Are Urban-Canopy Velocity Profiles Exponential?

Using analyses of data from extant direct numerical simulations and large-eddy simulations of boundary-layer and channel flows over and within urban-type canopies, sectional drag forces, Reynolds and dispersive shear stresses are examined for a range of roughness densities. Using the spatially-averaged mean velocity profiles these quantities allow deduction of the canopy mixing length and sectional drag coefficient. It is shown that the common assumptions about the behaviour of these quantities, needed to produce an analytical model for the canopy velocity profile, are usually invalid, in contrast to what is found in typical vegetative (e.g. forest) canopies. The consequence is that an exponential shape of the spatially-averaged mean velocity profile within the canopy cannot normally be expected, as indeed the data demonstrate. Nonetheless, recent canopy models that allow prediction of the roughness length appropriate for the inertial layer’s logarithmic profile above the canopy do not seem to depend crucially on their (invalid) assumption of an exponential profile within the canopy.     

Analytically Modelling Mean Wind and Stress Profiles in Canopies

An analytical model for mean wind profiles in sparse canopies (W. Wang, Boundary-Layer Meteorol 142:383–399, 2012) has been further developed, with (1) an explicit solution being derived, and (2) a linear term being added to the $K$ -closure scheme to improve the shear-stress parametrization when the contribution of non-local transport is significant. Results from large-eddy simulations and from laboratory experiments are used to evaluate the model and adjust model parameters, showing that the model can well simulate canopy wind and stress profiles not only for sparse-canopy scenarios, but also for dense-canopy scenarios. The analytical solution converges exactly to the standard surface-layer logarithmic wind profile in the case of zero canopy density, and tends to an exponential wind profile for a dense canopy.     

Study on a boundary-layer numerical model with inclusion of heterogeneous multi-layer vegetation

On the basis of improving the algorithm of the mixing length in and above forest canopies, a PBL numerical model including the multi-layer, heterogeneous vegetation is developed. Simulations indicate that different treatments of mixing length can make a great difference in the wind field especially for dense forest, and results from the improved mixing length scheme are in better agreement with observations than those from the original scheme. It may be expected that the improved mixing length scheme can lead to more ra-tional turbulent transfer than the original one. From the sensitivity experiments, we obtain the characteris-tics of both wind and temperature profiles in and above plant canopies, e.g., during the daytime, a stable thermal stratification exists near the surface in the canopies, but a neutral or slightly unstable condition ap-pears above plant canopies, while at night the reverse situations occur; the increase of the temperature of the dense-forest case is less than that of the sparse-forest case; the windspeed is reduced within the canopy lay-er and the large wind shear occurs near the treetop, etc.     

Study on a Boundary-layer Numerical Model with Inclusion of Heterogeneous Multi-layer Vegetational

1.IntroductionItiswellknownthattheecosystemcangreatlyinfluencebothlocalclimateandgeneralcirculation.Onthenumericalstudyoftheturbulenceinandaboveforestcanopies,alotofsignificantstudieshavebeendone.Inallthesestudies,modelsaregenerallydividedintotwotypes:oneis'K--theory'type(Waggoner,1975;Gross,1987;Gross,1988,Jietal.,1989;Schilling,I991;Dickinsonetal.,1993;Wang,1996),theotherappliesthehigher--orderclosuremethod(Wilsonetal.,1977,Yamada,1982;Yinetal.,1989)ortheLagrangianmethod(Rampach,1987;R…     

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.     

NUMERICAL SIMULATIONS OF TURBULENT FLOW IN AND ABOVE PLANT CANOPIES

The turbulent flow in and above plant canopies is of fundamental importance to the understanding oftransport processes of momentum,heat and mass between plant canopies and atmosphere,and to microme-teorology.The Reynolds stress equation model(RSM)has been applied to calculate the turbulence in cano-pies in this paper.The calculated mean wind velocity profiles,Reynolds stress,turbulent kinetic energy andviscous dissipation rate in a corn canopy and a spruce forest are compared with field observed data and withWilson's and Shaw's model.The velocity profiles and Rynolds stress calculated by both models are in goodagreement,and the length scale of turbulence appears to be similar.     

植被内部及其上方湍流场的数值模拟

植被内部及其上方的湍流流场对于了解植被与大气之间的动量、热量和质量交换过程极其重要。本文把高阶湍流封闭模型的Reynolds应力方程模型(RSM)应用于植被湍流的计算,得到了风速、湍流动能、Reynolds应力及能量耗散率的垂直分布,与现场观测数据比较,甚为满意。     

Study of near-surface models for large-eddy simulations of a neutrally stratified atmospheric boundary layer

In large-eddy simulations (LES) of the atmospheric boundary layer (ABL), near-surface models are often used to supplement subgrid-scale (SGS) turbulent stresses when a major fraction of the energetic scales within the surface layer cannot be resolved with the temporal and spatial resolution at hand. In this study, we investigate the performance of both dynamic and non-dynamic eddy viscosity models coupled with near-surface models in simulations of a neutrally stratified ABL. Two near-surface models that are commonly used in LES of the atmospheric boundary layer are considered. Additionally, a hybrid Reynolds- averaged/LES eddy viscosity model is presented, which uses Prandtl’s mixing length model in the vicinity of the surface, and blends in with the dynamic Smagorinsky model away from the surface. Present simulations show that significant portions of the modelled turbulent stresses are generated by the near-surface models, and they play a dominant role in capturing the expected logarithmic wind profile. Visualizations of the instantaneous vorticity field reveal that flow structures in the vicinity of the surface depend on the choice of the near-surface model. Among the three near-surface models studied, the hybrid eddy viscosity model gives the closest agreement with the logarithmic wind profile in the surface layer. It is also observed that high levels of resolved turbulence stresses can be maintained with the so-called canopy stress model while producing good agreement with the logarithmic wind profile.     

Analysis of canopy index values for various canopy densities

Canopy wind profiles can often be represented by an exponential function such that wind-speeds in these vegetative canopies are a function of height and the attenuation coefficient of this wind profile relationship. To be more precise, canopy flow is a function of canopy density, element flexibility, and height. An index of canopy flow, therefore, can be defined as a conservative measure of the gross flow response to the presence of various types of roughness elements. For this study, windspeed profile data of two quite different canopy density experiments — field and wind tunnel - have been analyzed based on least-square fittings. The results indicate that the two sets of index values of canopy flow behave in a similar manner with maxima occurring for optimum densities of one-third the potential full array of roughness elements. These index values also differ by some 0.2, but are still compatible when one accounts for the respective levels of turbulence within these dissimilar canopies.     

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.     

Simulation of Meteorological Fields Within and Above Urban and Rural Canopies with a Mesoscale Model

Accurate simulation of air quality at neighbourhood scales (on order of 1-km horizontal grid spacing) requires detailed meteorological fields inside the roughness sub-layer (RSL). Since the assumptions of the roughness approach, used by most of the mesoscale models, are unsatisfactory at this scale, a detailed urban and rural canopy parameterisation, called DA-SM2-U, is developed inside the Penn State/NCAR Mesoscale Model (MM5) to simulate the meteorological fields within and above the urban and rural canopies. DA-SM2-U uses the drag-force approach to represent the dynamic and turbulent effects of the buildings and vegetation, and a modified version of the soil model SM2-U, called SM2-U(3D), to represent the thermodynamic effects of the canopy elements. The turbulence length scale is also modified inside the canopies. SM2-U(3D) assesses the sensible and latent heat fluxes from rural and urban surfaces in each of the computational layers inside the canopies by considering the shadowing effect, the radiative trapping by the street canyons, and the storage heat flux by the artificial surfaces. DA-SM2-U is tested during one simulated day above the city of Philadelphia, U.S.A. It is shown that DA-SM2-U is capable of simulating the important features observed in the urban and rural RSL, as seen in the vertical profiles of the shear stress, turbulent kinetic energy budget components, eddy diffusivity, potential air temperature, and specific humidity. Within the canopies, DA-SM2-U simulates the decrease of the wind speed inside the dense canopies, the skirting of the flow around the canopy blocks, warmer air inside the vegetation canopy than above open areas during the night and conversely during the day, and constantly warmer air inside the urban canopy. The comparison with measurements shows that the surface air temperature above rural and urban areas is better simulated by DA-SM2-U than by the `standard version' of MM5.     

An Analytical Model for the Two-Scalar Covariance Budget Inside a Uniform Dense Canopy

The two-scalar covariance budget is significant within the canopy sublayer (CSL) given its role in modelling scalar flux budgets using higher-order closure principles and in estimating the segregation ratio for chemically reactive species. Despite its importance, an explicit expression describing how the two-scalar covariance is modified by inhomogeneity in the flow statistics and in the vertical variation in scalar emission or uptake rates within the canopy volume remains elusive even for passive scalars. To progress on a narrower version of this problem, an analytical solution to the two-scalar covariance budget in the CSL is proposed for the most idealized flow conditions: a stationary and planar homogeneous flow inside a uniform and dense canopy with a constant leaf area density distribution. The foliage emission (or uptake) source strengths are assumed to vary exponentially with depth while the forest floor emission is represented as a scalar flux. The analytical solution is a superposition of a homogeneous part that describes how the two-scalar covariance at the canopy top is transported and dissipated within the canopy volume, and an inhomogeneous part governed by local production mechanisms of the two-scalar covariance. The homogeneous part is primarily described by the canopy adjustment length scale, and the attenuation coefficients of the turbulent kinetic energy and the mean velocity. Conditions for which the vertical variation of the two-scalar covariance is controlled by the rapid attenuation in the mean velocity and turbulent kinetic energy profiles, vis-à-vis the vertical variation of the scalar source strength, are explicitly established. This model also demonstrates how dissimilarity in the emissions from the ground, even for the extreme binary case with one scalar turned ‘on’ and the other scalar turned ‘off’, modifies the vertical variation of the two-scalar covariance within the CSL. To assess its applicability to field conditions, the analytical model predictions were compared with observations made at two different forest types—a sparse pine forest at the Hyytiälä SMEAR II-station (in Finland) and a dense alpine hardwood forest at Lavarone (in Italy). While the model assumptions do not represent the precise canopy morphology, attenuation properties of the turbulent kinetic energy and the mean velocity, observed mixing length, and scalar source attenuation properties for these two forest types, good agreement was found between measured and modelled two scalar covariances for multiple scalars and for the triple moments at the Hyytiälä site.     

Mean and Turbulent Flow Statistics in a Trellised Agricultural Canopy

Flow physics is investigated in a two-dimensional trellised agricultural canopy to examine that architecture’s unique signature on turbulent transport. Analysis of meteorological data from an Oregon vineyard demonstrates that the canopy strongly influences the flow by channelling the mean flow into the vine-row direction regardless of the above-canopy wind direction. Additionally, other flow statistics in the canopy sub-layer show a dependance on the difference between the above-canopy wind direction and the vine-row direction. This includes an increase in the canopy displacement height and a decrease in the canopy-top shear length scale as the above-canopy flow rotates from row-parallel towards row-orthogonal. Distinct wind-direction-based variations are also observed in the components of the stress tensor, turbulent kinetic energy budget, and the energy spectra. Although spectral results suggest that sonic anemometry is insufficient for resolving all of the important scales of motion within the canopy, the energy spectra peaks still exhibit dependencies on the canopy and the wind direction. These variations demonstrate that the trellised-canopy’s effect on the flow during periods when the flow is row-aligned is similar to that seen by sparse canopies, and during periods when the flow is row-orthogonal, the effect is similar to that seen by dense canopies.     

Scalar Transport over Forested Hills

Numerical simulations of scalar transport in neutral flow over forested ridges are performed using both a 1.5-order mixing-length closure scheme and a large-eddy simulation. Such scalar transport (particularly of CO₂) has been a significant motivation for dynamical studies of forest canopy–atmosphere interactions. Results from the 1.5-order mixing-length simulations show that hills for which there is significant mean flow into and out of the canopy are more efficient at transporting scalars from the canopy to the boundary layer above. For the case with a source in the canopy this leads to lower mean concentrations of tracer within the canopy, although they can be very large horizontal variations over the hill. These variations are closed linked to flow separation and recirculation in the canopy and can lead to maximum concentrations near the separation point that exceed those over flat ground. Simple scaling arguments building on the analytical model of Finnigan and Belcher (Q J Roy Meteorol Soc 130:1–29, 2004) successfully predict the variations in scalar concentration near the canopy top over a range of hills. Interestingly this analysis suggests that variations in the components of the turbulent transport term, rather than advection, give rise to the leading order variations in scalar concentration. The scaling arguments provide a quantitative measure of the role of advection, and suggest that for smaller/steeper hills and deeper/sparser canopies advection will be more important. This agrees well with results from the numerical simulations. A large-eddy simulation is used to support the results from the mixing-length closure model and to allow more detailed investigation of the turbulent transport of scalars within and above the canopy. Scalar concentration profiles are very similar in both models, despite the fact that there are significant differences in the turbulent transport, highlighted by the strong variations in the turbulent Schmidt number both in the vertical and across the hill in the large-eddy simulation that are not represented in the mixing-length model.     

Aerodynamic roughness of vegetated surfaces

Available experimental results indicate that as the density of roughness elements over a horizontally homogeneous surface is varied, the roughness length, z ₀, varies in a manner that exhibits a maximum at intermediate density values. In an attempt to explain this behaviour, the available analytical solutions for the wind profile inside dense homogeneous canopies were reviewed. The review indicated that the variation of z ₀ with density depends on the interrelationship between the leaf density, a, and the mixing length, l. In view of this finding, a numerical model was devised based on a simple rule for constructing mixing-length profiles in the canopy. The rule states that the actual value of l is the maximum possible under the two constraints: l l _i and ¦dl/dz¦ k, where k is the von Karman constant and the intrinsic mixing length, l _i, is a function of the local internal structure of the canopy. The model which ensures a smooth transition from dense to thin canopy, was used to reproduce the observed maximum of z ₀. The model is also capable of handling vertically non-homogeneous canopies.     

Footprints and Fetches for Fluxes over Forest Canopies with Varying Structure and Density

A stochastic trajectory model was used to estimate scalar fluxfootprints in neutral stabilityfor canopies of varying leaf area distributions andleaf area indices. An analytical second-order closure model wasused to predict mean wind speed, second moments and the dissipationrate of turbulent kinetic energy within a forest canopy.The influence of source vertical profile on the flux footprint wasexamined. The fetch is longer for surface sourcesthan for sources at higher levels in the canopy. In order tomeasure all the flux components, and thus the total flux, with adesired accuracy, sources were located at the forest floor in thefootprint function estimation. The footprint functions werecalculated for five observation levels above the canopy top. Itwas found that at low observation heights both canopy density andcanopy structure affect the fetch. The higher abovethe canopy top the flux is measured, the more pronounced is the effectof the canopy structure. The forest fetch for flux measurements isstrongly dependent on the required accuracy: The 90% flux fetchis greater by a factor of two or more compared to the 75% fetch. Theupwind distance contributing 75% of flux is as large as 45 timesthe difference between canopy height and the observation heightabove the canopy top, being even larger for low observationlevels.     

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 .     

A wind tunnel study of air flow in waving wheat: Single-point velocity statistics

We analyse single-point velocity statistics obtained in a wind tunnel within and above a model of a waving wheat crop, consisting of nylon stalks 47 mm high and 0.25 mm wide in a square array with frontal area index 0.47. The variability of turbulence measurements in the wind tunnel is illustrated by using a set of 71 vertical traverses made in different locations, all in the horizontally-homogeneous (above-canopy) part of the boundary layer. Ensemble-averaged profiles of the statistical moments up to the fourth order and profiles of Eulerian length scales are presented and discussed. They are consistent with other similar experiments and reveal the existence of large-scale turbulent coherent structures in the flow. The drag coefficient in this canopy as well as in other reported experiments is shown to exhibit a characteristic height-dependency, for which we propose an interpretation. The velocity spectra are analysed in detail; within and just above the canopy, a scaling based on fixed length and velocity scales (canopy height and mean horizontal wind speed at canopy top) is proposed. Examination of the turbulent kinetic energy and shear stress budgets confirms the role of turbulent transport in the region around the canopy top, and indicates that pressure transport may be significant in both cases. The results obtained here show that near the top of the canopy, the turbulence properties are more reminiscent of a plane mixing layer than a wall boundary layer.     

Mean Winds Through an Inhomogeneous Urban Canopy

The mean flow within inhomogeneous urban areas is investigated using an urban canopy model. The urban canopy model provides a conceptual and computational tool for representing urban areas in a way suitable for parameterisation within numerical weather prediction and urban air quality models. Average aerodynamic properties of groups of buildings on a neighbourhood scale can be obtained in terms of the geometry and layout of the buildings. These canopy parameters then determine the spatially averaged mean wind speeds within the canopy as a whole. Using morphological data for real cities, computations are performed for representative sections of cities. Simulations are performed to study transitions between different urban neighbourhoods, such as residential areas and city centres. Such transitions are accompanied by changes in mean building density and building height. These are considered first in isolation, then in combination, and the generic effects of each type of change are identified. The simulation of winds through a selection of downtown Los Angeles is considered as an example. An increase in canopy density is usually associated with a decrease in the mean wind speed. The largest difference between mean winds in canopies of different densities occurs near ground level. Winds generally decrease upon encountering a taller canopy of the same density, but this effect may be reversed very near the ground, with possible speed-ups if the canopy is especially tall. In the vicinity of a transition there is an overshoot in the mean wind speed in the bottom part of the canopy. Mechanisms for these effects are discussed.