An extended Miles' theory for wave generation by wind

Miles' inviscid theory of surface wave generation by wind is (a) modified by replacing the logarithmic shear velocity profile with one which applies right down to the wave surface and which exhibits an explicit dependence on the roughness of the surface, and (b) extended to include the effects of the interaction of wave with air flow turbulence by considering the wave-modified mean flow as the mean of the actual turbulent air flow over water waves and using this in a mixing-length model.The surface pressure is shown to depend significantly on the flow conditions being aerodynamically smooth or rough. Its component in phase with the surface elevation is practically unaffected by the wave-turbulence interaction. However, such interaction tends to increase the rate of energy input ß from wind to waves travelling in the same direction, e.g., the increase is 2gk ² for aerodynamically rough flow, where gk is the Von Karman constant. It also provides damping of waves in an adverse wind which can be about 10% of the growth rate in a favourable wind.     

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.     

Analysis on the Interaction between Turbulence and Secondary Circulation of the Surface Layer at Jinta Oasis in Summer

The kinetic energy variations of mean flow and turbulence at three levels in the surface layer were calculated by using eddy covariance data from observations at Jinta oasis in 2005 summer.It is found that when the mean horizontal flow was stronger,the turbulent kinetic energy was increased at all levels,as well as the downward mean wind at the middle level.Since the mean vertical flow on the top and bottom were both negligible at that time,there was a secondary circulation with convergence in the upper half and divergence in the lower half of the column.After consideration of energy conversion,it was found that the interaction between turbulence and the secondary circulation caused the intensification of each other.The interaction reflected positive feedback between turbulence and the vertical shear of the mean flow.Turbulent sensible and latent heat flux anomaly were also analyzed.The results show that in both daytime and at night,when the surface layer turbulence was intensified as a result of strengthened mean flow,the sensible heat flux was decreased while the latent heat flux was increased.Both anomalous fluxes contributed to the cold island effect and the moisture island effect of the oasis.     

Boundary-Layer Similarity Under an Axisymmetric,Gradient Wind Vortex

We present similarity solutions for the mean boundary-layer profiles under an axisymmetric vortex that is in gradient wind balance; the similarity model includes the nonlinear momentum advection and curvature terms. These solutions are a generalization of the Ekman layer mean flow, which is the canonical boundary-layer basic state under a uniform, geostrophically-balanced flow. Near-surface properties such as inflow angle, surface wind factor, diffusive transport of kinetic energy into the surface layer and dissipational heating are calculated and shown to be sensitive to the choice of turbulence parameterization.     

A boundary-layer analysis of atmospheric motion over a semi-elliptical surface obstruction

Flow over surface obstructions can produce significantly large wind shears such that adverse flying conditions can occur for aeronautical systems (helicopters, V/STOL vehicles, etc.). The purpose of this analysis is to determine the kinds of flow fields that can result from surface obstructions in an otherwise horizontally homogeneous statistically stationary flow. The technique is based on the boundary-layer/Boussinesq-approximated equations of motion. The pressure gradient resulting from the surface obstruction is that consistent with a potential flow over a two-dimensional cylinder with elliptical cross-section, an approach commonly used for boundary-layer analyses in the engineering community. The dissipative effects of atmospheric turbulence on the mean flow are represented with eddy-viscosity models of the Reynolds stresses. The upstream flow is a neutral one and is characterized by a logarithmic profile for the mean wind. The following conclusions result from the analysis: (1) localized maxima in wind speed occur at the top of a surface obstruction, which are expected in physically real flow situations, (2) an increase in the elliptical aspect ratio decreases the wind speed within the boundary layer at the top of the ellipse and returns it to the logarithmic distribution characteristic of undisturbed flow, (3) increases in surface roughness affect the flow by decreasing the velocity in the boundary layer, with the most pronounced effect occurring near the surface of the smaller aspect-ratio ellipse, (4) Reynolds number has a negligible effect on the overall flow for the range of Reynolds numbers considered in this study, (5) a decrease in the elliptical aspect ratio and an increase in the surface roughness cause larger separation regions.     

Gustiness and coherent structure under weak wind period in atmospheric boundary layer

Statistical analysis of turbulent and gusty characteristics in the atmospheric boundary layer under weak wind period has been carried out.The data used in the analysis were from the multilevel ultrasonic anemometer-thermometers at 47 m,120 m,and 280 m levels on Beijing 325 m meteorological tower.The time series of 3D atmospheric velocity were analyzed by using conventional Fourier spectral analysis and decompose into three parts:basic mean flow(period 10 min),gusty disturbances(1 min period 10 min)and turbulence fluctuations(period 1 min).The results show that under weak mean wind condition:1)the gusty disturbances are the most strong fluctuations,contribute about 60% kinetic energy of eddy kinetic energy and 80% downward flux of momentum,although both the eddy kinetic energy and momentum transport are small in comparison with those in strong mean wind condition;2)the gusty wind disturbances are anisotropic;3)the gusty wind disturbances have obviously coherent structure,and their horizontal and vertical component are negatively correlated and make downward transport of momentum more effectively;4)the friction velocities related to turbulence and gusty wind are approximately constant with height in the surface layer.     

Large-eddy Simulations of Flow Over Forested Ridges

Large-eddy simulations (LES) of flow over a series of small forested ridges are performed, and compared with numerical simulations using a one-and-a-half order mixing length closure scheme. The qualitative and quantitative similarity between these results provides some confidence in the results of recent analytical and numerical studies of flow over forested hills using first-order mixing length schemes. Time series of model velocities at various locations within the canopy allow the application of various experimental techniques to study the turbulence in the LES. The application of conditional analysis shows that the structure of the turbulence over a forested hill is broadly similar to that over flat ground, with sweeps and ejections dominating. Differences are seen across the hill, particularly associated with regions of mean flow separation and recirculation near the summit and in the lee of the hill. Detailed comparison of derived mixing lengths from the LES with the assumed values used in mixing-length closure schemes show that the mixing length varies with location across the hill and with height in the canopy. This is consistent with previous wind-tunnel measurements, and demonstrates that a constant mixing-length assumption is not strictly valid within the canopy. Despite this, the first-order mixing-length schemes do give similar results both for the mean flow and the turbulence in such situations.     

A Wind-Tunnel Investigation of Wind-Turbine Wakes: Boundary-Layer Turbulence Effects

Wind-tunnel experiments were performed to study turbulence in the wake of a model wind turbine placed in a boundary layer developed over rough and smooth surfaces. Hot-wire anemometry was used to characterize the cross-sectional distribution of mean velocity, turbulence intensity and kinematic shear stress at different locations downwind of the turbine for both surface roughness cases. Special emphasis was placed on the spatial distribution of the velocity deficit and the turbulence intensity, which are important factors affecting turbine power generation and fatigue loads in wind energy parks. Non-axisymmetric behaviour of the wake is observed over both roughness types in response to the non-uniform incoming boundary-layer flow and the effect of the surface. Nonetheless, the velocity deficit with respect to the incoming velocity profile is nearly axisymmetric, except near the ground in the far wake where the wake interacts with the surface. It is found that the wind turbine induces a large enhancement of turbulence levels (positive added turbulence intensity) in the upper part of the wake. This is due to the effect of relatively large velocity fluctuations associated with helicoidal tip vortices near the wake edge, where the mean shear is strong. In the lower part of the wake, the mean shear and turbulence intensity are reduced with respect to the incoming flow. The non-axisymmetry of the turbulence intensity distribution of the wake is found to be stronger over the rough surface, where the incoming flow is less uniform at the turbine level. In the far wake the added turbulent intensity, its positive and negative contributions and its local maximum decay as a power law of downwind distance (with an exponent ranging from −0.3 to −0.5 for the rough surface, and with a wider variation for the smooth surface). Nevertheless, the effect of the turbine on the velocity defect and added turbulence intensity is not negligible even in the very far wake, at a distance of fifteen times the rotor diameter.     

Turbulence Structure in the Wake Region of a Meteorological Tower

A meteorological tower significantly modifies the air flow, the mean windspeed and wind direction as well as the turbulencestructure of the air. Suchchanges can be noticed in particular in the wake region of the tower.Measurementson the 200 m tower ofForschungszentrum Karlsruhewere carried outusing Solent sonic anemometers in the lee of the towerand cup anemometers on both sides.In the wake region, spectral energydensity is increased in the high-frequency range. Superposition of this disturbance spectrum on the undisturbedspectrum yields a `knee' in the resulting spectrum. In the case of low turbulence intensity with stable stratification,a plateau with a constant energy content is observed in front of the knee.This effect is caused by the new production of turbulence energy from the mean flow as well as by an energy transfer fromlarger to smaller vortices. Power spectra in strongly stable conditionsshow a more rapid decrease of intensity in the region where the inertialsubrange is expected.The relevant scales of wake turbulence are derived from the maximum of the disturbance spectrum.Locations of the high-frequency peak do not depend on atmospheric stability,but are controlled mainly by mean wind speed.Apart from the reduction of the mean wind speed, the spectra and cospectra exhibit a strong anisotropy for such cases.The results demonstrate the significant influence of a tower on turbulence spectra in the wake region.     

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。     

Measurements and predictions of turbulent recirculating flow over a rectangular depression

Measurements of mean velocity and turbulence intensity components are reported for flow over a two-dimensional rectangular depression; these include measurements in the highly turbulent regions of recirculating flow. Predictions of the mean-flow variables were obtained from three finite-difference models: (1) a vorticity stream-function model using constant effective viscosity, (2) a primitive variable model using constant effective viscosity, and (3) a primitive variable model in which effective viscosity is computed from a turbulence model. The turbulent kinetic energy was also predicted by the last of these models. These predictions were compared with the measurements in order to evaluate what accuracy can be expected when state-of-the-art finite-difference models are applied to complex flow situations in the atmospheric environment. Some areas are noted where improvement of modeling capabilities for complex flows is still needed.     

The turbulent wind flow over an embankment

Under neutral conditions and with low winds, profiles of mean and turbulent wind components have been measured at various points across an embankment with aspect ratio 0.3. These measurements have been compared with and related to those of undisturbed flow in a horizontal homogeneous area on the windward side. The speed-up ratio, the turbulent and mean kinetic energy and the turbulent shear stress are examined. It is found that the flow stagnates on the windward side, accelerates above the crest, and separates behind the crest. The results show a remarkable dependence on the angle of attack. With an angle smaller than 90 °, the influence of the embankment on the mean wind field is reduced but is increased on the turbulent part, as lateral gustiness components are amplified. With the incoming flow normal to the embankment, maximum turbulence is found on the top of the ridge near the surface but at greater heights farther downwind. The same is true for the shear stress, but only for oblique flow, whereas for normal flow a minimum is found above the crest and a maximum on the windward side. Therefore, with varying angle of attack the embankment acts in different ways on mean wind, turbulent kinetic energy, and turbulent stress. Although the winds were low, all effects are clearly evident in the data.     

Energy analysis of open regions of turbulent flows — mean eddy energetics of a numerical ocean circulation experiment

The concepts involved in the interpretation of energy budgets in subregions of a turbulent flow are examined in order to determine the processes responsible for the production, transport, and dissipation of energy throughout a dynamically inhomogeneous circulation. An interpretation of the effects of Reynolds stress—mean flow interaction work for open regions is presented in terms of the change in the total mean kinetic energy. In an arbitrary volume of fluid the changes in kinetic energy of the mean flow and the mean kinetic energy of the eddy flow are not generally equal and opposite, so this process is not generally responsible for a conversion of energy between the two forms. These ideas are then applied to a regional kinetic energy analysis of the mesoscale resolution general ocean circulation numerical experiment of Robinson et al. (1977). The spatial structure of the various terms in the equation for the mean eddy kinetic energy is examined. The issues involved in selection of a set of analysis regions are discussed and explored via examination of budgets over different subregions of this flow. Thereby a relatively simple picture of the regional energetics emerges. Mean eddy kinetic energy is produced by conversion of kinetic energy of the mean flow in the net over the recirculation and near field of the northern boundary current system and roughly half of this energy is lost to each of mean eddy pressure work transport and diffusion work. Budgets over subregions of this net source region are much more complex. The interior eddy field is driven by pressure work influx, while the southwestern region has eddy buoyancy work conversion of mean potential energy as its energy source. At every depth level the eddy field draws its kinetic energy from the mean flow, when averaged over the horizontal extent of the basin or over the recirculation and near field.     

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.     

Effects of Thermal Stability and Incoming Boundary-Layer Flow Characteristics on Wind-Turbine Wakes: A Wind-Tunnel Study

Wind-tunnel experiments were carried out to study turbulence statistics in the wake of a model wind turbine placed in a boundary-layer flow under both neutral and stably stratified conditions. High-resolution velocity and temperature measurements, obtained using a customized triple wire (cross-wire and cold wire) anemometer, were used to characterize the mean velocity, turbulence intensity, turbulent fluxes, and spectra at different locations in the wake. The effect of the wake on the turbulence statistics is found to extend as far as 20 rotor diameters downwind of the turbine. The velocity deficit has a nearly axisymmetric shape, which can be approximated by a Gaussian distribution and a power-law decay with distance. This decay in the near-wake region is found to be faster in the stable case. Turbulence intensity distribution is clearly non-axisymmetric due to the non-uniform distribution of the incoming velocity in the boundary layer. In the neutral case, the maximum turbulence intensity is located above the hub height, around the rotor tip location and at a distance of about 4–5.5 rotor diameters, which are common separations between wind turbines in wind farms. The enhancement of turbulence intensity is associated with strong shear and turbulent kinetic energy production in that region. In the stable case, the stronger shear in the incoming flow leads to a slightly stronger and larger region of enhanced turbulence intensity, which extends between 3 and 6 rotor diameters downwind of the turbine location. Power spectra of the streamwise and vertical velocities show a strong signature of the turbine blade tip vortices at the top tip height up to a distance of about 1–2 rotor diameters. This spectral signature is stronger in the vertical velocity component. At longer downwind distances, tip vortices are not evident and the von Kármán formulation agrees well with the measured velocity spectra.     

The Coupling State of an Idealized Stable Boundary Layer

The coupling state between the surface and the top of the stable boundary layer (SBL) is investigated using four different schemes to represent the turbulent exchange. An idealized SBL is assumed, with fixed wind speed and temperature at its top. At the surface, two cases are considered, first a constant temperature, 20 K lower than the SBL top, and later a constant 2 K h⁻¹ cooling rate is assumed for 10 h after a neutral initial condition. The idealized conditions have been chosen to isolate the influence of the turbulence formulations on the coupling state, and the intense stratification has the purpose of enhancing such a response. The formulations compared are those that solve a prognostic equation for turbulent kinetic energy (TKE) and those that directly prescribe turbulence intensity as a function of atmospheric stability. Two TKE formulations are considered, with and without a dependence of the exchange coefficients on stability, while short and long tail stability functions (SFs) are also compared. In each case, the dependence on the wind speed at the SBL top is considered and it is shown that, for all formulations, the SBL experiences a transition from a decoupled state to a coupled state at an intermediate value of mechanical forcing. The vertical profiles of potential temperature, wind speed and turbulence intensity are shown as a function of the wind speed at the SBL top, both for the decoupled and coupled states. The formulation influence on the coupling state is analyzed and it is concluded that, in general, the simple TKE formulation has a better response, although it also tends to overestimate turbulent mixing. The consequences are discussed.     

Some Aspects of the Characteristics of Monsoon Disturbances Using a Combined Barotropic－Baroclinic Model

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Characteristics of Near Surface Winds over Different Underlying Surfaces in China: Implications for Wind Power Development

Accurate wind and turbulence information are essential to wind energy research and utilization, among which wind shear and turbulence intensity/scale have seldom been investigated. In this paper, the observational data from the100-m high wind towers in Xilinhot in Inner Mongolia(2009–10; grassland region), Huanghua in Hebei Province(2009–10; coastal flat region), and Xingzi County in Jiangxi Province(2010–11; mountain–lake region) are used to study the variations in near surface winds and turbulence characteristics related to the development of local wind energy over different underlying surfaces. The results indicate that(1) the percentage of the observed wind shear exponents exceeding 0.3 for the grassland region is 6%, while the percentage is 13% for the coastal flat region and 10%for the mountain–lake region. In other words, if the wind speed at 10 m is 10 ms^–1, the percentage of the wind speed at 100 m exceeding 20 ms^–1 for the grassland region is 6%, while the percentage is 13% for the coastal flat region and 10% for the mountain–lake region.(2) In terms of the turbulent intensity in the zonal, meridional, and vertical directions(I_u, I_v, and I_w, respectively), the frequencies of I_v/I_u < 0.8 in the grassland, coastal flat, and mountain–lake regions are 23%–29%, 32%–38%, and 30%–37%, respectively. Additionally, the frequencies of I_w/I_u < 0.5 in the grassland, coastal flat, and mountain–lake regions are 45%–75%, 52%–70%, and 43%–53%, respectively. The frequencies of I_v/I_u < 0.8 and Iw/I_u < 0.5 in each region mean that I_u is large and the air flow is unstable and fluctuating,which will damage the wind turbines. Therefore, these conditions do not meet the wind turbine design requirements,which must be considered separately.(3) At 50-and 70-m heights, the value of the turbulence scale parameter Λ in the grassland region is greater than that in the coastal flat region, and the latter is greater than that in the mountain–lake region. Therefore, under the same conditions, some parameters, e.g., the extreme directional change and extreme operating gust at the hub height in the grassland region, are greater than those in the coastal flat region,which are greater than those in the mountain–lake region. These results provide a reference for harnessing local wind energy resources and for the selection and design of wind turbines.     

Turbulent transport within and above a maize canopy

Hot-wire anemometers were used to measure air temperature and the three velocity components of the wind within and above a maize canopy. From digitized anemometer outputs, correlation coefficients for vertical heat flux and turbulent momentum transfer were calculated. A comparison of these coefficients with profiles of mean wind speed and mean temperature indicates that the main features of the turbulence may be explained in terms of the usual mixing-length theory. Instantaneous records of heat and momentum flux, however, indicate the existence of other competing turbulent mechanisms due to the unsteady, non-equilibrium nature of the turbulent flow. Regimes of flow dominated by mechanical and/or thermal mixing are indicated. Spectral results show that high shear and turbulent intensity levels as well as the presence of the maize leaves and stalks as vortex-shedding surfaces complicate the energy transfer mechanism. An energy balance between radiation and convection reveals that the energy budget is primarily a balance between solar radiation and the flux of latent heat.Contribution of the Sibley School of Mechanical and Aerospace Engineering, Cornell University, in cooperation with the Agricultural Research Service, U.S. Department of Agriculture, Ithaca, N.Y., U.S.A. and the Cornell University Agricultural Experiment Station. Department of Agronomy Series No. 1116.Sibley School of Mechanical and Aerospace Engineering, Cornell University; U.S. Department of Agriculture, Gainesville, Florida Section for Estuary and Fjord Studies, River and Harbour Laboratory, Technical University of Norway, Trondheim, Norway; State Univ. of New York at Buffalo; and U.S. Department of Agriculture and Cornell University; respectively.