Turbulence Structure Within and Above a Canopy of Bluff Elements

Measurements of turbulence structure in a wind-tunnel model canopy of bluff elements show many of the features associated with vegetation canopies and roughness sublayers but also display features more characteristic of the inertial sublayer (ISL). Points of similarity include the existence of an inflexion point in the space-time averaged streamwise velocity at the canopy top, the variation with height of turbulent second moments and the departure of the turbulent kinetic energy budget from local equilibrium in and just above the canopy. Quadrant analysis shows characteristic dominance of sweep over ejection events within the canopy although sweeps are more frequent than usually seen in vegetation canopies. Points of difference are a u′, w′ correlation coefficient that is closer to the ISL value than to most canopy data, and a turbulent Prandtl number midway between canopy and ISL values. Within the canopy there is distinct spatial partitioning into two flow regimes, the wake and non-wake regions. Both time-mean and conditional statistics take different values in these different regions of the canopy flow. We explain many of these features by appealing to a modified version of the mixing-layer hypothesis that links the dominant turbulent eddies to the instability of the inflexion point at canopy top. However, it is evident that these eddies are perturbed by the quasi-coherent wakes of the bluff canopy elements. Based upon an equation for the instantaneous velocity perturbation, we propose a criterion for deciding when the eddies linked to the inflexion point will dominate flow structure and when that structure will be replaced by an array of superimposed element wakes. In particular, we show that the resemblance of some features of the flow to the ISL does not mean that ISL dynamics operate within bluff-body canopies in any sense.     

The Spatial Variability of Turbulence above a Forest

Summary The spatial variability of turbulence above a forest has been examined. Two measurement towers were erected 800 m apart within a heterogeneous mixed forest located in the north east of the Netherlands. The measurements of u ^* /u were analysed and subsequently used to test a surface layer model. The model simulated the magnitude of the measurements reasonably well, but measured trends were not always reproduced by the model. The variable (du/dz)/u did not adapt as quickly to the new surface as u ^* /u. This is in agreement with Schmid (1994), and can be explained by a local decrease in mixing length. It is recommended to adapt the mixing length near a surface transition to improve the accuracy of surface layer models of heterogeneous landscapes. Received September 8, 1997 Revised April 15, 1998     

Turbulence Spectra And Dissipation Rates Above And Within A Forest Canopy

Three velocity componentsand temperature were measured usingthree-dimensional sonic anemometers/thermometers attwo levels, above and within a forest canopy, in theChangbai Mountains of northeast China. Turbulencespectral structure, local isotropy anddissipation rates above and within the forest canopywere calculated using the eddy correlation method.Results show that the normalized turbulent spectralcurves have -2/3 slopes in the inertial subrange.While the shapes of the spectra are in good agreementwith the Kansas flat terrain results, the atmosphericturbulence is anisotropic above the forest canopy. Dueto breaking down of large eddies by the foliage,branches and trunks, the spectral peak frequencies forvelocity and temperature are higher withinthan above the forest canopy. Compared withmeasurements from previous studies over flat terrain,the velocity and temperature spectra above andinside the forest canopy appear to shift toward higherfrequencies. The turbulence is approximately isotropicin the inertial subrange within the forest canopy, and isanisotropic above the forest canopy. The turbulentkinetic energy and heat energy dissipation rates aboveand inside the forest canopy are much larger thanthose obtained by Kaimal and Hogstrom over grasslandand grazing land. The distinct features in the resultsof the present experiment may be attributed to thedynamic forcing caused by the rough surface of the forestcanopy.     

Effects of Fetch on Turbulent Flow and Pollutant Dispersion Within a Cubical Canopy

The effects of fetch on turbulent flow and pollutant dispersion within a canopy formed by regularly-spaced cubical objects is investigated using large-eddy simulation. Six tracer gases are simultaneously released from a ground-level continuous pollutant line source placed parallel to the spanwise axis at the first, second, third, fifth, seventh and tenth rows. Beyond the seventh row, the standard deviations of the fluctuations in the velocity components and the Reynolds shear stresses reach nearly equivalent states. Low-frequency turbulent flow is generated near the bottom surface around the first row and develops as the fetch increases. The turbulent flow eventually passes through the canopy at a near-constant interval. The mean concentration within the canopy reaches a near-constant value beyond the seventh row. In the first and second rows, narrow coherent structures frequently affect the pollutant escape from the top of the canopy. These structures increase in width as the fetch increases, and they mainly affect the removal of pollutants from the canopy.     

Improving a Two-Equation Turbulence Model for Canopy Flows Using Large-Eddy Simulation

Large-eddy simulations of the neutrally-stratified flow over an extended homogeneous forest were used to calibrate a canopy model for the Reynolds-averaged Navier–Stokes (RaNS) method with the $k-\varepsilon $ k - ε turbulence model. It was found that, when modelling the forest as a porous medium, the canopy drag dissipates the turbulent kinetic energy (acts as a sink term). The proposed model was then tested in more complex flows: a finite length forest and a forested hill. In the finite length forest, the destruction of the turbulent kinetic energy by the canopy was overestimated near the edge, for a length approximately twice the tree height. In the forested hill, the model was less accurate inside the recirculation zone and overestimated the turbulent kinetic energy, due to an incorrect prediction of the production term. Nevertheless, the canopy model presented here provided consistent results in both a priori and a posteriori tests and improved the accuracy of RaNS simulations with the $k-\varepsilon $ k - ε model.     

Canopy Architecture and Turbulence Structure in a Coniferous Forest

Synchronous sonic anemometric measurements at five heightswithin a mixed coniferous forest were used to test two different parameterisations ofcanopy architecture in the application of a second-order turbulence closure model. Inthe computation of the leaf drag area, the aerodynamic sheltering was replaced with anarchitectural sheltering, assumed to be analogous to the clumping index defined in radiativetransfer theory. Consequently, the ratio of leaf area density and sheltering factor was approximatedby the effective leaf area or the mean contact number, both obtained from the inversion of non-destructive optical measurements. The first parameter represents the equivalentrandomly dispersed leaf area in terms of shading, the second is the average number of leavesthat a straight line intercepts penetrating the canopy with a certain zenith angle. Theselection of this direction was determined by the analysis of the mean angle of the wind vectorduring sweep events. The drag coefficient values obtained from the inversion of themomentum flux equation, using the two proposed parameterisations, are in good agreement withvalues found in the literature. The predicted profiles of turbulence statistics reasonablymatch actual measurements, especially in the case of the mean contact numberparameterisation. The vertical profile of leaf drag area, obtained by forcing the turbulence modelto match the observed standard deviation of vertical velocity (_w), is intermediatebetween the two empirical ones. Finally, the proposed canopy parameterisations were appliedto a Lagrangian transport model to predict vertical profiles of air temperature, H₂O andCO₂ concentration.     

植被冠层湍流代数应力模式

从植被冠层湍流时空平均雷诺应力方程出发，根据植被冠层内有关参数化的准则，建立了湍流代数应力模式，并用玉米和小麦两种作物地的实测资料对模式进行了验证。     

Turbulence in a Katabatic Flow

Turbulence measurements performed in a stable boundary layer over the sloping ice surface of the Vatnajökull in Iceland are described. The boundary layer, in which katabatic forces are stronger than the large-scale forces, has a structure that closely resembles that of a stable boundary layer overlying a flat land surface, although there are some important differences. In order to compare the two situations the set-up of the instruments on an ice cap in Iceland was reproduced on a flat grass surface at Cabauw, the Netherlands. Wind speed and temperature gradients were calculated and combined with flux measurements made with a sonic anemometer in order to obtain the local stability functions _m and _h as a function of the local stability parameter z/L. Unlike the situation at Cabauw, where _m was linear as a function of z/L, in the katabatically forced boundary layer, the dependence of _m on stability was found to be non-linear and related to the height of the wind maximum. Thermal stratification and the depth of the stable boundary layer however seem to be rather similar under these two different forcing conditions.Furthermore, measurements on the ice were used to construct the energy balance. These showed good agreement between observed melt and components contributing to the energy balance: net radiation (supplying 55% of the energy), sensible heat flux (30%) and latent heat flux (15%).Local sources and sinks in the turbulent kinetic energy budget are summed and indicate a reasonable balance in near-neutral conditions but not in more stable situations. The standard deviation of the velocity fluctuations _u, _v, and _w, can be scaled satisfactorily with the local friction velocity u_* and the standard deviation of the temperature fluctuation with the local temperature scale _*.     

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

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

城市冠层中湍流运动的统计特征

对１９９７ 年夏天和冬天北京湍流运动的各种统计特征量进行了初步的统计分析。结果表明,城市冠层中湍流运动的各种统计特征量与平坦下垫面条件下边界层湍流运动的相比, 有不同的地方也有相似的地方; 无论白天还是夜晚, 垂直方向的湍流强度和湍流脉动风速标准差均小于水平方向的, 水平方向的相应湍流特征量则总是接近相等; 城市冠层中湍流脉动强度和标准差几乎均大于平坦下垫面边界层的; 平均风速ｕ≥１ ｍ ／ｓ 时的湍流统计特征量与ｕ＜ １ ｍ ／ｓ 时的有所不同; 城市冠层的阻力系数较大, 可达００６２５,Ｐａｎｏｆｓｋｙ 等提出的公式σｗ ／ｕ＊ ＝ １３ （１－ ３ｚ／Ｌ）１／３在城市冠层中并不适用。     

Spatial Variability of Flow Statistics within Regular Building Arrays

Turbulence statistics obtained by direct numerical simulations are analysed to investigate spatial heterogeneity within regular arrays of building-like cubical obstacles. Two different array layouts are studied, staggered and square, both at a packing density of . The flow statistics analysed are mean streamwise velocity (), shear stress (), turbulent kinetic energy (k) and dispersive stress fraction (). The spatial flow patterns and spatial distribution of these statistics in the two arrays are found to be very different. Local regions of high spatial variability are identified. The overall spatial variances of the statistics are shown to be generally very significant in comparison with their spatial averages within the arrays. Above the arrays the spatial variances as well as dispersive stresses decay rapidly to zero. The heterogeneity is explored further by separately considering six different flow regimes identified within the arrays, described here as: channelling region, constricted region, intersection region, building wake region, canyon region and front-recirculation region. It is found that the flow in the first three regions is relatively homogeneous, but that spatial variances in the latter three regions are large, especially in the building wake and canyon regions. The implication is that, in general, the flow immediately behind (and, to a lesser extent, in front of) a building is much more heterogeneous than elsewhere, even in the relatively dense arrays considered here. Most of the dispersive stress is concentrated in these regions. Considering the experimental difficulties of obtaining enough point measurements to form a representative spatial average, the error incurred by degrading the sampling resolution is investigated. It is found that a good estimate for both area and line averages can be obtained using a relatively small number of strategically located sampling points.     

Development and Validation of a Lagrangian Probability Density Function Model of Horizontally-Homogeneous Turbulence Within and Above Plant Canopies

Second- and third-order turbulence closure models have met with mixed success when applied to the prediction of turbulent flows within and above plant canopies and model predictions are typically no better than those obtained using simpler two-equation (k-e){(k-\varepsilon)} models. This is because the local gradient diffusion approximation (a crucial model requirement) cannot represent accurately turbulent transport that is dominated by the presence of ejections and sweeps whose length scales are comparable with the canopy height. To make progress, turbulent transport must be treated without approximation, as in Lagrangian probability density function (PDF) models. This study is the first to develop and to validate a PDF model of horizontally-homogeneous canopy flow. The model relies upon a prescribed length-scale that has been used elsewhere in the modelling of turbulent flows. Model predictions compare favourably with measurements of neutrally stratified turbulent flows within and above canopies of mature corn and forested eucalypt trees.     

Comparing Two Implementations of a Micromixing Model. Part II: Canopy Flow

The sequential particle micromixing model (SPMMM) is used to estimate concentration fluctuations in plumes dispersing into a canopy flow. SPMMM uses the familiar single-particle Lagrangian stochastic (LS) trajectory framework to pre-calculate the required conditional mean concentrations, which are then used by an interaction by exchange with the conditional mean (IECM) micromixing model to predict the higher-order fluctuations of the scalar concentration field. The predictions are compared with experimental wind-tunnel dispersion data for a neutrally stratified canopy flow, and with a previously reported implementation using simultaneous particle trajectories. The two implementations of the LS–IECM model are shown to be largely consistent with one another and are able to simulate dispersion in a canopy flow with fair to good accuracy.     

Numerical Simulation of Flow over Two-Dimensional Hills Using a Second-Order Turbulence Closure Model

We study turbulent flow over two-dimensional hills. The Reynolds stresses are represented by a second-order closure model, where advection, diffusion, production and dissipation processes are all accounted for. We solve a full set of primitive non-hydrostatic dynamic equations for mean flow quantities using a finite-difference numerical method. The model predictions for the mean velocity and Reynolds stresses are compared with the measured data from a wind-tunnel experiment that simulates the atmospheric boundary layer. The agreement is good. The performance of the second-order closure model is also compared withthat of lower level turbulence models, including the eddy-viscositymodel and algebraic Reynolds stress models. It is concluded that thepresent closure is a considerable improvement over the other modelsin representing various physical effects in flow over hills. Thefeasibility of running a finite-difference numerical simulationincorporating a full second-order closure model on an IBM workstationis also demonstrated.     

Temperature Profiles Within and Above an Urban Canopy

The seasonal trend of vertical temperature profiles within and above an urban canopy has been investigated. We measured air temperatures and wind velocities along a 29-m tower in a residential area of Tokyo, Japan continually for 14 months. The height of the daily maximum temperature Z_Tmax varied with the season; Z_Tmax was at the roof level in winter but near the ground in summer. The seasonal change of Z_Tmax is likely due to the change of height at which solar energy is absorbed. At the time of the maximum temperature, the atmosphere above the canopy is always unstable whereas the air within the canopy is unstable in summer but stable in winter.