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。     

On the downward transport of turbulent kinetic energy in the surface layer over plant canopies

Downward fluxes of turbulent kinetic energy have been frequently observed in the air layer just above plant canopies. In order to investigate the mechanism for such downward transport, analysis of observational data is attempted. Height-dependency of turbulent kinetic energy flux and turbulence statistics including higher order moments is represented as a function of a non-dimensional height z/H, where z is an observational height and H an average height of plant canopies. Downward fluxes and non-Gaussianity of wind velocity fluctuations are predominant just above plant canopies and decrease with increasing height. The downward flux is closely related to the high intensity of turbulence and the non-Gaussianity of wind velocity fluctuations, especially with a positive skewness in the longitudinal wind and a negative skewness in the vertical wind. The analysis method of conditional sampling and averaging is applied to the present observations. The results show that the predominance of the intermittent inrush phase over the intermittent ejection phase leads to the above-mentioned non-Gaussianity. Finally, a simple explanation is given in order to interpret the turbulent flow structure in the air layer near the plant canopies, which is associated with the downward energy transport process.     

The evolution of a convective planetary boundary layer — A higher-order-closure model study

The evolution of the boundary layer on day 33 of the Wangara experiment in southeast Australia is calculated with a higher-order-closure turbulence model. This model, which includes equations for the mean field as well as the second moments of the turbulent field, is described in detail. The mean profiles of wind, temperature, and humidity, the profiles of heat and humidity fluxes, the Reynolds stress distributions, and the height of the boundary layer are shown between 10 a.m. and 6 p.m. The results agree well with those from Deardorff's 3-D simulation and take relatively little computer time.     

重庆市区冬季小风条件下近地面层某些湍流特征量的分析

利用１９８９年１２月１６日－１９９０年１月１４日在重庆市用三轴风速仪所测得的风速资料，计算了小风条件下重庆近地面层的湍流参数，欧拉时间自相关系数，湍流时间积分尺度，湍流强度，摩擦速度，湍流应力等湍流特征量，以了解重庆地区小风条件下的近地面层的湍流场特征。     

An assessment of mixing-length closure schemes for models of turbulent boundary layers over complex terrain

The effectiveness of closure assumptions implemented in turbulent boundary-layer models is rather uncertain over complex terrain. Different closure schemes for Reynolds shear stress based on the mixing-length concept are compared with data from wind tunnel experiments over complex terrain and the results are analysed on the basis of second-order moment equations. A good estimation of the vertical momentum flux velocity scale turns out to be given by the standard deviation of the vertical velocity while the turbulent kinetic energy scaling gives less satisfactory results in regions where turbulence anisotropy is large. Fairly good results are given by closure models implementing a shear-limited mixing-length already proposed for non-logarithmic wind profiles, while large errors characterize traditional mixing-length formulations.     

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.     

An Investigation of Higher-Order Closure Models for a Forested Canopy

Simultaneous triaxial sonic anemometer velocity measurements vertically arrayed at six levels within and above a uniform pine forest were used to examine two parameterization schemes for the triple-velocity correlation tensor employed in higher-order closure models. These parameterizations are the gradient-diffusion approximation typically used in second-order closure models, and the full budget for the triple-velocity correlation tensor typically employed in third-order closure models. Both second- and third-order closure models failed to reproduce the measured profiles of the triple-velocity correlation within and above the canopy. However, the Reynolds stress tensor profiles (including velocity variances) deviated greatly from the measurements only within the lower levels of the canopy. It is shown that the Reynolds stresses are most sensitive to the parameterization of the triple-velocity correlation in these lower canopy regions where local turbulent production is negligible and turbulence is mainly sustained by the flux transport term. The failure of the third-order closure model to reproduce the measured third moments in the upper layers of the canopy-top contradicts conclusions from a previous study over shorter vegetation but agrees with another study for a deciduous forest. Whether the third-order closure model failure is due to the zero-fourth-cumulant closure approximation is therefore considered. Comparisons between measured and predicted quadruple velocity correlations suggest that the zero-fourth-cumulant approximation is valid close to the canopy-atmosphere in agreement with recent experiments.     

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.     

Large-eddy simulation of turbulent flow above and within a forest

A large-eddy simulation has been performed of an atmospheric surface layer in which the lower third of the domain is occupied by a drag layer and heat sources to represent a forest. Subgridscale processes are treated using second-order closure techniques. Lateral boundaries are periodic, while the upper boundary is a frictionless fixed lid. Mean vertical profiles of wind velocity derived from the output are realistic in their shape and response to forest density. Similarly, vertical profiles of Reynolds stress, turbulent kinetic energy and velocity skewness match observations, at least in a qualitative sense. The limited vertical extent of the domain and the artificial upper boundary, however, cause some departures from measured turbulence profiles in real forests. Instantaneous turbulent velocity and scalar fields are presented which show some of the features obtained by tower instrumentation in the field and in wind tunnels, such as the vertical coherence of vertical velocity and the slope of structures revealed by temperature patterns.     

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.     

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.     

Spatio-Temporal Surface Shear-Stress Variability in Live Plant Canopies and Cube Arrays

This study presents spatiotemporally-resolved measurements of surface shear-stress τ _s in live plant canopies and rigid wooden cube arrays to identify the sheltering capability against sediment erosion of these different roughness elements. Live plants have highly irregular structures that can be extremely flexible and porous resulting in considerable changes to the drag and flow regimes relative to rigid imitations mainly used in other wind-tunnel studies. Mean velocity and kinematic Reynolds stress profiles show that well-developed natural boundary layers were generated above the 8 m long wind-tunnel test section covered with the roughness elements at four different roughness densities (λ = 0, 0.017, 0.08, 0.18). Speed-up around the cubes caused higher peak surface shear stress than in experiments with plants at all roughness densities, demonstrating the more effective sheltering ability of the plants. The sheltered areas in the lee of the plants are significantly narrower with higher surface shear stress than those found in the lee of the cubes, and are dependent on the wind speed due to the plants ability to streamline with the flow. This streamlining behaviour results in a decreasing sheltering effect at increasing wind speeds and in lower net turbulence production than in experiments with cubes. Turbulence intensity distributions suggest a suppression of horseshoe vortices in the plant case. Comparison of the surface shear-stress measurements with sediment erosion patterns shows that the fraction of time a threshold skin friction velocity is exceeded can be used to assess erosion of, and deposition on, that surface.     

Turbulent flow over a wavy boundary

The linearized, two-dimensional flow of an incompressible fully turbulent fluid over a sinusoidal boundary is solved using the method of matched asymptotic expansions in the limit of vanishing skin-friction.A phenomenological turbulence model due to Saffman (1970, 1974) is utilized to incorporate the effects of the wavy boundary on the turbulence structure.Arbitrary lowest-order wave speed is allowed in order to consider both the stationary wavy wall, and the water wave moving with arbitrary positive or negative velocity.Good agreement is found with measured tangential velocity profiles and surface normal stress coefficients. The phase shift of the surface normal stress exhibits correct qualitative behavior with both positive and negative wave speeds, although predicted values are low.     

The Effect of Coherent Structures in the Atmospheric Surface Layer on Blowing-Snow Transport

While turbulent bursts are considered critical for blowing-snow transport and initiation, the interaction of the airflow with the snow surface is not fully understood. To better characterize the coupling of turbulent structures and blowing-snow transport, observations collected in natural environments at the necessary high-resolution time scales are needed. To address this, high-frequency measurements of turbulence, blowing-snow density and particle velocity were made in the Canadian Rockies. During blowing-snow storms, modified variable-interval time averaging enabled identification of periods of near-surface blowing-snow coupling with shear-stress-producing motions in the lowest 2 m of the atmospheric surface layer. The identification of those turbulent motions responsible for blowing snow yields a better understanding of the event-driven mechanics of initiation and sustained transport. The type of coherent structures generating the Reynolds stress are just as important as the magnitude of the Reynolds stress in initiating and sustaining near-surface blowing snow. Our results suggest that blowing-snow models driven by merely the time-averaged shear stress lack physical realism in the near-surface region. The next phase of the development of blowing-snow models should incorporate parametrizations of coherent turbulent structures.     

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.     

Effects of precipitation on the eddy exchange in a wind-driven sea

Effects of precipitation on the temperature and salinity profiles in the top 2 or 3 m of the sea are calculated for four models of turbulent exchange: (1) constant eddy exchange with depth; (2) drift-current eddy exchange; (3) eddy exchange produced by shear in the orbital velocity under a surface wave; and (4) drift current and wave turbulence acting together. The surface temperature and salinity are only weakly affected, but the density gradient can become significantly stabler. The resulting influence on the eddy exchange is modeled with empirical formulas employing the Richardson number. Stability strongly damps drift-current eddy exchange but has much less effect on the wave-induced turbulence.The energy budget shows an increase in turbulent dissipation near the surface for weak stability when the surface stress in assumed to remain constant. Beyond a critical Richardson number of about 0.9 energy consumed by turbulent energy dissipation decreases. This occurs more due to a reduction in mechanical energy production than because of energy being used for the redistribution of mass.     

A Flume Experiment on the Adjustment of the Mean and Turbulent Statistics to a Transition from Short to Tall Sparse Canopies

Water-flume experiments are conducted to study the structure of turbulent flow within and above a sparse model canopy consisting of two rigid canopies of different heights. This difference in height specifies a two-dimensional step change from a rough to a rougher surface, as opposed to a smooth-to-rough transition. Despite the fact that the flow is in transition from a rough to a rougher surface, the thickness of the internal boundary layer scales as x ^4/5, consistent with smooth-to-rough boundary layer adjustment studies, where x is the downstream distance from the step change. However, the analogy with smooth-to-rough transitions no longer holds when the flow inside the canopy and near the canopy top is considered. Results show that the step change in surface roughness significantly increases turbulence intensities and shear stress. In particular, there is an adjustment of the mean horizontal velocity and shear stress as the flow passes over the rougher canopy, so that their vertical profiles adjust to give maximum values at the top of this canopy. We also observe that the magnitude and shape of the inflection in the mean horizontal velocity profile is significantly affected by the transition. The horizontal and vertical turbulence spectra compare well with Kolmogorov’s theory, although a small deviation at high frequencies is observed in the horizontal spectrum within the canopy. Here, for relatively low leaf area index, shear is found to be a more effective mechanism for momentum transfer through the canopy structure than vortex shedding.     

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.     

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.     

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.