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.     

An application of boundary-layer similarity theories to an aircraft accident investigation

The vertical distribution of turbulence in the planetary boundary layer at the time and place of an aircraft accident is examined. Estimates of the surface stress are determined by means of the boundary-layer resistance laws with a correction for baroclinity. The response of the aircraft to turbulence during its approach, and the exceedance characteristics of the turbulence are given for an empirical spectrum of vertical velocity. Also, a simulation is made of the vertical velocity along the approach path.     

The effect of idealized water waves on the turbulence structure and kinetic energy budgets in the overlying airflow

The influence of an idealized moving wavy surface on the overlying airflow is investigated using direct numerical simulations (DNS). In the present simulations, the bulk Reynolds number is Re = 8000 (; where U₀ is the forcing velocity of the flow, h the height of the domain and v the kinematic viscosity) and the phase speed of the imposed waves relative to the friction velocity, i.e., the wave age varies from very slow to fast waves. The wave signal is clearly present in the airflow up to at least 0.15λ (where λ is the wave length) and is present up to higher levels for faster waves. In the kinetic energy budgets, pressure transport is mainly of importance for slow waves. For fast waves, viscous transport and turbulent transport dominate near the surface. Kinetic energy budgets for the wave and turbulent perturbations show a non-negligible transport of turbulent kinetic energy directed from turbulence to the wave perturbation in the airflow. The wave-turbulent energy transport depends on the size, tilt, and phase of the wave-induced part of the turbulent Reynolds stresses.According to the DNS data, slow waves are more efficient in generating isotropic turbulence than fast waves.Despite the differences in wave-shape as well as in Reynolds number between the idealized direct numerical simulations and the atmosphere, there are intriguing similarities in the turbulence structure. Important information about the turbulence above waves in the atmosphere can be obtained from DNS—the data must, however, be interpreted with care.     

Wave drag in the planetary boundary layer over complex terrain

The concepts of mountain-induced wave drag are applied to the smaller scale problem of the boundary layer over complex terrain. It is found that the Reynolds stress and surface drag caused by surface-generated waves can be at least as large as those conventionally associated with turbulence. Conditions in which wave effects are important are identified.ATDD Contribution No. 88/5.     

Wave-Modified Flux and Plume Dispersion in the Stable Boundary Layer

The effects of a pressure jump and a following internal gravity wave on turbulence and plume diffusion in the stable planetary boundary layer are examined. The pressure jump was accompanied by a sudden increase in turbulence and plume dispersion. The effects of wave perturbations on turbulence statistics are analysed by calculating fluxes and variances with and without the wave signal for averaging times ranging from 1 to 30 min. The wave signals are obtained using a band-pass filter. It is shown that second-order turbulence quantities calculated without first subtracting the wave perturbations from the time are greater than those calculated when the wave signal is separated from the turbulence. Estimates of the vertical dispersion of an elevated tracer plume in the stable boundary layer are made using an elastic backscatter lidar. Plume dispersion observed 25 m downwind of the source increases rapidly with the arrival of the flow disturbances. Measured plume dispersion and plume centreline height correlate with the standard deviation of the vertical velocity but not with the wave signal.     

Wavy Vertical Motions in the ABL Observed by Sodar

Some characteristics of wavelike motions in the atmospheric boundary layer observed by sodar are considered. In an experiment carried out in February 1993 in Milan, Italy, Doppler sodar measurements were accompanied by in situ measurements of temperature and wind velocity vertical profiles using a tethered balloon up to 600 m. The oscillations of elevated wavy layers containing intense thermal turbulence, usually associated with temperature-inversion zones, were studied by using correlation and spectral analysis methods. The statistics of the occurrence of wavelike and temperature-inversion events are presented. The height distributions of Brunt–Vaisala frequency and wind shear and their correlation within elevated inversion layers were determined, with a strong correlation observed between the drift rate of the wavy layers and the vertical velocity measured by Doppler sodar inside these layers. Spectral analysis showed similarities regarding their frequency characteristics. The phase speed and propagation direction of waves were estimated from the time delay of the signals at three antennae to provide estimates of wavelength. Moreover, wavelengths were estimated from the intrinsic frequency obtained from sodar measurements of the Doppler vertical velocity and oscillations of wavy turbulent layers. The two wavelength estimates are in good agreement.     

Reynolds-Number Dependence of Gas Dispersion Over a Wavy Wall

Direct numerical simulations of an Ekman layer are performed to study flow evolution during the response of an initially neutral boundary layer to stable stratification. The Obukhov length, L, is varied among cases by imposing a range of stable buoyancy fluxes at the surface to mimic ground cooling. The imposition of constant surface buoyancy flux , i.e. constant-flux stability, leads to a buoyancy difference between the ground and background that tends to increase with time, unlike the constant-temperature stability case where a constant surface temperature is imposed. The initial collapse of turbulence in the surface layer owing to surface cooling that occurs over a time scale proportional to \(L/u_*\), where \(u_*\) is the friction velocity, is followed by turbulence recovery. The flow accelerates, and a “low-level jet” (LLJ) with inertial oscillations forms during the turbulence collapse. Turbulence statistics and budgets are examined to understand the recovery of turbulence. Vertical turbulence exchange, primarily by pressure transport, is found to initiate fluctuations in the surface layer and there is rebirth of turbulence through enhanced turbulence production as the LLJ shear increases. The turbulence recovery is not monotonic and exhibits temporal intermittency with several collapse/rebirth episodes. The boundary layer adjusts to an increase in the surface buoyancy flux by increased super-geostrophic velocity and surface stress such that the Obukhov length becomes similar among the cases and sufficiently large to allow fluctuations with sustained momentum and heat fluxes. The eventual state of fluctuations, achieved after about two inertial periods (\(ft \approx 4\pi \)), corresponds to global intermittency with turbulent patches in an otherwise quiescent background. Our simplified configuration is sufficient to identify turbulence collapse and rebirth, global and temporal intermittency, as well as formation of low-level jets, as in observations of the stratified atmospheric boundary layer.     

A Lagrangian Stochastic Model for Sea-Spray Evaporation in the Atmospheric Marine Boundary Layer

The dispersion of heavy particles subjected to a turbulent forcing is often simulated with Lagrangian stochastic models. Although these models have been employed successfully over land, the implementation of traditional LS models in the marine boundary layer is significantly more challenging. We present an adaptation of traditional Lagrangian stochastic models to the atmospheric marine boundary layer with a particular focus on the representation of the scalar turbulence for temperature and humidity. In this new model, the atmosphere can be stratified and the bottom boundary is represented by a realistic wavy surface that moves and deforms. Hence, the correlation function for the turbulent flow following a particle is extended to the inhomogenous, anisotropic case. The results reproduce behaviour for scalar Lagrangian turbulence in a stratified airflow that departs only slightly from the expected behaviour in isotropic turbulence. When solving for the surface temperature and the radius of evaporating heavy water droplets in the airflow, the modelled turbulent forcing on the particle also behaves remarkably well. We anticipate that this model will prove especially useful in the context of sea-spray dispersion and its associated sensible heat, latent heat, and gas fluxes between spray droplets and the atmosphere.     

The resistance law for the atmospheric boundary layer over a wavy surface

In analogy with two-dimensional turbulent layers, the surface layer (where wall similarity is fulfilled) and the region near the outer edge of the boundary layer (where the flow described by the velocity defect belongs to then-parameter family) may be postulated to exist for the atmospheric boundary layer over a wavy surface. The matching of the two regions yields a resistance law.     

Characteristics of natural wind simulations in the TUM boundary layer wind tunnel

The boundary layer wind tunnel at the Technische Universit?t München was tested for atmospheric boundary layer (ABL) simulations. The ABLs developing above rural, suburban, and urban terrains were reproduced using the Counihan method, i.e., castellated barrier wall, vortex generators, and a fetch of surface roughness elements. A series of flow-characteristic evaluations was performed to investigate the flow development and uniformity. Experimental results presented as mean velocity, turbulence intensity, integral length scale of turbulence, Reynolds stress, and power spectral density of velocity fluctuations were compared with the ESDU data and/or theoretical models. Generated ABL wind-tunnel simulations compare well with the rural, suburban, and urban ABLs. In the test section area used for experiments on structural models, the ABL simulation is developed and uniform. Results of this study indicate the boundary layer wind tunnel at the Technische Universit?t München can be successfully employed in a broad spectrum of engineering, environmental, and micrometeorological studies, where it is required to accurately reproduce ABL characteristics.     

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 Lagrangian Stochastic Model for Heavy Particle Dispersion in the Atmospheric Marine Boundary Layer

The dispersion of heavy particles and pollutants is often simulated with Lagrangian stochastic (LS) models. Although these models have been employed successfully over land, the free surface at the air-sea interface complicates the implementation of traditional LS models. We present an adaptation of traditional LS models to the atmospheric marine boundary layer (MBL), where the bottom boundary is represented by a realistic wavy surface that moves and deforms. In addition, the correlation function for the turbulent flow following a particle is extended to the anisotropic, unsteady case. Our new model reproduces behaviour for Lagrangian turbulence in a stratified air flow that departs only slightly from the expected behaviour in isotropic turbulence. When solving for the trajectory of a heavy particle in the air flow, the modelled turbulent forcing on the particle also behaves remarkably well. For example, the spectrum of the turbulence at the particle location follows that of a massless particle for time scales approximately larger than the Stokes’ particle response time. We anticipate that this model will prove especially useful in the context of sea-spray dispersion and its associated momentum, sensible and latent heat, and gas fluxes between spray droplets and the atmosphere.     

大气边界层强风的阵性和相干结构

我国北方春季冷锋过境后,常骤发强风,甚至起沙扬尘,持续数小时甚至一二天,通过对边界层超声风温仪的资料分析,可知大风常叠加有周期为3～6 min的阵风,较有规律,且有明显的相干结构:阵风风速峰期有下沉运动,谷期有上升运动;阵风扰动以沿平均流的顺风方向分量为主,横向和垂直方向的分量都较小,其本质是低频次声波和重力波的混合;阵风沿顺风向且向下传播.周期小于1 min的脉动在水平面上基本是各向同性的不规则的湍涡.大风期间,无论是平均流、阵风和湍流脉动,至少在120 m高度以下,主要都有西风和北风动量下传,感热上传.平均流的动量下传强于由脉动下传的量,与一般天气情况不同,而且阵风与湍流的动量下传的量值差不多.平均流和阵风在动量传送上起相当大的作用.     

Intermittent Bursting of Turbulence in a Stable Boundary Layer with Low-level Jet

The atmospheric stable boundary layer (SBL) with a low-level jet is simulated experimentally using a thermally stratified wind tunnel. The turbulence structure and flow characteristics are investigated by simultaneous measurements of velocity and temperature fluctuations and by flow visualization. Attention is focused on the effect of strong wind shear due to a low-level jet on stratified boundary layers with strong stability. Occasional bursting of turbulence in the lower portion of the boundary layer can be found in the SBL with strong stability. This bursting originates aloft away from the surface and transports fluid with relatively low velocity and temperature upward and fluid with relatively high velocity and temperature downward. Furthermore, the relationship between the occurrence of turbulence bursting and the local gradient Richardson number (Ri) is investigated. The Ri becomes larger than the critical Ri, Ri_cr = 0.25, in quiescent periods. On the other hand, the Ri number becomes smaller than Ri_cr during bursting events.     

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.     

从湍流经典理论到大气湍流非平衡态热力学理论

湍流是日常生活中一种普遍的自然现象,也是经典物理学仍未完全解决的难题。湍流更是大气运动的最基本特征。本文系统地回顾了大气湍流经典理论发展简史,进一步详细介绍了大气湍流非平衡态热力学理论。大气湍流非平衡态热力学理论在熵平衡方程中引入动力过程,进而统一推导出大气湍流输送的Fourier定律、Flick定律和Newton定律,证明了Dufour效应、Soret效应、可逆动力过程与热力不可逆湍流输送过程之间的交叉耦合效应,以及湍流强度定理。这些定律和定理中得到了观测的事实验证,同时它们的唯象系数也由观测资料所确定。湍流强度定理揭示,湍流发展的宏观原因是速度和温度的剪切效应,Reynolds湍流和Rayleigh-Bénard湍流共存于大气湍流中。热力过程和动力过程间耦合效应现象的发现突破了传统湍流输送理论,即Fourier定律、Flick定律和Newton定律的观点——一个宏观量的输送通量等价于这个宏观量的梯度湍流输送通量。热力和动力过程间的耦合原理认为,一个宏观量的输送通量包括这个量的梯度湍流输送通量和速度耦合输送通量两部分。因此,能量和物质的垂直输送通量除了相应物理量梯度造成的湍流输送外,还应包括垂直速度耦合效应,即辐散或辐合运动造成的耦合效应。在一个很宽的尺度范围内,地表面的空间特征是非均匀的。下垫面非均匀性造成的对流运动将引起大气的辐散或辐合运动。这可能是导致地表能量收支不平衡的重要原因之一。垂直速度对垂直湍流输送的交叉耦合效应为非均匀下垫面大气边界层理论的发展,并为克服地表能量收支不平衡问题及非均匀下垫面大气边界层参数化遇到的困难提供了可能的线索。     

Resolved-scale turbulence in the atmospheric surface layer from a large eddy simulation

Large eddy simulation has encountered difficulties in handling turbulence in the atmospheric surface layer due to deficiencies in sub-grid scale models. This paper addresses the possibility of resolving the turbulence in the upper part of the surface layer by a low-aspect ratio of grid spacing. Results show that resolved-scale shear stresses dominate over the sub-grid scale components so that effects due to the sub-grid scale model can be ignored in this region. The effects of the lower boundary condition on the resolved-scale turbulence in the upper part of the surface layer are discussed. It is concluded that the normalized mean velocity shear and resolved turbulence in the upper part of the surface layer are not affected by the specification of the lower boundary condition. In addition, the present work proposes a new independent model parameter, the Smagorinsky Reynolds Number (Re_SM), and demonstrates that this number determines the resolved turbulence in the upper part of the surface layer.     

Large-Eddy Simulation of Katabatic Flows

A large-eddy simulation model with rotated coordinates and an open boundary is used to simulate the characteristics of katabatic flows over simple terrain. Experiments examine the effects of cross winds on the development of the slope-flow boundary layer for a steep (20°) slope and the role of drainage winds in preventing turbulence collapse on a gentle slope (1°). For the steep flow cases, comparisons between model average boundary-layer velocity, temperature deficit, and turbulence kinetic energy budget terms and tower observations show reasonable agreement. Results for different cross slope winds show that as the cross slope winds increase, the slope flow deepens faster and behaves more like a weakly stratified, sheared boundary layer. Analysis of the momentum budget shows that near the surface the flow is maintained by a balance between downslope buoyancy forcing and vertical turbulence flux from surface drag. Above the downslope jet, the turbulence vertical momentum flux reverses sign and acceleration of the flow by buoyancy is controlled by horizontal advection of slower moving ambient air. The turbulence budget is dominated by a balance between shear production and eddy dissipation, however, buoyancy and pressure transport both are significant in reducing the strength of turbulence above the jet. Results from the gentle slope case show that even a slight terrain variation can lead to significant drainage winds. Comparison of the gentle slope case with a flat terrain simulation indicates that drainage winds can effectively prevent the formation of very stable boundary layers, at least near the top of sloping terrain.     

Variability and Maintenance of Turbulence in the Very Stable Boundary Layer

The relationship of turbulence quantities to mean flow quantities, such as the Richardson number, degenerates substantially for strong stability, at least in those studies that do not place restrictions on minimum turbulence or non-stationarity. This study examines the large variability of the turbulence for very stable conditions by analyzing four months of turbulence data from a site with short grass. Brief comparisons are made with three additional sites, one over short grass on flat terrain and two with tall vegetation in complex terrain. For very stable conditions, any dependence of the turbulence quantities on the mean wind speed or bulk Richardson number becomes masked by large scatter, as found in some previous studies. The large variability of the turbulence quantities is due to random variations and other physical influences not represented by the bulk Richardson number. There is no critical Richardson number above which the turbulence vanishes. For very stable conditions, the record-averaged vertical velocity variance and the drag coefficient increase with the strength of the submeso motions (wave motions, solitary waves, horizontal modes and numerous more complex signatures). The submeso motions are on time scales of minutes and not normally considered part of the mean flow. The generation of turbulence by such unpredictable motions appears to preclude universal similarity theory for predicting the surface stress for very stable conditions. Large variation of the stress direction with respect to the wind direction for the very stable regime is also examined. Needed additional work is noted.