Wind-Turbine Wakes in a Convective Boundary Layer: A Wind-Tunnel Study

Thermal stability changes the properties of the turbulent atmospheric boundary layer, and in turn affects the behaviour of wind-turbine wakes. To better understand the effects of thermal stability on the wind-turbine wake structure, wind-tunnel experiments were carried out with a simulated convective boundary layer (CBL) and a neutral boundary layer. The CBL was generated by cooling the airflow to 12–15 °C and heating up the test section floor to 73–75 °C. The freestream wind speed was set at about 2.5 m s^?1, resulting in a bulk Richardson number of ?0.13. The wake of a horizontal-axis 3-blade wind-turbine model, whose height was within the lowest one third of the boundary layer, was studied using stereoscopic particle image velocimetry (S-PIV) and triple-wire (x-wire/cold-wire) anemometry. Data acquired with the S-PIV were analyzed to characterize the highly three-dimensional turbulent flow in the near wake (0.2–3.2 rotor diameters) as well as to visualize the shedding of tip vortices. Profiles of the mean flow, turbulence intensity, and turbulent momentum and heat fluxes were measured with the triple-wire anemometer at downwind locations from 2–20 rotor diameters in the centre plane of the wake. In comparison with the wake of the same wind turbine in a neutral boundary layer, a smaller velocity deficit (about 15 % at the wake centre) is observed in the CBL, where an enhanced radial momentum transport leads to a more rapid momentum recovery, particularly in the lower part of the wake. The velocity deficit at the wake centre decays following a power law regardless of the thermal stability. While the peak turbulence intensity (and the maximum added turbulence) occurs at the top-tip height at a downwind distance of about three rotor diameters in both cases, the magnitude is about 20 % higher in the CBL than in the neutral boundary layer. Correspondingly, the turbulent heat flux is also enhanced by approximately 25 % in the lower part of the wake, compared to that in the undisturbed CBL inflow. This study represents the first controlled wind-tunnel experiment to study the effects of the CBL on wind-turbine wakes. The results on decreased velocity deficit and increased turbulence in wind-turbine wakes associated with atmospheric thermal stability are important to be taken into account in the design of wind farms, in order to reduce the impact of wakes on power output and fatigue loads on downwind wind turbines.     

Impact of the Diurnal Cycle of the Atmospheric Boundary Layer on Wind-Turbine Wakes: A Numerical Modelling Study

The wake characteristics of a wind turbine for different regimes occurring throughout the diurnal cycle are investigated systematically by means of large-eddy simulation. Idealized diurnal cycle simulations of the atmospheric boundary layer are performed with the geophysical flow solver EULAG over both homogeneous and heterogeneous terrain. Under homogeneous conditions, the diurnal cycle significantly affects the low-level wind shear and atmospheric turbulence. A strong vertical wind shear and veering with height occur in the nocturnal stable boundary layer and in the morning boundary layer, whereas atmospheric turbulence is much larger in the convective boundary layer and in the evening boundary layer. The increased shear under heterogeneous conditions changes these wind characteristics, counteracting the formation of the night-time Ekman spiral. The convective, stable, evening, and morning regimes of the atmospheric boundary layer over a homogeneous surface as well as the convective and stable regimes over a heterogeneous surface are used to study the flow in a wind-turbine wake. Synchronized turbulent inflow data from the idealized atmospheric boundary-layer simulations with periodic horizontal boundary conditions are applied to the wind-turbine simulations with open streamwise boundary conditions. The resulting wake is strongly influenced by the stability of the atmosphere. In both cases, the flow in the wake recovers more rapidly under convective conditions during the day than under stable conditions at night. The simulated wakes produced for the night-time situation completely differ between heterogeneous and homogeneous surface conditions. The wake characteristics of the transitional periods are influenced by the flow regime prior to the transition. Furthermore, there are different wake deflections over the height of the rotor, which reflect the incoming wind direction.     

A Numerically Efficient Parametrization of Turbulent Wind-Turbine Flows for Different Thermal Stratifications

The wake characteristics of a wind turbine in a turbulent atmospheric boundary layer under different thermal stratifications are investigated by means of large-eddy simulation with the geophysical flow solver EULAG. The turbulent inflow is based on a method that imposes the spectral energy distribution of a neutral boundary-layer precursor simulation, the turbulence-preserving method. This method is extended herein to make it applicable for different thermal stratification regimes (convective, stable, neutral) by including suitable turbulence assumptions, which are deduced from velocity fields of a diurnal-cycle precursor simulation. The wind-turbine-wake characteristics derived from simulations that include the parametrization result in good agreement with diurnal-cycle-driven wind-turbine simulations. Furthermore, different levels of accuracy are tested in the parametrization assumptions, representing the thermal stratification. These range from three-dimensional matrices of the precursor-simulation wind field to individual values. The resulting wake characteristics are similar, even for the simplest parametrization set-up, making the diurnal-cycle precursor simulation non-essential for the wind-turbine simulations. Therefore, the proposed parametrization results in a computationally fast, simple, and efficient tool for analyzing the effects of different thermal stratifications on wind-turbine wakes by means of large-eddy simulation.     

Turbulent Flow Properties Around a Staggered Wind Farm

The fundamental properties of turbulent flow around a perfectly staggered wind farm are investigated in a wind tunnel. The wind farm consisted of a series of 10 rows by 2–3 columns of miniature wind turbines spaced 5 and 4 rotor diameters in the streamwise and spanwise directions respectively. It was placed in a boundary-layer flow developed over a smooth surface under thermally neutral conditions. Cross-wire anemometry was used to obtain high resolution measurements of streamwise and vertical velocity components at various locations within and above the wind farm. The results show that the staggered configuration is more efficient in terms of momentum transfer from the background flow to the turbines compared to the case of an aligned wind turbine array under similar turbine separations in the streamwise and spanwise directions. This leads to improved power output of the overall wind farm. A simplified analysis suggests that the difference in power output between the two configurations is on the order of 10%. The maximum levels of turbulence intensity in the staggered wind farm were found to be very similar to that observed in the wake of a single wind turbine, differing substantially with that observed in an aligned configuration with similar spacing. The dramatic changes in momentum and turbulence characteristics in the two configurations show the importance of turbine layout in engineering design. Lateral homogenization of the turbulence statistics above the wind farm allows for the development of simple parametrizations for the adjustment of flow properties, similar to the case of a surface roughness transition. The development of an internal boundary layer was observed at the upper edge of the wind farm within which the flow statistics are affected by the superposition of the ambient flow and the flow disturbance induced by the wind turbines. The adjustment of the flow in this layer is much slower in the staggered situation (with respect to its aligned counterpart), implying a change in the momentum/power available at turbine locations. Additionally, power spectra of the streamwise and vertical velocity components indicate that the signature of each turbine-tip vortex structure persists to locations deep within the wind farm.     

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.     

Simulation of Turbulent Flow Inside and Above Wind Farms: Model Validation and Layout Effects

A recently-developed large-eddy simulation framework is validated and used to investigate turbulent flow within and above wind farms under neutral conditions. Two different layouts are considered, consisting of thirty wind turbines occupying the same total area and arranged in aligned and staggered configurations, respectively. The subgrid-scale (SGS) turbulent stress is parametrized using a tuning-free Lagrangian scale-dependent dynamic SGS model. The turbine-induced forces are modelled using two types of actuator-disk models: (a) the ‘standard’ actuator-disk model (ADM-NR), which calculates only the thrust force based on one-dimensional momentum theory and distributes it uniformly over the rotor area; and (b) the actuator-disk model with rotation (ADM-R), which uses blade-element momentum theory to calculate the lift and drag forces (that produce both thrust and rotation), and distributes them over the rotor disk based on the local blade and flow characteristics. Validation is performed by comparing simulation results with turbulence measurements collected with hot-wire anemometry inside and above an aligned model wind farm placed in a boundary-layer wind tunnel. In general, the ADM-R model yields improved predictions compared with the ADM-NR in the wakes of all the wind turbines, where including turbine-induced flow rotation and accounting for the non-uniformity of the turbine-induced forces in the ADM-R appear to be important. Another advantage of the ADM-R model is that, unlike the ADM-NR, it does not require a priori specification of the thrust coefficient (which varies within a wind farm). Finally, comparison of simulations of flow through both aligned and staggered wind farms shows important effects of farm layout on the flow structure and wind-turbine performance. For the limited-size wind farms considered in this study, the lateral interaction between cumulated wakes is stronger in the staggered case, which results in a farm wake that is more homogeneous in the spanwise direction, thus resembling more an internal boundary layer. Inside the staggered farm, the relatively longer separation between consecutive downwind turbines allows the wakes to recover more, exposing the turbines to higher local wind speeds (leading to higher turbine efficiency) and lower turbulence intensity levels (leading to lower fatigue loads), compared with the aligned farm. Above the wind farms, the area-averaged velocity profile is found to be logarithmic, with an effective wind-farm aerodynamic roughness that is larger for the staggered case.     

日间对流边界层中的非局地动量混合

日间对流边界层最显著的结构特征是在热力作用下所形成的组织化对流。与小尺度湍涡不同的是，组织化对流具有边界层尺度的垂直相干性，可实现垂直贯穿边界层的非局地物质和能量传输。本文针对对流边界层中的动量混合，探究组织化对流对动量输送的贡献。以高精度大涡模拟数据为研究资料，通过傅里叶变换、本征正交分解和经验模态分解3种滤波方法，分离组织化对流和背景湍涡，计算与两者相关的非局地和局地动量通量，发现与组织化对流相关的非局地动量通量是总通量的重要组成部分，并主导混合层中的垂直动量输送。而后，基于协谱和相位谱分析，探究组织化对流的空间结构对动量传输的影响，发现在热力主导的不稳定环境中，单体型环流结构对动量的传输效率较低。而在风切较强的近中性环境中，滚涡型组织化结构可使垂直和水平流向扰动速度的相位差减小，从而提升动量传输效率。研究结果表明，边界层方案需要包含非局地动量通量项，其参数化应考虑整体稳定度对传输效率的影响。     

A Numerical Study of Wind-Turbine Wakes for Three Atmospheric Stability Conditions

The effects of atmospheric stability on wind-turbine wakes are studied via large-eddy simulations. Three stability conditions are considered: stable, neutral, and unstable, with the same geostrophic wind speed aloft and the same Coriolis frequency. Both a single 5-MW turbine and a wind farm of five turbines are studied. The single-turbine wake is strongly correlated with stability, in terms of velocity deficit, turbulence kinetic energy (TKE) and temperature distribution. Because of the Coriolis effect, the wake shape deviates from a Gaussian distribution. For the wind-farm simulations, the separation of the core region and outer region is clear for the stable and neutral cases, but less distinct for the unstable case. The unstable case exhibits strong horizontal variations in wind speed. Local accelerations such as related to aisle jets are also observed, whose features depend on stability. The added TKE in the wind farm increases with stability. The highest power extraction and lowest power deficit are observed for the unstable case.     

Observing and Simulating Wind-Turbine Wakes During the Evening Transition

Wind-turbine-wake evolution during the evening transition introduces variability to wind-farm power production at a time of day typically characterized by high electricity demand. During the evening transition, the atmosphere evolves from an unstable to a stable regime, and vertical stratification of the wind profile develops as the residual planetary boundary layer decouples from the surface layer. The evolution of wind-turbine wakes during the evening transition is examined from two perspectives: wake observations from single turbines, and simulations of multiple turbine wakes using the mesoscale Weather Research and Forecasting (WRF) model. Throughout the evening transition, the wake’s wind-speed deficit and turbulence enhancement are confined within the rotor layer when the atmospheric stability changes from unstable to stable. The height variations of maximum upwind-downwind differences of wind speed and turbulence intensity gradually decrease during the evening transition. After verifying the WRF-model-simulated upwind wind speed, wind direction and turbulent kinetic energy profiles with observations, the wind-farm-scale wake evolution during the evening transition is investigated using the WRF-model wind-farm parametrization scheme. As the evening progresses, due to the presence of the wind farm, the modelled hub-height wind-speed deficit monotonically increases, the relative turbulence enhancement at hub height grows by 50%, and the downwind surface sensible heat flux increases, reducing surface cooling. Overall, the intensifying wakes from upwind turbines respond to the evolving atmospheric boundary layer during the evening transition, and undermine the power production of downwind turbines in the evening.     

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.     

Fractional Flow Speed-Up from Porous Windbreaks for Enhanced Wind-Turbine Power

The potential for porous windbreaks to enhance wind-turbine power production is studied using linearized theory and wind-tunnel experiments. Results suggest that windbreaks have the potential to substantially increase power production, while lowering mean shear, and leading to negligible changes in turbulence intensity. The fractional increase in turbine power output is found to vary roughly linearly with windbreak height, where a windbreak 10% the height of the turbine hub increases power by around 10%. Wind-tunnel experiments with a windbreak imposed beneath a turbulent boundary layer show the linearized predictions to be in good agreement with particle-image-velocimetry data. Power measurements from a model turbine further corroborate predictions in power increase. Moreover, the wake of the windbreak showed a significant interaction with the turbine wake, which may inform windbreak use in large wind farms. Power measurements from a second turbine downwind of the first with its own windbreak show that the net effect for multiple turbines is dependent on windbreak height.     

Conditionally Averaged Large-Scale Motions in the Neutral Atmospheric Boundary Layer: Insights for Aeolian Processes

Aeolian erosion of flat, arid landscapes is induced (and sustained) by the aerodynamic surface stress imposed by flow in the atmospheric surface layer. Conceptual models typically indicate that sediment mass flux, Q (via saltation or drift), scales with imposed aerodynamic stress raised to some exponent, n, where \(n > 1\). This scaling demonstrates the importance of turbulent fluctuations in driving aeolian processes. In order to illustrate the importance of surface-stress intermittency in aeolian processes, and to elucidate the role of turbulence, conditional averaging predicated on aerodynamic surface stress has been used within large-eddy simulation of atmospheric boundary-layer flow over an arid, flat landscape. The conditional-sampling thresholds are defined based on probability distribution functions of surface stress. The simulations have been performed for a computational domain with \(\approx 25 H\) streamwise extent, where H is the prescribed depth of the neutrally-stratified boundary layer. Thus, the full hierarchy of spatial scales are captured, from surface-layer turbulence to large- and very-large-scale outer-layer coherent motions. Spectrograms are used to support this argument, and also to illustrate how turbulent energy is distributed across wavelengths with elevation. Conditional averaging provides an ensemble-mean visualization of flow structures responsible for erosion ‘events’. Results indicate that surface-stress peaks are associated with the passage of inclined, high-momentum regions flanked by adjacent low-momentum regions. Fluid in the interfacial shear layers between these adjacent quasi-uniform momentum regions exhibits high streamwise and vertical vorticity.     

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.     

Experiments on scalar dispersion within a model plant canopy part I: The turbulence structure

This is the first of a series of three papers describing experiments on the dispersion of trace heat from elevated line and plane sources within a model plant canopy in a wind tunnel. Here we consider the wind field and turbulence structure. The model canopy consisted of bluff elements 60 mm high and 10 mm wide in a diamond array with frontal area index 0.23; streamwise and vertical velocity components were measured with a special three-hot-wire anemometer designed for optimum performance in flows of high turbulence intensity. We found that:

1. The momentum flux due to spatial correlations between time-averaged streamwise and vertical velocity components (the dispersive flux) was negligible, at heights near and above the top of the canopy.
2. In the turbulent energy budget, turbulent transport was a major loss (of about one-third of local production) near the top of the canopy, and was the principal gain mechanism lower down. Wake production was greater than shear production throughout the canopy. Pressure transport just above the canopy, inferred by difference, appeared to be a gain in approximate balance with the turbulent transport loss.
3. In the shear stress budget, wake production was negligible. The role of turbulent transport was equivalent to that in the turbulent energy budget, though smaller.
4. Velocity spectra above and within the canopy showed the dominance of large eddies occupying much of the boundary layer and moving downstream with a height-independent convection velocity. Within the canopy, much of the vertical but relatively little of the streamwise variance occurred at frequencies characteristic of wake turbulence.
5. Quadrant analysis of the shear stress showed only a slight excess of sweeps over ejections near the top of the canopy, in contrast with previous studies. This is a result of improved measurement techniques; it suggests some reappraisal of inferences previously drawn from quadrant analysis.

     

The Impact of Landscape Fragmentation on Atmospheric Flow: A Wind-Tunnel Study

Landscape discontinuities such as forest edges play an important role in determining the characteristics of the atmospheric flow by generating increased turbulence and triggering the formation of coherent tree-scale structures. In a fragmented landscape, consisting of surfaces of different heights and roughness, the multiplicity of edges may lead to complex patterns of flow and turbulence that are potentially difficult to predict. Here, we investigate the effects of different levels of forest fragmentation on the airflow. Five gap spacings (of length approximately 5h, 10h, 15h, 20h, 30h, where h is the canopy height) between forest blocks of length 8.7h, as well as a reference case consisting of a continuous forest after a single edge, were investigated in a wind tunnel. The results reveal a consistent pattern downstream from the first edge of each simulated case, with the streamwise velocity component at tree top increasing and turbulent kinetic energy decreasing as gap size increases, but with overshoots in shear stress and turbulent kinetic energy observed at the forest edges. As the gap spacing increases, the flow appears to change monotonically from a flow over a single edge to a flow over isolated forest blocks. The apparent roughness of the different fragmented configurations also decreases with increasing gap size. No overall enhancement of turbulence is observed at any particular level of fragmentation.     

On Wind Forces in the Forest-Edge Region During Extreme-Gust Passages and Their Implications for Damage Patterns

We use large-eddy simulations (LES) to investigate the impact of stable stratification on gravity-wave excitation and energy extraction in a large wind farm. To this end, the development of an equilibrium conventionally neutral boundary layer into a stable boundary layer over a period of 8 h is considered, using two different cooling rates. We find that turbulence decay has considerable influence on the energy extraction at the beginning of the boundary-layer transition, but afterwards, energy extraction is dominated by geometrical and jet effects induced by an inertial oscillation. It is further shown that the inertial oscillation enhances gravity-wave excitation. By comparing LES results with a simple one-dimensional model, we show that this is related to an interplay between wind-farm drag, variations in the Froude number and the dispersive effects of vertically-propagating gravity waves. We further find that the pressure gradients induced by gravity waves lead to significant upstream flow deceleration, reducing the average turbine output compared to a turbine in isolated operation. This leads us to the definition of a non-local wind-farm efficiency, next to a more standard wind-farm wake efficiency, and we show that both can be of the same order of magnitude. Finally, an energy flux analysis is performed to further elucidate the effect of gravity waves on the flow in the wind farm.     

Wind-Tunnel Simulation of the Wake of a Large Wind Turbine in a Stable Boundary Layer: Part 2, the Wake Flow

Measurements have been made in the wake of a model wind turbine in both a neutral and a stable atmospheric boundary layer, in the EnFlo stratified-flow wind tunnel, between 0.5 and 10 rotor diameters from the turbine, as part of an investigation of wakes in offshore winds. In the stable case the velocity deficit decreased more slowly than in the neutral case, partly because the boundary-layer turbulence levels are lower and the consequentially reduced level of mixing, an ‘indirect’ effect of stratification. A correlation for velocity deficit showed the effect of stratification to be the same over the whole of the measured extent, following a polynomial form from about five diameters. After about this distance (for the present stratification) the vertical growth of the wake became almost completely suppressed, though with an increased lateral growth; the wake in effect became ‘squashed’, with peaks of quantities occurring at a lower height, a ‘direct’ effect of stratification. Generally, the Reynolds stresses were lower in magnitude, though the effect of stratification was larger in the streamwise fluctuation than on the vertical fluctuations. The vertical heat flux did not change much from the undisturbed level in the first part of the wake, but became much larger in the later part, from about five diameters onwards, and exceeded the surface level at a point above hub height.     

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.     

Experimental Study on the Wake Meandering Within a Scale Model Wind Farm Subject to a Wind-Tunnel Flow Simulating an Atmospheric Boundary Layer

The phenomenon of meandering of the wind-turbine wake comprises the motion of the wake as a whole in both horizontal and vertical directions as it is advected downstream. The oscillatory motion of the wake is a crucial factor in wind farms, because it increases the fatigue loads, and, in particular, the yaw loads on downstream turbines. To address this phenomenon, experimental investigations are carried out in a wind-tunnel flow simulating an atmospheric boundary layer with the Coriolis effect neglected. A \(3 \times 3\) scaled wind farm composed of three-bladed rotating wind-turbine models is subject to a neutral boundary layer over a slightly-rough surface, i.e. corresponding to offshore conditions. Particle-image-velocimetry measurements are performed in a horizontal plane at hub height in the wakes of the three wind turbines occupying the wind-farm centreline. These measurements allow determination of the wake centrelines, with spectral analysis indicating the characteristic wavelength of the wake-meandering phenomenon. In addition, measurements with hot-wire anemometry are performed along a vertical line in the wakes of the same wind turbines, with both techniques revealing the presence of wake meandering behind all three turbines. The spectral analysis performed with the spatial and temporal signals obtained from these two measurement techniques indicates a Strouhal number of \(\approx 0.20 - 0.22\) based on the characteristic wake-meandering frequency, the rotor diameter and the flow speed at hub height.     

Analytical Model for Mean Flow and Fluxes of Momentum and Energy in Very Large Wind Farms

As wind-turbine arrays continue to be installed and the array size continues to grow, there is an increasing need to represent very large wind-turbine arrays in numerical weather prediction models, for wind-farm optimization, and for environmental assessment. We propose a simple analytical model for boundary-layer flow in fully-developed wind-turbine arrays, based on the concept of sparsely-obstructed shear flows. In describing the vertical distribution of the mean wind speed and shear stress within wind farms, our model estimates the mean kinetic energy harvested from the atmospheric boundary layer, and determines the partitioning between the wind power captured by the wind turbines and that absorbed by the underlying land or water. A length scale based on the turbine geometry, spacing, and performance characteristics, is able to estimate the asymptotic limit for the fully-developed flow through wind-turbine arrays, and thereby determine if the wind-farm flow is fully developed for very large turbine arrays. Our model is validated using data collected in controlled wind-tunnel experiments, and its usefulness for the prediction of wind-farm performance and optimization of turbine-array spacing are described. Our model may also be useful for assessing the extent to which the extraction of wind power affects the land–atmosphere coupling or air–water exchange of momentum, with implications for the transport of heat, moisture, trace gases such as carbon dioxide, methane, and nitrous oxide, and ecologically important oxygen.