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.     

A Modulated-Gradient Parametrization for the Large-Eddy Simulation of the Atmospheric Boundary Layer Using the Weather Research and Forecasting Model

The performance of the modulated-gradient subgrid-scale (SGS) model is investigated using large-eddy simulation (LES) of the neutral atmospheric boundary layer within the weather research and forecasting model. Since the model includes a finite-difference scheme for spatial derivatives, the discretization errors may affect the simulation results. We focus here on understanding the effects of finite-difference schemes on the momentum balance and the mean velocity distribution, and the requirement (or not) of the ad hoc canopy model. We find that, unlike the Smagorinsky and turbulent kinetic energy (TKE) models, the calculated mean velocity and vertical shear using the modulated-gradient model, are in good agreement with Monin–Obukhov similarity theory, without the need for an extra near-wall canopy model. The structure of the near-wall turbulent eddies is better resolved using the modulated-gradient model in comparison with the classical Smagorinsky and TKE models, which are too dissipative and yield unrealistic smoothing of the smallest resolved scales. Moreover, the SGS fluxes obtained from the modulated-gradient model are much smaller near the wall in comparison with those obtained from the regular Smagorinsky and TKE models. The apparent inability of the LES model in reproducing the mean streamwise component of the momentum balance using the total (resolved plus SGS) stress near the surface is probably due to the effect of the discretization errors, which can be calculated a posteriori using the Taylor-series expansion of the resolved velocity field. Overall, we demonstrate that the modulated-gradient model is less dissipative and yields more accurate results in comparison with the classical Smagorinsky model, with similar computational costs.     

Some Basic Properties of the Surrogate Subgrid-Scale Heat Flux in the Atmospheric Boundary Layer

The development of improved subgrid-scale (SGS) models for large-eddy simulation of scalar transport in the atmospheric boundary layer requires an improved understanding of basic properties of the SGS fluxes. High frequency atmospheric wind speed and temperature data sampled at a height of 1.7 m are used to measure SGS heat fluxes and dissipation of temperature variance, by means of one-dimensional filtering and invoking Taylor's hypothesis. Conditional averaging is used to isolate interesting features of the SGS signals, and to relate them to the large-scale characteristics of the flow, such as the presence of coherent structures. Both mean and conditionally averaged SGS quantities are compared with those obtained using a standard eddy-diffusivity model. Within the limitations imposed by the one-dimensional data analysis, we observe that the model appears unable to reproduce important features of the real signals, such as the negative dissipation of temperature variance associated with strong negative resolved temperature gradients due to the ejection of warm air under unstable atmospheric stability conditions.     

A Linear Analysis of the Interaction Between the Atmosphere and an Underlying Compliant Plant Canopy

We summarise the results of a theoretical investigation of the interaction between the lower atmosphere and a compliant plant canopy. In this investigation, plant collisions were modelled as simple spring or dashpot interactions between adjacent plants. Linearised canopy models show that dashpot collisions and spring collisions are effective at reducing the amplitude of a canopy’s response to wind forcing, and may thus serve to stabilise plants against lodging and windthrow. Both types of collisions can also induce shifts in the stand resonance frequency and may thus serve to stabilise stands even further by shifting the canopy resonance frequency away from the most energetic frequencies in the atmospheric power spectrum. We also include a linear analysis of the shear layer instability over a waving canopy, and show that canopy drag has a strong effect on the instability. However, stem stiffness and inter-plant collisions have only minor effects on the wavenumber, growth rate, and frequency of the most unstable wave.     

Large-Eddy Simulation of Wind-Turbine Wakes: Evaluation of Turbine Parametrisations

Large-eddy simulation (LES), coupled with a wind-turbine model, is used to investigate the characteristics of a wind-turbine wake in a neutral turbulent boundary-layer flow. The tuning-free Lagrangian scale-dependent dynamic subgrid-scale (SGS) model is used for the parametrisation of the SGS stresses. The turbine-induced forces (e.g., thrust, lift and drag) are parametrised using two models: (a) the ‘standard’ actuator-disk model (ADM-NR), which calculates only the thrust force and distributes it uniformly over the rotor area; and (b) the actuator-disk model with rotation (ADM-R), which uses the blade-element theory to calculate the lift and drag forces (that produce both thrust and rotation), and distribute them over the rotor disk based on the local blade and flow characteristics. Simulation results are compared to high-resolution measurements collected with hot-wire anemometry in the wake of a miniature wind turbine at the St. Anthony Falls Laboratory atmospheric boundary-layer wind tunnel. In general, the characteristics of the wakes simulated with the proposed LES framework are in good agreement with the measurements in the far-wake region. The ADM-R yields improved predictions compared with the ADM-NR in the near-wake region, where including turbine-induced flow rotation and accounting for the non-uniformity of the turbine-induced forces appear to be important. Our results also show that the Lagrangian scale-dependent dynamic SGS model is able to account, without any tuning, for the effects of local shear and flow anisotropy on the distribution of the SGS model coefficient.     

Urban Dispersion Modelling and Experiments in the Daytime and Nighttime Atmosphere

An analytical model of atmospheric dispersion in urban areas in both daytime and nighttime conditions is presented. The model is based on a Gaussian formulation where the horizontal and vertical diffusion coefficients are determined according to analytical theories. The model is validated with dispersion measurements from field experiments conducted in Oklahoma City, Salt Lake City, St. Louis and London, U.K. The theory is in good agreement with the data for both daytime and nighttime conditions. The data support the conclusion that the magnitude of the nighttime stratification in the urban atmosphere is weak; however, its effects on dispersion are not negligible. The predicted existence of two distinct dispersion regimes, in the near and in the far field, is also confirmed by the data. The good collapse of the data suggests that urban dispersion is governed by the characteristic length scales of atmospheric boundary-layer turbulence, rather than urban canopy length scales that are more likely to affect dispersion only in the vicinity of the source.     

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 Effect of Vegetation Density on Canopy Sub-Layer Turbulence

The canonical form of atmospheric flows near theland surface, in the absence of a canopy, resembles a rough-wallboundary layer. However, in the presence of an extensive and densecanopy, the flow within and just above the foliage behaves as aperturbed mixing layer. To date, no analogous formulation existsfor intermediate canopy densities. Using detailed laser Dopplervelocity measurements conducted in an open channel over a widerange of canopy densities, a phenomenological model that describesthe structure of turbulence within the canopy sublayer (CSL) isdeveloped. The model decomposes the space within the CSL intothree distinct zones: the deep zone in which the flow field isshown to be dominated by vortices connected with vonKármán vortex streets, butperiodically interrupted by strong sweep events whose features areinfluenced by canopy density. The second zone, which is near thecanopy top, is a superposition of attached eddies andKelvin–Helmholtz waves produced by inflectional instability in themean longitudinal velocity profile. Here, the relative importanceof the mixing layer and attached eddies are shown to vary withcanopy density through a coefficient . We show that therelative enhancement of turbulent diffusivity over its surface-layer value near the canopy top depends on the magnitude of. In the uppermost zone, the flow follows the classicalsurface-layer similarity theory. Finally, we demonstrate that thecombination of this newly proposed length scale and first-orderclosure models can accurately reproduce measured mean velocity andReynolds stresses for a wide range of roughness densities. Withrecent advancement in remote sensing of canopy morphology, thismodel offers a promising physically based approach to connect theland surface and the atmosphere without resorting to empiricalmomentum roughness lengths.     

On the flow structure and turbulence during sweep and ejection events in a wind-tunnel model canopy

Particle image velocimetry (PIV) data obtained in a wind-tunnel model of a canopy boundary layer is used to examine the characteristics of mean flow and turbulence. The vector spacing varies between 1.7 and 2.5 times the Kolmogorov scales. Conditional sampling based on quadrants, i.e. based on the signs of velocity fluctuations, reveals fundamental differences in flow structure, especially between sweep and ejection events, which dominate the flow. During sweeps, the downward flow generates a narrow, highly turbulent, shear layer containing multiple small-scale vortices just below canopy height. During ejections, the upward flow expands this shear layer and the associated small-scale flow structures to a broad region located above the canopy. Consequently, during sweeps the turbulent kinetic energy (TKE), Reynolds stresses, as well as production and dissipation rates, have distinct narrow peaks just below canopy height, whereas during ejections these variables have broad maxima well above the canopy. Three methods to estimate the dissipation rate are compared, including spectral fits, measured subgrid-scale (SGS) energy fluxes at different scales, and direct measurements of slightly underresolved instantaneous velocity gradients. The SGS energy flux is 40–60% of the gradient-based (direct) estimates for filter sizes inside the inertial range, while decreasing with scale, as expected, within the dissipation range. The spectral fits are within 5–30% of the direct estimates. The spectral fits exceed the direct estimates near canopy height, but are lower well above and below canopy height. The dissipation rate below canopy height increases with velocity magnitude, i.e. it has the highest values during sweep and quadrant 1 events, and is significantly lower during ejection and quadrant 3 events. Well above the canopy, ejections are the most dissipative. Turbulent transport during sweep events acts as a source below the narrow shear layer within the canopy and as a sink above it. Transport during ejection events is a source only well above the canopy. The residual term in the TKE transport equation, representing mostly the effect of pressure–velocity correlations, is substantial only within the canopy, and is dominated by sweeps.     

Numerical Simulation Experiment of Land Surface Physical Processes and Local Climate Effect in Forest Underlying Surface

Based on the basic principles of atmospheric boundary layer and plant canopy micrometeorology, a forest underlying surface land surface physical process model and a two-dimensional atmospheric boundary layer numerical model are developed and numerical simulation experiments of biosphere and physiological processes of vegetation and soil volumetric water content have been done on land surface processes with local climate effect. The numerical simulation results are in good agreement with realistic observations, which can be used to obtain reasonable simulations for diurnal variations of canopy temperature, air temperature in canopy, ground surface temperature, and temporal and spatial distributions of potential temperature and vertical wind velocity as well as relative humidity and turbulence exchange coefficient over non-homogeneous underlying surfaces. It indicates that the model developed can be used to study the interaction between land surface process and atmospheric boundary layer over various underlying surfaces and can be extended to local climate studies. This work will settle a solid foundation for coupling climate models with the biosphere.     

大气边界层动力学和植被生态过程耦合的一个简单解析理论

发展了一个大气边界层动力学和植被某些生态过程相互作用的简单模式,求得了这个耦合模式的解析解,分析了植被反照率和冠层阻抗(气孔阻力)对大气运动及植被温度的影响,这一相互作用的方式可为进一步发展大气运动和生态过程相互作用的、更复杂的数值模拟模式提供参考.     

A Velocity–Dissipation Lagrangian Stochastic Model for Turbulent Dispersion in Atmospheric Boundary-Layer and Canopy Flows

An extended Lagrangian stochastic dispersion model that includes time variations of the turbulent kinetic energy dissipation rate is proposed. The instantaneous dissipation rate is described by a log-normal distribution to account for rare and intense bursts of dissipation occurring over short durations. This behaviour of the instantaneous dissipation rate is consistent with field measurements inside a pine forest and with published dissipation rate measurements in the atmospheric surface layer. The extended model is also shown to satisfy the well-mixed condition even for the highly inhomogeneous case of canopy flow. Application of this model to atmospheric boundary-layer and canopy flows reveals two types of motion that cannot be predicted by conventional dispersion models: a strong sweeping motion of particles towards the ground, and strong intermittent ejections of particles from the surface or canopy layer, which allows these particles to escape low-velocity regions to a high-velocity zone in the free air above. This ejective phenomenon increases the probability of marked fluid particles to reach far regions, creating a heavy tail in the mean concentration far from the scalar source.     

复杂构型涡旋能量频散波列的形成过程

能量频散是一个基础性的科学问题,与台风、暴雨以及地震等灾害密切相关,一直受到多学科研究人员和广大预报员的关注。孤立圆涡能量频散波列形成过程己经清楚。但是,造成天气灾害的往往是非孤立圆涡,这里,非孤立圆涡指的是:一个热带气旋(Tropical Cyclone,TC)涡旋和一个中尺度涡构成的复杂构型。非孤立圆涡能量频散波列的形成过程研究目前尚未见报道。本文用线性化的正压无辐散涡度方程,研究了复杂构型的非孤立圆涡能量频散波列的形成过程,并指出该形成过程由三个阶段构成:涡旋东西向非对称结构的形成;涡旋主体东侧,频散高值系统的出现、持续和发展;在频散高值系统的东侧,频散低值系统的出现和加强。这些结果在台风预测中具有应用前景。     

A note on vertical coherence of streamwise turbulence inside and above a model plant canopy

Measurements of longitudinal turbulent velocity were made at pairs of levels inside and above a model plant canopy in the wind tunnel. It was found that above approximately the zero-plane displacement level, the coherence and phase results were similar in many respects to atmospheric data, but that deviations from this behaviour appeared deeper in the model canopy.     

An Analytical one-Dimensional Second-Order Closure Model of Turbulence Statistics and the Lagrangian Time Scale Within and Above Plant Canopies of Arbitrary Structure

An analytical one-dimensional second-order closure model is developed to describe the within canopy velocity variances, turbulent intensities, dissipation rates, Lagrangian time scale and Lagrangian far field diffusivities for vegetation canopies of arbitrary structure and density. The model incorporates and extends the model of momentum transfer developed by Massman (1997) and the model of within canopy velocity variances developed by Weil (unpublished) from the second-order closure model of Wilson and Shaw (1977). Model predictions of within and above canopy velocity variances, turbulent intensities, dissipation rates and the Lagrangian time scale are in reasonable agreement with previously measured or estimated values for these parameters. The present model suggests that the Lagrangian time scale and the far field diffusivity could be strongly dependent upon foliage structure and density through the foliage effects on the velocity variances. A simple formulation for the Lagrangian time scale at canopy height is derived from model results. Taken as a whole, the present model may provide a relatively simple way to incorporate turbulence parameters into models of soil/canopy/atmosphere mass transfer.     

Geometric Alignments of the Subgrid-Scale Force in the Atmospheric Boundary Layer

In recent years field experiments have been undertaken in the lower atmosphere to perform a priori tests of subgrid-scale (SGS) models for large-eddy simulations (LES). The experimental arrangements and data collected have facilitated studies of variables such as the filtered strain rate, SGS stress and dissipation, and the eddy viscosity coefficient. However, the experimental set-ups did not permit analysis of the divergence of the SGS stress (the SGS force vector), which is the term that enters directly in the LES momentum balance equations. Data from a field experiment (SGS2002) in the west desert of Utah, allows the calculation of the SGS force due to the unique 4 × 4 sonic anemometer array. The vector alignment of the SGS force is investigated under a range of atmospheric stabilities. The eddy viscosity model is likely aligned with the measured SGS force under near-neutral and unstable conditions, while its performance is unsatisfactory under stable conditions.     

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.     

双叶模型在冬小麦田冠层CO2通量多层模拟中的应用

综合考虑农田生态系统中水、热、CO2输送所涉及的大气、水文、生物等生物物理过程,以Farquhar等提出的叶片尺度光合作用生物化学过程机理模型为理论基础,对其进行空间尺度扩展,并改进冠层分层方法,建立了均匀农田与大气之间物质输送和能量交换的多层模式,在模式中运用双叶模型,同时考虑叶片氮素水平垂直差异,对2008年4—5月华北平原冬小麦生长旺季农田生态系统中冠层CO2通量进行了模拟研究,并利用涡度相关观测的通量数据对模型的有效性加以验证,结果表明:在冠层多层空间,小麦拔节至孕穗期和开花至乳熟期叶片氮含量随冠层高度的衰减系数分别为0.793(R2=0.698)和1.374(R2=0.728),冠层内叶片氮含量的空间分布可以用以相对累积叶面积指数为自变量的函数来描述;模型分别计算各层阴、阳叶的光截取、气孔传导、光合作用等,最终计算冠层上方CO2通量,冬小麦农田净生态系统生产力模拟值与实测值相关显著(R2=0.78),模拟的CO2通量日变化特征晴天昼间比阴雨天和夜间的效果好;在考虑丛聚影响的叶片非随机分布的密集农田中,阴叶对总初始生产力的贡献率在35.7%左右,对生产力贡献很重要。分层统计显示,作物最终产量的形成主要...     

Large-Eddy Simulation of the Stable Atmospheric Boundary Layer using Dynamic Models with Different Averaging Schemes

Large-eddy simulation (LES) of a stable atmospheric boundary layer is performed using recently developed dynamic subgrid-scale (SGS) models. These models not only calculate the Smagorinsky coefficient and SGS Prandtl number dynamically based on the smallest resolved motions in the flow, they also allow for scale dependence of those coefficients. This dynamic calculation requires statistical averaging for numerical stability. Here, we evaluate three commonly used averaging schemes in stable atmospheric boundary-layer simulations: averaging over horizontal planes, over adjacent grid points, and following fluid particle trajectories. Particular attention is focused on assessing the effect of the different averaging methods on resolved flow statistics and SGS model coefficients. Our results indicate that averaging schemes that allow the coefficients to fluctuate locally give results that are in better agreement with boundary-layer similarity theory and previous LES studies. Even among models that are local, the averaging method is found to affect model coefficient probability density function distributions and turbulent spectra of the resolved velocity and temperature fields. Overall, averaging along fluid pathlines is found to produce the best combination of self consistent model coefficients, first- and second-order flow statistics and insensitivity to grid resolution.     

影响植被内部辐射状况的冠层结构特征研究

植被冠层结构特征是影响植被内部辐射状况的重要因子之一,对于植被群体的光合特性来说,冠层结构特性影响了光合有效辐射的截获、吸收和透射。本文着重分析了冠层结构的数量特征（如叶面积指数）和冠层几何结构特征,综合考虑叶倾角、叶方位角和Ｇ函数等群体几何特征,以便直接用于遥感光合植被生物量机理估测模型的建立。