The Budget of Turbulent Kinetic Energy in the Urban Roughness Sublayer

Full-scale observations from two urban sites in Basel, Switzerland were analysed to identify the magnitude of different processes that create, relocate, and dissipate turbulent kinetic energy (TKE) in the urban atmosphere. Two towers equipped with a profile of six ultrasonic anemometers each sampled the flow in the urban roughness sublayer, i.e. from street canyon base up to roughly 2.5 times the mean building height. This observational study suggests a conceptual division of the urban roughness sublayer into three layers: (1) the layer above the highest roofs, where local buoyancy production and local shear production of TKE are counterbalanced by local viscous dissipation rate and scaled turbulence statistics are close to to surface-layer values; (2) the layer around mean building height with a distinct inflexional mean wind profile, a strong shear and wake production of TKE, a more efficient turbulent exchange of momentum, and a notable export of TKE by transport processes; (3) the lower street canyon with imported TKE by transport processes and negligible local production. Averaged integral velocity variances vary significantly with height in the urban roughness sublayer and reflect the driving processes that create or relocate TKE at a particular height. The observed profiles of the terms of the TKE budget and the velocity variances show many similarities to observations within and above vegetation canopies.     

Near Wall Flow over Urban-like Roughness

In this study, comprehensive measurements over a number of urban-type surfaces with the same area density of 25% have been performed in a wind tunnel. The experiments were conducted at a free stream velocity of 10 m s^-1 and the main instrumentation was 120 ° x-wire anemometry, but measurement accuracy was checked using laser Doppler anemometry.The results haveconfirmed the strong three-dimensionalityof the turbulent flow inthe roughness sublayer and the depths of the inertial sublayer (log-law region) and roughness sublayer for each surface have been determined. Spatial averaging has been used to remove the variability of the flow in the roughness sublayer due to individual obstacles and it is shown that the spatially averaged mean velocity in the inertial sublayer and roughness sublayer can,together, be described by a single log-law with a mean zero-plane displacement and roughness length for the surface, provided that the proper surface stress is known. The spatially averaged shear stresses in the inertial sublayer and roughness sublayer are compared with the surface stress deduced from form drag measurements on the roughness elements themselves.The dispersive stress arising from the spatial inhomogeneity in the mean flow profiles was deduced from the data and is shown to be negligible compared with the usual Reynolds stresses in the roughness sublayer. Comparisons have been made between a homogeneous (regular element array) surface and one consisting of random height elements of the same total volume. Although the upper limits of the inertial sublayer for both surfaces were almost identical at equivalent fetch, the roughness sublayer was much thicker for the random surface than for the uniform surface, the friction velocity and the roughness length were significantly larger and the `roughness efficiency' was greater. It is argued that the inertial sublayer may not exist at all in some of the more extreme rough urban areas. These results will provide fundamental information for modelling urban air quality and forecasting urban wind climates.     

Derivation of the aerodynamic roughness parameters for a Sahelian savannah site using the eddy correlation technique

Vertical exchange of heat, moisture and momentum above the earth's surface depends strongly on the turbulence generated by surface roughness. This roughness is best specified through the roughness length and the zero plane displacement. The ratio of windspeed to friction velocity was measured at four heights using the eddy correlation technique at a fallow savannah site in the Sahel. The change in this ratio with height was used to derive the zero plane displacement and the roughness length of the surface, together with an estimate of the error in each parameter. These were estimated as 0.93 ± 0.35 m and 0.17 ± 0.01 m, respectively. The method appears to be a more robust alternative to wind profile derivation.     

A simple unified theory for flow in the canopy and roughness sublayer

The mean flow profile within and above a tall canopy is well known to violate the standard boundary-layer flux–gradient relationships. Here we present a theory for the flow profile that is comprised of a canopy model coupled to a modified surface-layer model. The coupling between the two components and the modifications to the surface-layer profiles are formulated through the mixing layer analogy for the flow at a canopy top. This analogy provides an additional length scale—the vorticity thickness—upon which the flow just above the canopy, within the so-called roughness sublayer, depends. A natural form for the vertical profiles within the roughness sublayer follows that overcomes problems with many earlier forms in the literature. Predictions of the mean flow profiles are shown to match observations over a range of canopy types and stabilities. The unified theory predicts that key parameters, such as the displacement height and roughness length, have a significant dependence on the boundary-layer stability. Assuming one of these parameters a priori leads to the incorrect variation with stability of the others and incorrect predictions of the mean wind speed profile. The roughness sublayer has a greater impact on the mean wind speed in stable than unstable conditions. The presence of a roughness sublayer also allows the surface to exert a greater drag on the boundary layer for an equivalent value of the near-surface wind speed than would otherwise occur. This characteristic would alter predictions of the evolution of the boundary layer and surface states if included within numerical weather prediction models.     

Study on Effects of Building Morphology on Urban Boundary Layer Using an Urban Canopy Model

An urban canopy model is incorporated into the Nanjing University Regional Boundary Layer Model. Temperature simulated by the urban canopy model is in better agreement with the observation, especially in the night time, than that simulated by the traditional slab model. The coupled model is used to study the effects of building morphology on urban boundary layer and meteorological environment by changing urban area, building height, and building density.It is found that when the urban area is expanded, the urban boundary layer heat flux, thermal turbulence, and the turbulent momentum flux and kinetic energy all increase or enhance, causing the surface air temperature to rise up. The stability of urban atmospheric stratification is affected to different extent at different times of the day.When the building height goes up, the aerodynamic roughness height, zero plane displacement height of urban area, and ratio of building height to street width all increase. Therefore, the increase in building height results in the decrease of the surface heat flux, urban surface temperature, mean wind speed, and turbulent kinetic energy in daytime. While at night, as more heat storage is released by higher buildings, thermal turbulence is more active and surface heat flux increases, leading to a higher urban temperature.As the building density increases, the aerodynamic roughness height of urban area decreases, and the effect of urban canopy on radiation strengthens. The increase of building density results in the decrease in urban surface heat flux, momentum flux, and air temperature, the increase in mean wind speed, and the weakening of turbulence in the daytime. While at night, the urban temperature increases due to the release of more heat storage.     

冬季北京城市近地层的气象特征

运用2001年1～3月北京大气边界层和大气化学综合试验期间,中国科学院大气物理研究所铁塔上所获得的8～320 m 15层风、温度和湿度梯度资料,对冬季北京城市边界层特征进行了诊断分析.结果表明,在冬季北京城市边界层中,平均而言地表粗糙度为1.34、零平均位移约为20 m;温度基本上随高度呈线性变化;风速随高度的变化并不总遵循对数关系,尤其是在午前和夜间,风速与高度之间对数关系的不显著率可达30%～40%.不能简单套用在Monin-Obuhov相似理论中由Businger-Dve风廓线层结订正获得的近地面层动量、热量和水汽湍流输送计算公式.     

Mean Flow and Turbulence Characteristics in an Urban Roughness Sublayer

In this study, a detailed model of an urban landscape has been re-constructed inthe wind tunnel and the flow structure inside and above the urban canopy has beeninvestigated. Vertical profiles of all three velocity components have been measuredwith a Laser-Doppler velocimeter, and an extensive analysis of the measured meanflow and turbulence profiles carried out. With respect to the flow structure inside thecanopy, two types of velocity profiles can be distinguished. Within street canyons,the mean wind velocities are almost zero or negative below roof level, while closeto intersections or open squares, significantly higher mean velocities are observed.In the latter case, the turbulent velocities inside the canopy also tend to be higherthan at street-canyon locations. For both types, turbulence kinetic energy and shearstress profiles show pronounced maxima in the flow region immediately above rooflevel.Based on the experimental data, a shear-stress parameterization is proposed, inwhich the velocity scale, u_s, and length scale, z_s, are based on the level and magnitude of the shear stress peak value. In order to account for a flow region inside the canopy with negligible momentum transport, a shear stress displacement height, d_s, is introduced. The proposed scaling and parameterization perform well for the measured profiles and shear-stress data published in the literature.The length scales derived from the shear-stress parameterization also allowdetermination of appropriate scales for the mean wind profile. The roughnesslength, z₀, and displacement height, d₀, can both be described as fractions of the distance, z_s - d_s, between the level of the shear-stress peak and the shear-stress displacement height. This result can be interpreted in such a way that the flow only feels the zone of depth z_s - d_s as the roughness layer. With respect to the lower part of the canopy (z < d_s) the flow behaves as a skimming flow. Correlations between the length scales z_s and d_s and morphometric parameters are discussed.The mean wind profiles above the urban structure follow a logarithmic windlaw. A combination of morphometric estimation methods for d₀ and z₀ with wind velocity measurements at a reference height, which allow calculation of the shear-stress velocity, u_*, appears to be the most reliable and easiest procedure to determine mean wind profile parameters. Inside the roughnesssublayer, a local scaling approach results in good agreement between measuredand predicted mean wind profiles.     

Turbulent flow over a very rough,random surface

A knowledge of the nature of turbulent flow over very rough surfaces is important for an understanding of the environment of crops, forests, and cities. For this reason, a wind-tunnel investigation was carried out on the variations in mean velocity, Reynolds shear-stress, and other turbulence quantities in a deep turbulent flow over a rough surface having a fair degree of randomness in the shapes, sizes, and positions of its elements.There was a layer close to the surface with considerable variations in both mean velocity and shear-stress, and the horizontal scale over which the mean velocity varied was much larger than the average distance between roughness elements. Above this layer, whose depth was of the order of the spacing between roughness elements, shear stress was constant with height, and the velocity profile had a logarithmic form. The usefulness of both mean profile and eddy-correlation methods for estimating fluxes above very rough terrain is discussed in the light of these findings.     

Near-Wall Flow Development After A Step Change In Surface Roughness

An experimental study of the initial flow field downstream of a step change in surface roughness is presented. The roughness length of the downstream surface was approximately tenfold that of the upstream roughness and, unlike all previous studies, attention was concentrated on the roughness sublayer region beneath the inertial (log-law) region. The experiments were conducted at a boundary layer Reynolds number of about 6 × 10⁴ (based on layer thickness andfree-stream velocity) and around a longitudinal location where the (downstream) roughness length, z_o2, was about 1% of the boundary-layer thickness atthe roughness change point.The thickness of the roughness sublayer was found for the two roughness. It was observed that the vertical profiles of mean velocity and turbulence characteristics started to show similarity after about 160z₀₂ downstream of the roughness change. The presence of a shear stress overshoot is shown to depend strongly on the precise location (with respect to the roughness elements) at which the measurements are made and the thickness of the equilibrium layer is shown to be very sensitive to the way it is defined. It is demonstrated that the growing equilibrium layer has first to encompass the roughness sublayer before any thickness of inertial sublayer can be developed. It follows that, in somepractical cases, like flows across some urban environments, the latter(log-law) region may never exist at all.     

A New Aerodynamic Parametrization for Real Urban Surfaces

This study conducted large-eddy simulations (LES) of fully developed turbulent flow within and above explicitly resolved buildings in Tokyo and Nagoya, Japan. The more than 100 LES results, each covering a 1,000 $\times $ 1,000 m $^{2}$ area with 2-m resolution, provide a database of the horizontally-averaged turbulent statistics and surface drag corresponding to various urban morphologies. The vertical profiles of horizontally-averaged wind velocity mostly follow a logarithmic law even for districts with high-rise buildings, allowing estimates of aerodynamic parameters such as displacement height and roughness length using the von Karman constant $=$ 0.4. As an alternative derivation of the aerodynamic parameters, a regression of roughness length and variable Karman constant was also attempted, using a displacement height physically determined as the central height of drag action. Although both the regression methods worked, the former gives larger (smaller) values of displacement height (roughness length) by 20–25 % than the latter. The LES database clearly illustrates the essential difference in bulk flow properties between real urban surfaces and simplified arrays. The vertical profiles of horizontally-averaged momentum flux were influenced by the maximum building height and the standard deviation of building height, as well as conventional geometric parameters such as the average building height, frontal area index, and plane area index. On the basis of these investigations, a new aerodynamic parametrization of roughness length and displacement height in terms of the five geometric parameters described above was empirically proposed. The new parametrizations work well for both real urban morphologies and simplified model geometries.     

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

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

峨眉山地区近地层微气象特征研究

基于2019年12月至2020年11月峨眉山站梯度塔资料、辐射观测资料和地表通量资料,采用涡动相关法对峨眉山地区近地层的地表通量和蒸散发量的变化进行分析,并估算了零平面位移、空气动力粗糙度、空气热力粗糙度、动量通量输送系数和感热通量输送系数等重要的空气动力学和热力学参数.研究表明:近地面风速呈现高层高、低层低的特征,且...     

Characteristics of the Drag Coefficient in the Roughness Sublayer over a Complex Urban Surface

The statistics of momentum exchange in the urban roughness sublayer are investigated. The analysis focuses on the characteristics of the dimensionless friction velocity, \({u_{*}}/U\) , which is defined as the square root of the drag coefficient. The turbulence observations were made at a height of 47 m above the ground on the 325-m meteorological tower, which is located in a very inhomogeneous urban area in Beijing. Under neutral conditions, the dependence of the drag coefficient on wind speed varies with wind direction. When the airflow is from the area of densely built-up buildings, the drag coefficient does not vary with wind speed, while when the airflow is from the area covered by vegetation, the drag coefficient appears to decrease with increasing wind speed. Also, the drag coefficient does not vary monotonically with the atmospheric stability. Both increasing stability and increasing instability lead to the decrease of the drag coefficient, implying that the roughness length and zero-plane displacement may vary in urban areas.     

应用城市冠层模式研究建筑物形态对城市边界层的影响

文中将城市冠层模式耦合到南京大学城市尺度边界层模式中,通过模拟对比发现,耦合模式对城市地区气温模拟结果更接近于观测值,尤其是对城市地区夜间气温模拟的改进.运用改进耦合模式通过多个敏感性试验的模拟,从城市面积扩张、建筑物高度增加、建筑物分布密度变化等角度研究城市建筑物三维几何形态变化对城市边界层及城市气象环境的影响,试验结果表明:(1)城市面积扩张使得城市下垫面的热通量增大,热力湍流活动增强,动量通量输送增强,城市湍能增大,湍流扩散系数变大,城市气温升高,且对不同时刻城市区域大气层结稳定度均有不同程度的影响.(2)建筑物高度增加增大了城市下垫面的粗糙度和零平面位移.同时也增大了城市街渠高宽比.城市建筑物越高,白天城市地区地表热通量越小,城市上空大气温度越低,平均风速减小,湍能减小;夜间由于高大建筑物释放储热比低矮建筑物要多,其热力湍流相对活跃,地表热通量增大,使得城市区域气温较高.(3)建筑物密度增大,会减小城市下垫面的粗糙度同时增强街渠对辐射的影响.建筑物密度增大在白天会减小地表热通量和动量通量,使城市气温降低,平均风速增大,城市湍流活动能力减弱;夜间城市释放较多储热使得气温较高.     

A comparative study of some mathematical models of the mean wind structure and aerodynamic drag of plant canopies

A semi-analytical method for describing the mean wind profile and shear stress within plant canopies and for estimating the roughness length and the displacement height is presented. This method incorporates density and vertical structure of the canopy and includes simple parameterizations of the roughness sublayer and shelter factor. Some of the wind profiles examined are consistent with first-order closure techniques while others are consistent with second-order closure techniques. Some profiles show a shearless region near the base of the canopy; however, none displays a secondary maximum there. Comparing several different analytical expressions for the canopy wind profile against observations suggests that one particular type of profile (an Airy function which is associated with the triangular foliage surface area density distribution) is superior to the others. Because of the numerical simplicity of the methods outlined, it is suggested that they may be profitably used in large-scale models of plant-atmosphere exchanges.     

Observed Wind Profiles and Turbulence Fluxes over an ice Surface with Changing Surface Roughness

Wind profile and eddy-correlation data obtained at two sites on a melting glacier surface in Iceland during the summer of 1996 are presented. Throughout the experiment the surface roughness increased rapidly from smooth to very rough, with the largest roughness element height obtained being about 1.7 m. In a layer close to the rough surface we find that the wind speed profiles were disturbed showing horizontal inhomogeneities as in a roughness sublayer. Its height was approximately two times the height of the main roughness elements (h) at both sites throughout the experiment. From the wind profiles and eddy-correlation data we calculated corrections for the displaced zero plane as a function of time and compared these with results obtained from a drag partitioning model. In general, the agreement was reasonable considering the ranges of uncertainty but the results indicate that the increasing horizontal anisotropy of the surface probably limits the use of the model. The values obtained for the roughness lengths are in good agreement with those calculated from a simple linear model, i.e., z₀/h = 0.5 with the frontal area index. Above the roughness sublayer the wind profiles, normalised standard deviations of wind speed, and the balance of the turbulence kinetic energy budget behaved as over an ideal homogeneous surface thereby confirming similarity of the flow.     

Impact of Eddy Characteristics on Turbulent Heat and Momentum Fluxes in the Urban Roughness Sublayer

Eddy-covariance observations above the densely built-up Centre of Nanjing were made from December 2011 to August 2012. Separate eddy-covariance systems installed at two levels on a 36-m tower located on a rooftop were operated simultaneously, and observations grouped into two sectors (A, B) according to the prevalent wind directions. For sector A, where the nearby buildings are all below the lower measurement level, the sensible heat and momentum fluxes are generally greater at the upper level. For sector B, where several high-rise buildings are located upwind, the sensible heat and momentum fluxes at the upper level are close to those at the lower level. The analysis shows that the turbulent eddy characteristics differ between the two wind sectors, leading to a different behaviour of turbulent exchange between the two levels. A hypothesis is proposed that addresses the vertical variation of turbulent fluxes in the urban roughness sublayer (RSL). For sector A, the buildings block the flow, change the trajectory of scalars, and distort the footprint of scalar fluxes; this ‘blocking effect’ is believed to lead to a smaller sensible heat flux above the canopy layer. Such an effect should decrease with height in the RSL, explaining the increase of the observed turbulent heat flux with height. In addition, the presence of non-uniform building heights adversely affects turbulence organization around the canopy top, and likely elevates the inflection point of the mean flow to a higher elevation close to the upper measurement level, where larger shear results in a larger momentum flux. For sector B, wake effects from the nearby high-rise buildings strongly reduce turbulence organization at higher elevations, leading to similar sensible heat and momentum fluxes at both measurement levels.     

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.