A Wind Tunnel Model for Quantifying Fluxes in the Urban Boundary Layer

Transport of pollution and heatout of streets into the boundary layer above is not currently understood and so fluxes cannot be quantified. Scalar concentration within the street is determined by the flux out of it and so quantifying fluxes for turbulent flow over a rough urban surface is essential. We have developed a naphthalene sublimation technique to measure transfer from a two-dimensional street canyon in a wind tunnel for the case of flow perpendicular to the street. The street was coated with naphthalene, which sublimes at room temperature, so that the vapour represented the scalar source. The transfer velocity w_T relates the flux out of the canyon to the concentration within it and is shown to be linearly related to windspeed above the street. The dimensionless transfer coefficient w_T/U represents the ventilation efficiency of the canyon (here, w_T is a transfer velocity,U is the wind speed at the boundary-layer top). Observed values are between 1.5 and 2.7 ×10^-3 and, for the case where H/W0 (ratio of buildingheight to street width), values are in the same range as estimates of transfer from a flat plate, giving confidence that the technique yields accurate values for street canyon scalar transfer. w_T/U varies with aspect ratio (H/W), reaching a maximum in the wake interference regime (0.3 < H/W < 0.65). However, when upstream roughness is increased, the maximum in w_T/U reduces, suggesting that street ventilation is less sensitive to H/W when the flow is in equilibrium with the urban surface. The results suggest that using naphthalene sublimation with wind-tunnel models of urban surfaces can provide a direct measure of area-averaged scalar fluxes.     

Pollutant Concentrations in Street Canyons of Different Aspect Ratio with Avenues of Trees for Various Wind Directions

This study summarizes the effects of avenues of trees in urban street canyons on traffic pollutant dispersion. We describe various wind-tunnel experiments with different tree-avenue models in combination with variations in street-canyon aspect ratio W/H (with W the street-canyon width and H the building height) and approaching wind direction. Compared to tree-free street canyons, in general, higher pollutant concentrations are found. Avenues of trees do not suppress canyon vortices, although the air ventilation in canyons is hindered significantly. For a perpendicular wind direction, increases in wall-average and wall-maximum concentrations at the leeward canyon wall and decreases in wall-average concentrations at the windward wall are found. For oblique and perpendicular wind directions, increases at both canyon walls are obtained. The strongest effects of avenues of trees on traffic pollutant dispersion are observed for oblique wind directions for which also the largest concentrations at the canyon walls are found. Thus, the prevailing assumption that attributes the most harmful dispersion conditions to a perpendicular wind direction does not hold for street canyons with avenues of trees. Furthermore, following dimensional analysis, an estimate of the normalized wall-maximum traffic pollutant concentration in street canyons with avenues of trees is derived.     

Scalar Fluxes from Urban Street Canyons Part II: Model

A practical model is developed for the vertical flux of a scalar, such as heat, from an urban street canyon that accounts for variations of the flow and turbulence with canyon geometry. The model gives the magnitude and geometric dependence of the flux from each facet of the urban street canyon, and is shown to agree well with wind-tunnel measurements described in Part I. The geometric dependence of the flux from an urban street canyon is shown to be determined by two physical processes. Firstly, as the height-to-width ratio of the street canyon increases, so does the roughness length and displacement height of the surface. This increase leads to a reduction in the wind speed in the inertial sublayer above the street canyons. Since the speed of the circulations in the street are proportional to this inertial sublayer wind speed, the flux then reduces with the inertial sublayer wind speed. This process is dominant at low height-to-width ratios. Secondly, the character of the circulations within the street canyon also varies as the height-to-width ratio increases. The flow in the street is partitioned into a recirculation region and a ventilated region. When the street canyon has high height-to-width ratios the recirculation region occupies the whole street canyon and the wind speeds within the street are low. This tendency decreases the flux at high height-to-width ratios. These processes tend to reduce the flux density from the individual facets of the street canyon, when compared to the flux density from a horizontal surface of the same material. But the street canyon has an increased total surface area, which means that the total flux from the street canyon is larger than from a horizontal surface. The variations in scalar flux from an urban street canyon with geometry is over a factor of two, which means that the physical mechanisms responsible should be incorporated into energy balance models for urban areas.     

Mass Transfer Velocity and Momentum Vertical Exchange in Simulated Deep Street Canyons

A box model to simulate mass transfer inside deep street canyons and with atmospheric flow above is introduced and discussed. Two ideal deep street canyons with aspect ratios of 3 and 5 (the aspect ratio being the ratio between building height and street width H/W) are considered. This range of aspect ratios, found in many densely populated historical centres in Mediterranean cities as well as in other cities around the world, potentially creates high air pollutant concentration levels. Our model is based on a combination of analytical solutions and computation fluid dynamics (CFD) simulations using carbon monoxide (CO) as a tracer pollutant. The analytical part of the model is based on mass transfer velocity concepts while CFD simulations are used both for a preliminary validation of the physical hypothesis underlying the model (steady-state simulations) and to evaluate the concentration pattern with time (transient or wash-out simulations). Wash-out simulation curves were fitted by model curves, and mass transfer velocities were evaluated through a best-fitting procedure. Upon introducing into the model the contribution of traffic-produced turbulence, the modelled CO concentration levels became comparable with those obtained in real-world monitoring campaigns. The mass transfer rate between the canyon and the above atmosphere was then expressed in terms of an overall mass transfer velocity, which directly allows the evaluation of the mass transfer rate between the bottom volume of the canyon (pedestrian level) with the above atmosphere. Overall mass transfer velocities are reported as a function of the operating conditions studied (H/W = 3–5 and wind speeds = 2–8 ms⁻¹). Finally, a simple expression is reported for determining pollutant concentrations at the pedestrian level based on the overall mass transfer velocity defined.     

Large-Eddy Simulation of Pollutant Removal from a Three-Dimensional Street Canyon

Large-eddy simulations were conducted to investigate the mechanism of pollutant removal from a three-dimensional street canyon. Five block configurations with aspect ratios (building height to length) of 1, 2, 4, 8 and $\infty $ were used to create an urban-like array. A pollutant was released from a ground-level line source at the centre of the target canyon floor. For smaller aspect ratios, the relative contribution of the turbulent mass flux to net mass flux at the roof level, which was spatially averaged along the roof-level ventilation area, was closer to unity, indicating that turbulent motions mainly affected pollutant removal from the top of the canyon. As aspect ratio increased, the relative contribution became smaller, owing to strong upwind motions. However, the relative contribution again reached near unity for the infinite aspect ratio (i.e. a two-dimensional street canyon) because of lowered lateral flow convergence. At least 75 % of total emissions from the three-dimensional street canyon were attributable to turbulent motions. Pollutant removal by turbulent motions was related to the coherent structures of low-momentum fluid above the canyons. Though the coherent structure size of the low-momentum fluid differed, the positions of low-momentum fluid largely corresponded to instantaneous high concentrations of pollutant above the target canyon, irrespective of canyon geometry.     

Flow in a Street Canyon for any External Wind Direction

An analytical model has been developed for the flow along a street canyon (of height H and width W), generated by an external wind blowing at any angle relative to the axis of the street. Initially, we consider the special case of a wind blowing parallel to the street. The interior of the street is decomposed into three regions, and the flow within each region is assumed to depend only on the external wind and the distance to the closest solid boundary. This decomposition leads to two different flow regimes: one for narrow streets (H/W > 1/2) and one for wide streets (H/W < 1/2). The theoretical model agrees well with results obtained from numerical simulations using a Reynolds-Averaged Navier–Stokes model. We then generalize the model to the case of arbitrary wind direction. Numerical solutions show that the streamlines of the mean flow in the street have a spiral form, and for most angles of incidence, the mass flux along the street scales on the component of the external wind resolved parallel to the street. We use this result to generalize the model derived for wind blowing parallel to the street, and the results from this model agree well with the numerical simulations. The model that has been developed can be evaluated rapidly using only very modest computing power, so it is suitable for use as an operational tool.     

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.     

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

A validated large-eddy simulation model was employed to study the effect of the aspect ratio and ground heating on the flow and pollutant dispersion in urban street canyons. Three ground-heating intensities (neutral, weak and strong) were imposed in street canyons of aspect ratio 1, 2, and 0.5. The detailed patterns of flow, turbulence, temperature and pollutant transport were analyzed and compared. Significant changes of flow and scalar patterns were caused by ground heating in the street canyon of aspect ratio 2 and 0.5, while only the street canyon of aspect ratio 0.5 showed a change in flow regime (from wake interference flow to skimming flow). The street canyon of aspect ratio 1 does not show any significant change in the flow field. Ground heating generated strong mixing of heat and pollutant; the normalized temperature inside street canyons was approximately spatially uniform and somewhat insensitive to the aspect ratio and heating intensity. This study helps elucidate the combined effects of urban geometry and thermal stratification on the urban canyon flow and pollutant dispersion.     

Numerical estimation of the effective albedo of an urban canyon

Summary The paper focuses on the absorption of shortwave radiation in an urban street canyon. To test the effective albedo of the canyon an analytic solution of the multiple reflection problem is applied. The infinitesimally long canyon is divided into slices and a matrix of view factors for the slices is defined. Incoming shortwave radiation includes direct and diffuse parts and shadowing effects are included in the analysis. The model is validated against Aida’s (1982) scale model data and measurements in a real canyon. The results demonstrate a rapid decrease of the effective albedo as the canyon aspect ratio (its height to width, H/W) are increased. It is also shown that diurnal changes of the effective albedo can be very complex depending on the particular combination of H/W ratio, surface reflectivity and canyon orientation. Author’s address: Krzysztof Fortuniak, Department of Meteorology and Climatology, University of Łódź, Narutowicza 88, 09-139 Łódź, Poland.     

Flux Footprint Simulation Downwind of a Forest Edge

Surface fluxes, originating from forest patches, are commonly calculated from atmospheric flux measurements at some height above that patch using a correction for flux arising from upwind surfaces. Footprint models have been developed to calculate such a correction. These models commonly assume homogeneous turbulence, resulting in a simulated atmospheric flux equal to the average surface flux in the footprint area. However, atmospheric scalar fluxes downwind of a forest edge have been observed to exceed surface fluxes in the footprint area. Variations in atmospheric turbulence downwind of the forest edge, as simulated with an E – model, can explain enhanced atmospheric scalar fluxes. This E – model is used to calculate the footprint of atmospheric measurements downwind of a forest edge. Atmospheric fluxes appear mainly enhanced as a result of a stronger sensitivity to fluxes from the upwind surface. A sensitivity analysis shows that the fetch over forest, necessary to reach equilibrium between atmospheric fluxes and surface fluxes, tends to be longer for scalar fluxes as compared to momentum fluxes. With increasing forest density, atmospheric fluxes deviate even more strongly from surface fluxes, but over shorter fetches. It is concluded that scalar fluxes over forests are commonly affected by inhomogeneous turbulence over large fetches downwind of an edge. It is recommended to take horizontal variations in turbulence into account when the footprint is calculated for atmospheric flux measurements downwind of a forest edge. The spatially integrated footprint is recommended to describe the ratio between the atmospheric flux and the average surface flux in the footprint.     

Comprehensive Evaluation of Fast-Response,Reynolds-Averaged Navier–Stokes,and Large-Eddy Simulation Methods Against High-Spatial-Resolution Wind-Tunnel Data in Step-Down Street Canyons

Three computational fluid dynamics (CFD) methods with different levels of flow-physics modelling are comprehensively evaluated against high-spatial-resolution wind-tunnel velocity data from step-down street canyons (i.e., a short building downwind of a tall building). The first method is a semi-empirical fast-response approach using the Quick Urban Industrial Complex (QUIC-URB) model. The second method solves the Reynolds-averaged Navier–Stokes (RANS) equations, and the third one utilizes a fully-coupled fluid-structure interaction large-eddy simulation (LES) model with a grid-turbulence inflow generator. Unlike typical point-by-point evaluation comparisons, here the entire two-dimensional wind-tunnel dataset is used to evaluate the dynamics of dominant flow topological features in the street canyon. Each CFD method is scrutinized for several geometric configurations by varying the downwind-to-upwind building-height ratio (\(H_\mathrm{d}/H_\mathrm{u}\)) and street canyon-width to building-width aspect ratio (S / W) for inflow winds perpendicular to the upwind building front face. Disparities between the numerical results and experimental data are quantified in terms of their ability to capture flow topological features for different geometric configurations. Overall, all three methods qualitatively predict the primary flow topological features, including a saddle point and a primary vortex. However, the secondary flow topological features, namely an in-canyon separation point and secondary vortices, are only well represented by the LES method despite its failure for taller downwind building cases. Misrepresentation of flow-regime transitions, exaggeration of the coherence of recirculation zones and wake fields, and overestimation of downwards vertical velocity into the canyon are the main defects in QUIC-URB, RANS and LES results, respectively. All three methods underestimate the updrafts and, surprisingly, QUIC-URB outperforms RANS for the streamwise velocity component, while RANS is superior to QUIC-URB for the vertical velocity component in the street canyon.     

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.     

Experimental study of the transfer velocity for urban surfaces with a water evaporation method

A major problem in urban climate modelling is determining how the heat fluxes from various canyon surfaces are affected by canyon flow. To address this problem, we developed a water evaporation method involving filter paper to study the distribution of the convective transfer velocity in urban street canyons. In this method, filter paper is pasted onto a building model and the evaporation rate from the paper is measured with an electric balance. The method was tested on 2D (two-dimensional) street canyon models and 3D model arrangements. Moreover, in this technique, it is easy to restrict the flux within an arbitrary surface in question. That is, the evaporation distribution on a surface can be studied by using several small pieces of filter paper. In the 2D case, the wall transfer velocity was strongly dependent on the canyon aspect ratio for perpendicular wind directions and it varied widely with height within both windward and leeward wall surfaces. For 3D cubic arrays, the relation to canyon aspect ratio was largely different from that of the 2D canyon. And, as a case study, the variation of wind direction was investigated for a city-like setting. The area-averaged transfer velocity was insensitive to wind direction but its local deviation was significant. Finally, we measured the transfer velocity for a clustered block array surrounded by relatively wide streets. The effect of spatial heterogeneity on the transfer velocity was significant. Moreover, for a fixed total building volume, the transfer velocity was considerably larger when the building height varied than when it was uniform. Therefore, the water evaporation method with filter paper is expected to be useful for studying the transfer velocity and ventilation rates in urban areas with various canyon shapes.     

城市街谷几何结构对街谷内流场及污染物浓度场影响的数值模拟

利用数值模拟方法研究了微尺度街道峡谷范围内街谷几何结构及街道两侧建筑物高度对称性对街谷内流场及机动车排放污染物扩散规律的影响。结果表明:当街道峡谷高宽比>2.1时,街谷内的流场结构由一个完整的垂直涡旋变为上下两个反向运动的强弱不同的垂直涡旋。各类型街谷内污染物扩散水平从强到弱依次为迎风面建筑物高度大于背风面建筑物高度的街道峡谷,迎风面建筑物高度小于背风面建筑物高度的街道峡谷;平行型街道峡谷。     

Numerical Study on the Impact of Ground Heating and Ambient Wind Speed on Flow Fields in Street Canyons

The impact of ground heating on flow fields in street canyons under different ambient wind speed conditions was studied based on numerical methods.A series of numerical tests were performed,and three factors including height-to-width(H/W) ratio,ambient wind speed and ground heating intensity were taken into account.Three types of street canyon with H/W ratios of 0.5,1.0 and 2.0,respectively,were used in the simulation and seven speed values ranging from 0.0 to 3.0 m s 1 were set for the ambient wind speed.The ground heating intensity,which was defined as the difference between the ground temperature and air temperature,ranged from 10 to 40 K with an increase of 10 K in the tests.The results showed that under calm conditions,ground heating could induce circulation with a wind speed of around 1.0 m s 1,which is enough to disperse pollutants in a street canyon.It was also found that an ambient wind speed threshold may exist for street canyons with a fixed H/W ratio.When ambient wind speed was lower than the threshold identified in this study,the impact of the thermal effect on the flow field was obvious,and there existed a multi-vortex flow pattern in the street canyon.When the ambient wind speed was higher than the threshold,the circulation pattern was basically determined by dynamic effects.The tests on the impact of heating intensity showed that a higher ground heating intensity could strengthen the vortical flow within the street canyon,which would help improve pollutant diffusion capability in street canyons.     

Investigation of the Flow Structure in Step-Up Street Canyons—Mean Flow and Turbulence Statistics

A step-up street canyon is a characteristic urban element composed of two buildings in which the height of the upwind building ( $H_\mathrm{u}$ ) is less than the height of the downwind building ( $H_\mathrm{d}$ ). Here, the effect of canyon geometry on the flow structure in isolated step-up street canyons is investigated through isothermal wind-tunnel measurements. The measurements were acquired along the vertical symmetry plane of model buildings using two-dimensional particle image velocimetry (PIV) for normal approach flow. The building-height ratios considered were: $H_\mathrm{d}/ H_\mathrm{u} \approx 3$ , and $H_\mathrm{d}/ H_\mathrm{u} \approx 1.67$ . For each building-height ratio, the along-wind lengths (L) of the upwind and downwind buildings, and the street-canyon width (S) were kept constant, with $L \approx S$ . The cross-wind widths (W) of the upwind and downwind buildings were varied uniformly from $W/S \approx 1$ through $W/S \approx 4$ , in increments of $W/S \approx 1$ . The objective of the work was to characterize the changes in the flow structure in step-up canyons as a function of W/S, for fixed L, S, and $H_\mathrm{d}/H_\mathrm{u}$ values. The results indicate that the in-canyon flow structure does not vary significantly for $H_\mathrm{d}/H_\mathrm{u} \approx 3$ for the W/S values considered. Qualitatively, for $H_\mathrm{d}/H_\mathrm{u} \approx 3$ , the upwind building behaves as an obstacle in the upwind cavity of the downwind building. In contrast, the flow patterns observed for the $H_\mathrm{d}/H_\mathrm{u} \approx 1.67$ configurations are unique and counter-intuitive, and depend strongly on building width (W/S). For $W/S \approx 1$ and $W/S \approx 2$ , the effect of lateral flow into the canyon is so prominent that even the mean flow patterns are highly ambiguous. For $W/S \approx 3$ and 4, the flow along the vertical symmetry plane is more shielded from the lateral flow, and hence a stable counter-rotating vortex pair is observed in the canyon. In addition to these qualitative features, a quantitative analysis of the mean flow field and turbulence stress field is presented.     

An Improved Three-Dimensional Simulation of the Diurnally Varying Street-Canyon Flow

The impact of diurnal variations of the heat fluxes from building and ground surfaces on the fluid flow and air temperature distribution in street canyons is numerically investigated using the PArallelized Large-eddy Simulation Model (PALM). Simulations are performed for a 3 by 5 array of buildings with canyon aspect ratio of one for two clear summer days that differ in atmospheric instability. A detailed building energy model with a three-dimensional raster-type geometry—Temperature of Urban Facets Indoor-Outdoor Building Energy Simulator (TUF-IOBES)—provides urban surface heat fluxes as thermal boundary conditions for PALM. In vertical cross-sections at the centre of the spanwise canyon the mechanical forcing and the horizontal streamwise thermal forcing at roof level outweigh the thermal forces from the heated surfaces inside the canyon in defining the general flow pattern throughout the day. This results in a dominant canyon vortex with a persistent speed, centered at a constant height. Compared to neutral simulations, non-uniform heating of the urban canyon surfaces significantly modifies the pressure field and turbulence statistics in street canyons. Strong horizontal pressure gradients were detected in streamwise and spanwise canyons throughout the day, and which motivate larger turbulent velocity fluctuations in the horizontal directions rather than in the vertical direction. Canyon-averaged turbulent kinetic energy in all non-neutral simulations exhibits a diurnal cycle following the insolation on the ground in both spanwise and streamwise canyons, and it is larger when the canopy bottom surface is paved with darker materials and the ground surface temperature is higher as a result. Compared to uniformly distributed thermal forcing on urban surfaces, the present analysis shows that realistic non-uniform thermal forcing can result in complex local airflow patterns, as evident, for example, from the location of the vortices in horizontal planes in the spanwise canyon. This study shows the importance of three-dimensional simulations with detailed thermal boundary conditions to explore the heat and mass transport in an urban area.     

城市街道峡谷对称性对内部气流场的影响研究

应用雷诺应力湍流模型,模拟了不同高度比的城市街道峡谷的气流场。结果表明:峡谷的对称性对其内部气流场有显著影响。前高后低型峡谷下部为逆时针旋涡,上部为顺时针旋涡,峡谷越深,流场发展的越充分;峡谷内部墙面存在明显的驻点。前低后高型峡谷只存在一个大的顺时针旋涡,随着峡谷的加深,内部气流速率有减小的趋势;峡谷达到一定深度后出现驻点。对称型峡谷内部形成了顺时针旋涡,强度不大;随着峡谷的加深,内部流场转为一顺一反2个旋涡的二元结构;仅当峡谷很深时才出现明显驻点。前低后高型峡谷的气流场形式更有利于污染物的迁移、扩散,在城市规划中应尽量结合主导风向设计这类建筑布局。     

On the Impact of Trees on Dispersion Processes of Traffic Emissions in Street Canyons

Wind-tunnel studies of dispersion processes of traffic exhaust in urban street canyons with tree planting were performed and tracer gas concentrations using electron capture detection (ECD) and flow fields using laser Doppler velocimetry (LDV) were measured. It was found that tree planting reduces the air exchange between street canyons and the ambience. In comparison to treeless street canyons, higher overall pollutant concentrations and lower flow velocities were measured. In particular, for perpendicular approaching wind, markedly higher concentrations at the leeward canyon wall and slightly lower concentrations at the windward canyon wall were observed. Furthermore, a new approach is suggested to model porous vegetative structures such as tree crowns for small-scale wind-tunnel applications. The approach is based on creating different model tree crown porosities by incorporating a certain amount of wadding material into a specified volume. A significant influence of the crown porosity on pollutant concentrations was found for high degrees of porosity, however, when it falls below a certain threshold, no further changes in pollutant concentrations were observed.     

A model of airflow above changes in surface heat flux,temperature and roughness for neutral and unstable conditions

A numerical model of airflow in the lowest 50–100 m of the atmosphere above changes in surface roughness and temperature or heat flux has been developed based on boundary layer approximations, the Businger-Dyer hypotheses for the non-dimensional wind shear and heat flux and a mixing length hypothesis.Results have been obtained for several situations, in particular, airflow with neutral upstream conditions encountering a step change in surface temperature or heat flux with no roughness change. In these cases large increases in shear stress at the outer edge of the internal boundary layer are predicted. The case of unstable upstream flow encountering a step change to zero heat flux is also considered.Two situations that may be encountered near the shores of the Great Lakes are considered.Notation B Businger-Dyer constant (= 16.0) in form for _M, _H - c _p Specific heat at constant pressure - g Acceleration due to gravity - H Upward vertical heat flux - H ₀ , H ₁ Surface heat fluxes for x < 0, x 0 - k von Kármán's constant ( = 0.4) - l Mixing length - L Monin-Obukhov length - L ₀ Upstream value of L - m Ratio of roughness lengths (= z ₁/z ₀) - RL ^* Non-dimensional parameter, see Equations (20, 22 and 24) - RL ₁ ^* Same as RL ^* but with z ₁ scaling (= mRL ^*) - T Scaled temperature - T ₀ (z) Upstream temperature profile - u ₀, u ₁(x) Surface friction velocities for x < 0, x 0 - U, W Horizontal and vertical mean velocities - U ₀ (z) Upstream velocity profile - x, z Horizontal and vertical coordinates - z _i Local roughness length