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.     

Radiative Processes in the Stable Boundary Layer: Part II. The Development of the Nocturnal Boundary Layer

The interaction between radiation and turbulence in the stable boundary layer over land is explored using an idealized model, with a focus on the surface layer after the evening transition. It is shown that finer vertical resolution is required in transitional boundary layers than in developed ones. In very light winds radiative cooling determines the temperature profile, even if similarity functions without a critical Richardson number are used; standard surface similarity theory applied over thick layers then yields poor forecasts of near-surface air temperatures. These points are illustrated with field data. Simulations of the developing nocturnal boundary layer are used to explore the wider role of radiation. Comparatively, radiation is less significant within the developed stable boundary layer than during the transition; although, as previous studies have found, it remains important towards the top of the stable layer and in the residual layer. Near the ground, reducing the surface emissivity below one is found to yield modest relative radiative warming rather than intense cooling, which reduces the potential importance of radiation in the developed surface layer. The profile of the radiative heating rate may be strongly dependent on other processes, leading to quite varied behaviour.     

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.     

Wind-Tunnel Simulation of Approximately Horizontally Homogeneous Stable Atmospheric Boundary Layers

Boundary-Layer Meteorology - Two cases of an overlying inversion imposed on a stable boundary layer are investigated, extending the work of Hancock and Hayden (Boundary-Layer Meteorol...     

Wind-Tunnel Simulation of Weakly and Moderately Stable Atmospheric Boundary Layers

The simulation of horizontally homogeneous boundary layers that have characteristics of weakly and moderately stable atmospheric flow is investigated, where the well-established wind engineering practice of using ‘flow generators’ to provide a deep boundary layer is employed. Primary attention is given to the flow above the surface layer, in the absence of an overlying inversion, as assessed from first- and second-order moments of velocity and temperature. A uniform inlet temperature profile ahead of a deep layer, allowing initially neutral flow, results in the upper part of the boundary layer remaining neutral. A non-uniform inlet temperature profile is required but needs careful specification if odd characteristics are to be avoided, attributed to long-lasting effects inherent of stability, and to a reduced level of turbulent mixing. The first part of the wind-tunnel floor must not be cooled if turbulence quantities are to vary smoothly with height. Closely horizontally homogeneous flow is demonstrated, where profiles are comparable or closely comparable with atmospheric data in terms of local similarity and functions of normalized height. The ratio of boundary-layer height to surface Obukhov length, and the surface heat flux, are functions of the bulk Richardson number, independent of horizontal homogeneity. Surface heat flux rises to a maximum and then decreases.     

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.     

Radiative Processes in the Stable Boundary Layer: Part I. Radiative Aspects

The structure of the radiatively dominated stable boundary layer is analysed using idealized calculations at high vertical and spectral resolution. The temperature profile of a nocturnal radiative boundary layer, developing after the evening transition, is found to be well described in terms of radiative cooling to the surface, although radiative exchanges within the atmosphere become increasingly important with time. The treatment of non-black surfaces is discussed in some detail and it is shown that the effect of reducing the surface emissivity is to decrease rather than to increase the radiative cooling rate in the surface layer. It is also argued that an accurate assessment of the impact of non-black surfaces requires careful attention to the spectral and directional characteristics of the surface emissivity. A polar nocturnal boundary layer, developing above snow-covered ground, is simulated and found to reach a slowly evolving state characterized by a strong radiative divergence near the surface that is comparable to observed values. Radiative boundary layers are characterized by large temperature gradients near the surface. An erratum to this article can be found at     

Flux-profile Relationships for Wind Speed and Temperature in the Stable Atmospheric Boundary Layer

Wind and temperature profiles in the stable boundary layer were analyzed in the context of MoninObukhov similarity. The measurements were made on a 60-m tower in Kansas during October 1999 (CASES-99). Fluxprofile relationships, obtained from these measurements in their integral forms, were established for wind speed and temperature. Use of the integral forms eliminates the uncertainty and accuracy issues resulting from gradient computations. The corresponding stability functions, which were nearly the same for momentum and virtual sensible heat, were found to exhibit different features under weakly stable conditions compared to those under strongly stable conditions. The gradient stability functions were found to be linear, namely _m = 1+ 5.8 and _h = 1 + 5.4 up to a limit of the MoninObukhov stability parameter = 0.8; this is consistent with earlier findings. However, for stronger stabilities beyond a transition range, both functions were observed gradually to approach a constant, with a value of approximately 7. To link these two distinct regimes, a general but pliable functional form with only two parameters is proposed for the stability functions, covering the entire stability range from neutral to very stable conditions.     

Wind-Tunnel and Numerical Simulations of the Coastal Thermal Internal Boundary Layer

Wind-tunnel experiments in a thermally stratified wind tunnel and direct numerical simulations were performed to simulate the thermal internal boundary layer (TIBL) that developed over a coastal area in a sea-breeze flow. The results of the simulations were analyzed to investigate turbulence structure in the TIBL. To study the effects of the atmospheric stability over the sea on the TIBL, two vertical profiles of temperature were created in the upstream portion of the wind-tunnel experiment and the direct numerical simulation. Turbulence statistics of the TIBL changed significantly according to the temperature profile over the sea, indicating that the stability of the flow over the sea has a significant effect on the structure and turbulence characteristics of the TIBL. Furthermore, the TIBL heights were estimated from the vertical profiles of the local Richardson number. The estimated TIBL heights agreed with those predicted by a pre-existing relation, suggesting that both the wind-tunnel experiment and the direct numerical simulation accurately reproduced the growth of the TIBL.     

对流边界层中泡状结构的大涡模拟研究

本文提出“连续垂直运动区”的概念，对边界层中的对流泡状运动进行了重新定义。由此将对流边界层划分为上升泡区、下沉泡区和环境气流区，并利用大涡模拟提供的对流边界层数值模拟结果研究这种泡状运动的结构。研究结果较好地解释了一些有关泡状运动结构方面的似乎相互矛盾的观测事实，并揭示了对流泡状运动的一些新的特征。     

Assessment of Gradient-Based Similarity Functions in the Stable Boundary Layer Derived from a Large-Eddy Simulation

Most of our knowledge on forest-edge flows comes from numerical and wind-tunnel experiments where canopies are horizontally homogeneous. To investigate the impact of tree-scale heterogeneities (\({>}1\) m) on the edge-flow dynamics, the flow in an inhomogeneous forest edge on Falster island in Denmark is investigated using large-eddy simulation. The three-dimensional forest structure is prescribed in the model using high resolution helicopter-based lidar scans. After evaluating the simulation against wind measurements upwind and downwind of the forest leading edge, the flow dynamics are compared between the scanned forest and an equivalent homogeneous forest. The simulations reveal that forest inhomogeneities facilitate flow penetration into the canopy from the edge, inducing important dispersive fluxes in the edge region as a consequence of the flow spatial variability. Further downstream from the edge, the forest inhomogeneities accentuate the canopy-top turbulence and the skewness of the wind-velocity components while the momentum flux remains unchanged. This leads to a lower efficiency in the turbulent transport of momentum within the canopy. Dispersive fluxes are only significant in the upper canopy. Above the canopy, the mean flow is less affected by the forest inhomogeneities. The inhomogeneities induce an increase in the mean wind speed that was found to be equivalent to a decrease in the aerodynamic height of the canopy. Overall, these results highlight the importance of forest inhomogeneities when looking at canopy–atmosphere exchanges in forest-edge regions.     

The Nighttime Accelerations of the Wind in the Boundary Layer

Blackadar’s inertial relaxation of the nighttime boundary layer is modified to account for the finite scale of the pressure gradient normal to the jet. Even though this horizontal dimension may be several thousand times the depth of the daytime convective layer, it severely reduces the period of the free oscillation in the relaxation process and replaces the harmonic acceleration of the jet with a linear growth rate.     

Turbulence Characteristics Of The Stable Boundary Layer Over A Mid-Latitude Glacier. Part Ii: Pure Katabatic Forcing Conditions

Observations obtained over a glacier surface in a predominantlykatabatic flow and with a distinctwind maximum below 13-m height are presented. The data werecollected using a 13-m high profilemast and two sonic anemometers (at about 2.5-m and 10-m heights).The spectra at frequencies belowthat of the turbulence range appear to deviate considerably fromthe curves obtained by Kaimal andco-workers during the 1968 Kansas experiment. The characteristicsof these deviations are compared tothe observations of others in surface-layers disturbed by anykind of large-scale outer-layer (orinactive) turbulence. In our case the disturbances arelikely to be induced by the highmountain ridges that surround the glacier. Moreover, the deviationsobserved in the cospectra seemto result from an, as yet, unspecified interaction between theinactive outer-layer turbulenceand the local surface-layer turbulence. Near the distinctwind maximum turbulence production ceasedwhile turbulence itself did not, probably the result ofturbulence transport from other levels. Consequently, we studied thelocal similarity relations using _w instead of u_* as an alternative velocity scale. Wellbelow the wind maximum, and for relatively low stability(0< Ri_g <0.2), the flow behaves accordingto well established local-scaling similarity relationshipsin the stable boundary layer. For higherstability (Ri_g > 0.2), and near or above the wind maximum, the boundary-layer structure conforms tothat of z-less stratification suggesting that the eddy sizeis restricted by the local stability ofthe flow. In line with this we observed that the sensibleheat fluxes relate remarkably well to thelocal flow parameters.     

Modelling of the Evolving Stable Boundary Layer

A single-column model of the evolving stable boundary layer (SBL) is tested for self-similar properties of the flow and effects of ambient forcing. The turbulence closure of the model is diagnostic, based on the K-theory approach, with a semi-empirical form of the mixing length, and empirical stability functions of the Richardson number. The model results, expressed in terms of local similarity scales, are universal functions, satisfied in the entire SBL. Based on similarity expression, a realizability condition is derived for the minimum allowable turbulent heat flux in the SBL. Numerical experiments show that the development of “horse-shoe” shaped, fixed-elevation hodographs in the interior of the SBL around sunrise is controlled by effects imposed by surface thermal forcing.     

A Note on Turbulence Stationarity and Wind Persistence Within the Stable Planetary Boundary Layer

This note presents initial results of an analysis of the stationarity of turbulence kinetic energy and the persistence of winds within the stable boundary layer (SBL). Measurements were made at 1.5 and 11 m above ground level from 0100 to 0600 local time on five nights during the JORNADA field experiment. The average stationarity ranged from about 160 to about 570 s. Wind persistence ranged from about ± 40° (3-min average) to about ± 36° (30-min average) on a weakly stable night, and from about ± 40° (3-min average) to about ± 27° (30-min average) on an strongly stable night. It is shown that, at 1.5 m, which we take to be within the surface layer, the average duration of stationarity of turbulent kinetic energy tends to correlate with the kurtosis of the heat flux; however, at 11 m, which we take to be outside of the surface layer, this correlation is poorly approximated.     

The Height Correction of Similarity Functions in the Stable Boundary Layer

Empirical similarity functions of the Richardson number, obtained from bin-averaged data in the lower part of the stable boundary layer, show an undesired dependence on height at which the observations are collected. A correction of this flaw is proposed and tested by employing the neutral mixing length l _o as a similarity scale for height. The function of height describing l _o is assumed to be linear in the surface layer, and approaching a specified value with increasing height. The modification does not alter the dependence of similarity functions on the Richardson number, and is shown to be supported by the Cooperative Atmospheric-Surface Exchange Study-1999 (CASES-99) data.