速和风切变, 分析了其时空变化特征。得出如下结论: (1) 深圳地区低空大气ε的量级在10^-7~10^-1 m^-2·s^-3之间, 与理论模拟值基本一致; (2) 时间分布特征为, 2 km以下ε有很明显的日变化特征, 夜晚和上午ε较大, 下午及傍晚减少;(3) 空间分布特征表现为, ε随高度大致呈递减分布;ε量级达10^-2.5 m²·s^-3所在高度可作为深圳地区2010年1月14-15日边界层顶高度的判断依据。     

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.     

Transfer processes in a simulated urban street canyon

The transfer processes within and above a simulated urban street canyon were investigated in a generic manner. Computational fluid dynamics (CFD) was used to aid understanding and to produce some simple operational parameterisations. In this study we addressed specifically the commonly met situation where buoyancy effects arising from elevated surface temperatures are not important, i.e. when mechanical forces outweigh buoyancy forces. In a geophysical context this requires that some suitably defined Richardson number is small. From an engineering perspective this is interpreted as the important case when heat transfer within and above urban street canyons is by forced convection. Surprisingly, this particular scenario (for which the heat transfer coefficient between buildings and the flow is largest), has been less well studied than the situation where buoyancy effects are important. The CFD technique was compared against wind-tunnel experiments to provide model evaluation. The height-to-width ratio of the canyon was varied through the range 0.5–5 and the flow was normal to the canyon axis. By setting the canyon’s facets to have the same or different temperatures or to have a partial temperature distribution, simulations were carried out to investigate: (a) the influence of geometry on the flow and mixing within the canyon and (b) the exchange processes within the canyon and across the canyon top interface. Results showed that the vortex-type circulation and turbulence developed within the canyon produced a temperature distribution that was, essentially, spatially uniform (apart from a relatively thin near-wall thermal boundary layer) This allowed the temperatures within the street canyon to be specified by just one value T _can , the canyon temperature. The variation of T _can with wind speed, surface temperatures and geometry was extensively studied. Finally, the exchange velocity u _E across the interface between the canyon and the flow above was calculated based on a heat flux balance within the canyon and between the canyon and the flow above. Results showed that u _E was approximately 1% of a characteristic wind velocity above the street canyon. The problem of radiative exchange is not addressed but it can, of course, be introduced analytically, or computationally, when necessary.     

An application of the E-ε turbulence model for studying coupled air-sea boundary-layer structure

An E- turbulence model is used to study air-sea interaction characteristics and turbulence structure using a coupled model for air-sea boundary layers. The E- turbulence model consists of equations for the turbulent kinetic energy, the energy-dissipation, and for the turbulent exchange coefficient expressed in terms of turbulent kinetic energy and energy-dissipation. The energy-dissipation equations for the air-sea interface are solved analytically to obtain boundary conditions for energy-dissipation at the interface. The air-sea interaction and turbulence characteristics of the E- model are compared with those of the mixing-length model and with available observations.The simulations demonstrate that the air-sea interaction parameters obtained by the E- model agree well with observations. The numerical studies also show that the E- turbulence model with appropriate constants can give good results in modeling coupled air-sea boundary-layer flows.     

Windbreak Aerodynamics: Is Computational Fluid Dynamics Reliable?

To investigate the suitability of computational fluid dynamics (CFD) with regard to windbreak aerodynamics, simulations are performed with a state-of-the-art numerical scheme (Fluent) and compared against experimental data for two- and three-dimensional disturbances, namely the case of a long straight porous shelter fence and the case of a shelter fence erected in a square about an enclosed plot. A thorough sensitivity study quantifies the impact of numerical choices on the simulation (e.g. grid-point density, domain size, turbulence closure), and leads to guidelines that should ensure objective simulation of windbreak flows. On a fine grid Fluent’s “realizable k–ε closure” gives results that are in qualitative accord with the observed mean winds.     

A Mixed Spectral-Integration Model for Neutral Mean Wind Flow Over Hills

A linear model for neutral surface-layer flow over orography is presented. The Reynolds-Averaged Navier-Stokes and E– turbulence closure equations are expressed in a terrain-following coordinate system created from a simple analytical expression in the Fourier domain. The perturbation equations are solved spectrally horizontally and by numerical integration vertically. Non-dimensional solutions are stored in look-up tables for quick re-use. Model results are compared to measurements, as well as other authors’ flow models in three test cases. The model is implemented and tested in two-dimensional space; the equations for a full three-dimensional version are presented.     

Three-Dimensional Lagrangian Simulation of Suspended Particles in the Neutrally Stratified Atmospheric Surface Layer

A three-dimensional (3-D) inertial particle – Lagrangian stochastic model for heavy particles in turbulent flows has been constructed. In this model, particle velocities are computed by adopting a non-linear drag law, while fluid velocity in the vicinity of a particle is calculated using a 3-D Langevin equation. Our model results have shown that the inclusion of the horizontal fluid velocity fluctuation computations and a non-linear drag law have an impact on the statistics of both fluid and particles when compared with our earlier one-dimensional (1-D) model with a linear drag law. Model results are compared and contrasted with Businger’s 1965 theory in terms of effective settling velocity.     

Topographically forced three-wave quasi-esonant and non-resonant interactions among barotropic rossby waves on an infinnite beta-plane

In this paper, we first apply the assumption h = εh′ of topographic variation (h is the nondimensional topographic height and is a small parameter) to obtain nonlinear equations describing three-wave quasi-resonant and non-resonant interactions among Rossby waves for zonal wavenumbers 1—3 over a wavenumber-two bottom topography (WTBT). Some numerical calculations are made with the fourt-order Rung-Kutta Scheme. It is found that for the case without topographic forcing, the period of three-wave quasi-resonance (TWQR) is found to be independent of the zonal basic westerly wind, but dependent on the meridional wavenumber and the initial amplitudes. For the fixed initial data, when the frequency mismatch is smaller and the meridional wavelength is moderate, its period will belong to the 30–60-day period band. However, when the wavenumber-two topography is included, the periods of the forced quasi-resonant Rossby waves are also found to be strongly dependent on the setting of the zonal basic westerly wind. Under the same conditions, only when the zonal basic westerly wind reaches a moderate extent, intraseasonal oscillations in the 30–60-day period band can be found for zonal wavenumbers 1–3. On the other hand, if three Rossby waves considered have the same meridional wavenumber, three-wave non-resonant interaction over a WTBT can occur in this case. When the WTBT vanishes, the amplitudes of these Rossby waves are conserved. But in the presence of a WTBT, the three Rossby waves oscillate with the identical period. The period, over a moderate range of the zonal basic westerly wind, is in the intraseasonal, 30–60-Day range.