The Effects of Thermal Stratification on Clustering Properties of Canopy Turbulence

The intermittent structure of turbulence within the canopy sublayer (CSL) is sensitive to the presence of foliage and to the atmospheric stability regime. How much of this intermittency originates from amplitude variability or clustering properties remains a vexing research problem for CSL flows. Using a five-level set of measurements collected within a dense hardwood canopy, the clustering properties of CSL turbulence and their dependence on atmospheric stability are explored using the telegraphic approximation (TA). The binary structure of the TA removes any amplitude variability from turbulent excursions but retains their zero-crossing behaviour, and thereby isolating the role of clustering in intermittency. A relationship between the spectral exponents of the actual and the TA series is derived across a wide range of atmospheric stability regimes and for several flow variables. This relationship is shown to be consistent with a relationship derived for long-memory and monofractal processes such as fractional Brownian motion (fBm). Moreover, it is demonstrated that for the longitudinal and vertical velocity components, the vegetation does not appreciably alter fine-scale clustering but atmospheric stability does. Stable atmospheric stability conditions is characterized by more fine scale clustering when compared to other atmospheric stability regimes. For scalars, fine-scale clustering above the canopy is similar to its velocity counterpart but is significantly increased inside the canopy, especially under stable stratification. Using simplified scaling analysis, it is demonstrated that clustering is much more connected to space than to time within the CSL. When comparing intermittency for flow variables and their TA series, it is shown that for velocity, amplitude variations modulate intermittency for all stability regimes. However, amplitude variations play only a minor role in scalar intermittency. Within the crown region of the canopy, a ‘double regime’ emerges in the inter-pulse duration probability distributions not observed in classical turbulence studies away from boundaries. The double regime is characterized by a power-law distribution for shorter inter-pulse periods and a log-normal distribution for large inter-pulse periods. The co-existence of these two regimes is shown to be consistent with near-field/far-field scaling arguments. In the near-field, short inter-pulse periods are controlled by the source strength, while in the far-field long inter-pulse periods are less affected by the precise source strength details and more affected by the transport properties of the background turbulence.     

The Effects of Non-stationarity on the Clustering Properties of the Boundary-layer Vertical Wind Velocity

Non-stationarity is a common feature in geophysical flows, though it still remains an open question on how the non-stationarity of flow affects its statistical structure. Using the telegraph approximation (TA) method, we quantified how non-stationarity in the measured atmospheric turbulent vertical velocity time series affects its clustering properties—one of the two main components of intermittency in turbulence. We compare different TA results between stationary and non-stationary atmospheric turbulent vertical velocity records, and find that the non-stationary data possess different cluster and intermittency exponents from stationary data. The inter-pulse period of the non-stationary records takes a near power-law distribution while the inter-pulse period of the stationary records exhibits a stretched exponential distribution. These results suggest that non-stationarity of the underlying processes can affect the statistical structure of turbulence, especially the clustering properties.     

On the Prediction of the Kurtosis of Velocity Derivatives in a Turbulent Field

The prediction of the values of non-dimensional fourth-order moment (kurtosis) of the velocity derivative in a turbulent field is made under the assumption that the values of kurtosis depend on both the turbulence Reynolds number and the intermittency factor. The method consists of modeling a suitable probability density of the variable in a given turbulence Reynolds number and the intermittency factor. A crude model of the probability density function is derived, and the numerical calculations based on the model show excellent agreement with many of the experimental data. The analysis shows that the values of kurtosis depend strongly on the intermittency factor, and that depending on the value of the intermittency factor, it is entirely possible to have values of kurtosis as low as five in a flow with a turbulence Reynolds number of 5000.     

On the prediction of the kurtosis of velocity derivatives in a turbulent field

The prediction of the values of non-dimensional fourth-order moment (kurtosis) of the velocity derivative in a turbulent field is made under the assumption that the values of kurtosis depend on both the turbulence Reynolds number and the intermittency factor. The method consists of modeling a suitable probability density of the variable in a given turbulence Reynolds number and the intermittency factor. A crude model of the probability density function is derived, and the numerical calculations based on the model show excellent agreement with many of the experimental data. The analysis shows that the values of kurtosis depend strongly on the intermittency factor, and that depending on the value of the intermittency factor, it is entirely possible to have values of kurtosis as low as five in a flow with a turbulence Reynolds number of 5000.     

Turbulence in Sparse, Organized Vegetative Canopies: A Large-Eddy Simulation Study

A large-eddy simulation study was performed to characterize turbulence in sparse, row-oriented canopies. This was accomplished by simulating a set of heterogeneous row-oriented canopies with varying row vegetation density and spacing. To determine the effects of heterogeneity, results were compared to horizontally homogeneous canopies with an equivalent ‘effective’ leaf area index. By using a proper effective leaf area index, plane-averaged mean velocities and bulk scaling parameters contained only small errors when heterogeneity was ignored. However, many cases had significantly larger second- and third-order velocity moments in the presence of heterogeneity. Some heterogeneous canopies also contained dispersive fluxes in the lower canopy that were over 20 % as large as the turbulent flux. Impacts of heterogeneity were most pronounced in the cases of large row leaf area density and widely spaced rows. Despite the substantial amount of open space in the sparse canopies, vertical velocity skewness and quadrant-hole analysis indicated that the flow behaved predominantly as a canopy layer even though integral length scales at the canopy top no longer followed mixing-layer scaling. This was supported by the fact that similar composite-averaged coherent structures could be readily identified in both the heterogeneous and homogeneous canopies. Heterogeneity had an effect on coherent structures, in that structure detection events were most likely to occur just upwind of the vegetation rows. In simulations with large row spacing, these structures also penetrated deeper into the canopy when compared to the equivalent homogeneous canopy.     

Drag coefficients and turbulence spectra within three boreal forest canopies

Atmospheric turbulence was measured within a black spruce forest, a jack pine forest, and a trembling aspen forest, located in southeastern Manitoba, Canada. Drag coefficients (C _d ) varied little with height within the pine and aspen canopies, but showed some height dependence within the dense spruce canopy. A constant C _d of 0.15, with the measured momentum flux and velocity profiles, gave good estimates of leaf-area-index (LAI) profiles for the pine and aspen canopies, but underestimated LAI for the spruce canopy.Velocity spectra were scaled using the Eulerian integral time scales and showed a substantial inertial subrange above the canopies. In the bottom part of the canopies, the streamwise and cross-stream spectra showed rapid energy loss whereas the vertical spectra showed an apparent energy gain, in the region where the inertial subrange is expected. The temperature spectra showed an inertial subrange with the expected -2/3 slope at all heights. Cospectra of momentum and heat flux had slopes of about -1 in much of the inertial subrange. Possible mechanisms to explain some of the spectral features are discussed.     

Intensity of turbulence within canopies with simple and complex roughness elements

From a large group of both simple and complex canopies, the following properties have been identified. (1) For simple canopies (rice paddy, wheat field, larch tree plantation, and wind-tunnel wooden pegs), the intensity of turbulence was constant with height and decreased slowly above the vegetation. (2) For forests, wind-tunnel model trees and immature corn plants, the intensity of turbulence had a maximum in the main crown layer, a minimum in the trunk space and decreased gradually above the vegetation. (3) Seasonal variations of the turbulence intensities occurred in deciduous vegetation where the turbulence levels increased from the bare branch case to the leafy crown case. (4) In regard to thermal stability, the intensity of turbulence increased as the stability ratio decreased in a forest canopy. (5) Passage of larger-scale eddies and disturbances over or through the roughness elements produced high intensity levels both immediately above and below the canopy-air interface. (6) The intensity of turbulence increased as the density and structural complexity of the vegetation increased.     

Hilbert方法在大气边界层湍流特征分析中的有效性

介绍一种新的建立在经验模态分解(EMD)方法基础上的非线性、非平稳数据分析技术一Hilbert分析技术,并首次将其应用于大气边界层(PBL)湍流数据的分析,初步探讨了其在PBL湍流研究中的有效性.通过对城市与森林冠层上湍流资料的能量分布特征和统计平稳度进行分析、比较,结果表明:Hilbert谱分析能有效地对PBL湍流信号进行分析.它的边缘谱分析能够有效地探测PBL湍流信号的能量分布特征,统计平稳度分析也能有效地给出PBL湍流信号平稳性的定量化测量,这些将有助于建立合适的数据质量控制方法,以及对现有空气质量与扩散模式中扩散参数的计算加以改进.文中个例分析中,城市和森林冠层上空的湍流有一定相似性,湍流混合都比较充分,但森林冠层上湍流信号的能量更多地集中在大尺度湍涡,且扰动风速的高频部分具有更强的间歇性.对于相近高度的湍流信号来说,多数情况下,森林冠层上相同尺度的湍涡表现得比城市冠层上更不稳定,但湍涡的含能量要更低.     

Turbulence structure in a deciduous forest

Three-dimensional wind velocity components were measured at two levels above and at six levels within a fully-leafed deciduous forest. Greatest shear occurs in the upper 20% of the canopy, where over 70% of the foliage is concentrated. The turbulence structure inside the canopy is characterized as non-Gaussian, intermittant and highly turbulent. This feature is supported by large turbulence intensities, skewness and kurtosis values and by the large infrequent sweeps and ejections that dominate tangential momentum transfer. Considerable day/night differences were observed in the vertical profiles of the mean streamwise wind velocity and turbulence intensities since the stability of the nocturnal boundary layer dampens turbulence above and within the canopy.     

An Analytical Model for Mean Wind Profiles in Sparse Canopies

Existing analytical models for mean wind profiles within canopies are applicable only in dense canopy scenarios, where all momentum is absorbed by canopy elements and, hence, the effect of the ground on turbulent mixing is not important. Here, we propose a new analytical model that can simulate mean wind profiles within sparse canopies under neutral conditions. The model adopts a linearized canopy-drag parametrization and a first-order turbulence closure scheme taking into account the effects of both the ground and canopy elements on turbulent mixing. The resulting wind profile within a sparser canopy appears to be more like a logarithmic form, with the no-slip condition at the ground being satisfied. The analytical solution converges exactly to the standard surface-layer logarithmic wind profile in the case of zero canopy density (i.e., no-canopy scenario) and tends to be an exponential wind profile for a dense canopy; this feature is unique compared with existing analytical models for canopy wind profiles. Results from the new model are in good agreement with those from laboratory experiments and numerical simulations.     

The Influence of Local Stability on Heat and Momentum Transfer within Open Canopies

Eddy-covariance data have been analyzed to investigate the influence of local stability on heat transfer within open canopies. The flux–gradient relationship for heat is derived from the temperature variance equation, and the stability dependence of the flux–gradient relationship is examined and discussed. The results indicate that the strong stability dependence of the nondimensional standard deviation of temperature, and the small contributions of turbulent transport to the temperature variance, lead to a strong stability dependence of the nondimensional temperature gradient within open canopies. Quadrant analysis and hole size analysis were performed for momentum and heat fluxes in the subcanopy, and the results indicate that the contribution of each quadrant to the total flux depends on both the local stability and canopy depth. The intermittency of the turbulent flux does not show a clear dependence on local stability. As the contribution of ejections to the heat flux increases, the vertical flux of the temperature variance changes sign from negative to positive, leading to small temperature variance transport in unstable conditions. Multi-resolution analysis indicates that heat and momentum are transported with different dominant time scales in very unstable conditions, suggesting a different role of local buoyancy in heat and momentum transfer.     

Pseudo-wavelet analysis of turbulence patterns in three vegetation layers

Ramp patterns in scalar traces such as temperature are the signature of coherent structures. A pseudo-wavelet analysis technique was developed in which ideal saw-tooth patterns of varying size were used as basis functions and fitted to temperature and velocity data. Data recorded from three very different vegetation stands were examined in this study. It was found that the most probable structure duration for the forest canopy was in the range 35–40 s, for the orchard canopy it was 20–25 s and for the maize it was 15–20 s. When expressed in non-dimensional form, the structure duration probability distribution for the maize canopy was about a decade larger than for the forest canopy, with the orchard canopy intermediate. The mean eddy duration versus wind shear relation falls on a narrow band for all three canopies, indicating that wind shear at the canopy top is the determining factor for the scale of the coherent eddies. The inverse of duration and intermittency of coherent structures exhibits a tendency of independence from wind shear at higher wind shear values. Coherent structures transport heat in a more efficient way than do smaller scale, less coherent motions. In all the canopies, the heat flux fractions associated with coherent structures are at least 10% higher than the corresponding time fraction.     

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。     

A spectral and lag-correlation analysis of turbulence in a deciduous forest canopy

The processes influencing turbulence in a deciduous forest and the relevant length and time scales are investigated with spectral and cross-correlation analysis. Wind velocity power spectra were computed from three-dimensional wind velocity measurements made at six levels inside the plant canopy and at one level above the canopy. Velocity spectra measured within the plant canopy differ from those measured in the surface boundary layer. Noted features associated with the within-canopy turbulence spectra are: (a) power spectra measured in the canopy crown peak at higher wavenumbers than do those measured in the subcanopy trunkspace and above the canopy; (b) peak spectral values collapse to a relatively universal value when scaled according to a non-dimensional frequency comprised of the product of the natural frequency and the Eulerian time scale for vertical velocity; (c) at wavenumbers exceeding the spectral peak, the slopes of the power spectra are more negative than those observed in the surface boundary layer; (d) Eulerian length scales decrease with depth into the canopy crown, then increase with further depth into the canopy; (e) turbulent events below crown closure are more correlated with turbulent events above the canopy than are those occurring in the canopy crown; and (f) Taylor's frozen eddy hypothesis is not valid in a plant canopy. Interactions between plant elements and the mean wind and turbulence alter the processes that produce, transport and remove turbulent kinetic energy and account for the noted observations.     

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.     

Comparison of turbulence statistics within three boreal forest canopies

Three-dimensional sonic anemometers were used to measure velocities and temperatures within three natural boreal forest canopies. Vertical profiles of atmospheric turbulence statistics for a black spruce forest, a jack pine forest, and a trembling aspen forest, all located in southeastern Manitoba, were plotted and compared. The canopy structures were quite different, with total leaf-area indices of 2, 4 and 10, for the pine, aspen, and spruce forests, respectively.The profiles of the first and second moments differed among the canopies, where velocities decreased more rapidly in the top portions of the denser canopies. The velocity distributions were skewed and kurtotic within all canopies, and showed some differences among the canopies. Eulerian time scale profiles were generally similar among the canopies, and the vertical and streamwise time scale profiles were almost mirror images of each other. Eulerian length scale profiles showed some differences among canopies caused by differences in the velocity profiles. Ratios of vertical-to-horizontal time and length scales had a maximum in mid-canopy.Shear stress profiles were similar in the top parts of all canopies, and upward momentum fluxes were occasionally observed within the canopy trunk space. Countergradient heat fluxes were also observed sometimes. The countergradient fluxes and the skewed, kurtotic velocity distributions indicate the contribution of intermittent, large-scale eddies that are important for energy and mass transfer within canopies.     

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.     

A two-dimensional trajectory-simulation model for non-Gaussian,inhomogeneous turbulence within plant canopies

We report a two-dimensional (alongwind u, vertical w) trajectory-simulation model, consistent with Thomson's (1987) well-mixed criteria, that allows for the non-Gaussian turbulence typical of flow within a plant canopy. The effect of non-Gaussian turbulence was examined by formulating a non-Gaussian u, w joint probability density function (PDF) as the sum of two Gaussian joint-PDFs. The resultant PDF reproduced the desired means, variances, skewnesses, and kurtoses, and the correct covariance. In prediction of the location of maximum concentration downwind of a line source in homogeneous, slightly non-Gaussian turbulence, it proved advantageous to incorporate skewness and kurtosis. However, in the case of inhomogeneous, highly non-Gaussian turbulence, the addition of skewness and kurtosis in the model resulted in substantially worse agreement with measurements than the results of the model using Gaussian PDFs. This may be due to inaccuracy in our PDF formulation. Dispersion predictions from the model with Gaussian PDFs were generally not statistically different from measurements. These results indicate that a two-dimensional Gaussian trajectory-simulation approach is adequate to predict mean concentrations and fluxes resulting from sources within plant canopies.     

Turbulence in an almond orchard: Vertical variations in turbulent statistics

Three-dimensional wind velocity components were measured above and within a uniform almond orchard. Turbulent statistics associated with the turbulent flow inside the canopy are examined in detail. Turbulence in an almond orchard is characterized by relatively high turbulent intensities and large skewness and kurtosis values. These results indicate that the frequency distribution of wind velocity components is non-Gaussian. Conditional sampling of the turbulent measurements show that large, infrequent sweeps provide the predominant mechanism for tangential momentum stress in the canopy crown. Deep inside the canopy, a secondary wind maximum and small, but positive, tangential momentum stresses are observed.     

Large-Eddy Simulation of Flow Over a Vegetation-Like Canopy Modelled as Arrays of Bluff-Body Elements

Turbulent flow over a vegetation canopy under neutral atmospheric conditions is investigated using large-eddy simulation. Each model tree, which consists of a sphere-shaped tree crown and a cylindrical trunk, is fully resolved. The resulting turbulence statistics and the drag force on the vegetation agree well with measurements from the corresponding wind-tunnel experiment described by Böhm et al. (Boundary-Layer Meteorol, 146:393–419, 2013). Statistically, this kind of model canopy exhibits both vegetation and bluff-body-flow characteristics. The time-averaged flow skims over the top of the underlying canopy, forming a low-momentum recirculation zone on the lee-side of the bluff elements, which causes significant dispersive stress within the canopy layer. Two other numerical representations of vegetation canopies, referred to as the drag-element and drag-crown approaches, have also been developed to assess the performance of simulations. Turbulence statistics suggest that the canopy shear layer interferes with wakes behind stems and crowns. The drag-crown approach yields better agreement between numerical results and experimental measurements than does the traditional drag-element approach, thus providing a promising numerical model for simulating canopy turbulence.