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.     

Fluctuations of line integrated concentrations across plume diffusion in grid generated turbulence and in shear flows

The fluctuations of the instantaneous values of line integrated concentrations across plumes from point sources diffusing in turbulent shear flows, and in grid generated turbulence, have been studied experimentally using a fast response system which measured the attenuation of the intensity of an infrared beam crossing the plume. Analysis of the measurements show that the dimensionless statistical properties of the fluctuations at different distances from the source at each flow are approximately similar, in the sense that they depend primarily on the relative off-center location of the line of integration and almost independent of the distance from the source and the nature of the turbulence in the flows, as long as the characteristic length of the mean plume is not large compared to the size of the large eddies. The characteristic time of the fluctuations, on the other hand, was found to grow with the distance from the source and the autocorrelations of the fluctuations, particularly in the case of a plume diffusing in grid generated turbulence, were it found to be proportional to the lateral size of the mean plume. A—5/3 decay law of the power spectrum of the fluctuations was observed in the low frequency range which corresponds to the scale of the large eddies. The decay of the fluctuations caused by smaller eddies was much faster, as expected.     

An estimate of space-time correlations

Laboratory measurements of the autocorrelation and space-time correlations for probe separations alined with the mean flow are used to test a hypothesis of Pielke and Panofsky (1970) which relates these measures by means of an empirical decay parameter taken from coherence data. The direct laboratory measurements of the space-time correlations are in good agreement with the functions estimated using the method of Pielke and Panofsky (1970). However, the decay parameters implied for the laboratory measurements are much smaller than those reported for atmospheric turbulence.     

Role of Shear and the Inversion Strength During Sunset Turbulence Over Land: Characteristic Length Scales

The role of shear and inversion strength on the decay of convective turbulence during sunset over land is systematically studied by means of large-eddy simulations. Different decay rates have been found for the vertical and horizontal velocity fluctuations, resulting in an increase of the anisotropy for all the studied cases. Entrainment, which persists during the decay process, favours the appearance of vertical upward movements associated with a conversion from kinetic to potential energy. Particular attention is paid to the evolution of the characteristic length scale of the various turbulent variables during this process. The length scale evolution is found to depend on the wind shear characteristics, but not on the strength of the inversion. In general the length scales of the variables grow during decay because small-scale fluctuations dissipate faster than large-scale fluctuations. Only the length scale of the vertical velocity component remains nearly constant during decay. Spectral analysis of the variance budgets shows that pressure correlations are responsible for fixing this length scale, effectively compensating the strong but oscillating influence of buoyancy. In the shear cases, after an initial period of growth, the length scales start to decrease once the buoyancy-generated variance has sufficiently subsided. Also here the effect of pressure redistribution is crucial, as it transfers the spectral influence of shear to the other velocity components.     

Horizontal, Two Point Coherence for Separations Greater Than the Measurement Height

Wind speed measurements from the test site at Rutherford Appleton Laboratory have been evaluated with respect to the spatial coherence function. The experimental arrangement provides coherence information for separation distances of 62, 80 and 102 m. These are at least three times greater than the measurement heights of 18 m and 18.7 m. Based on these experimental data and data published in the literature, different theoretical formulations are compared and a new, but simple, model for longitudinal and lateral coherence is proposed. At large separations the turbulent wind field is not isotropic, theoretical models to describe the coherence function for such distances are not available. The new model we propose builds on the classical exponential approach. It takes into account the influence of turbulence intensity and models the angular dependence of horizontal coherence. It is found that, for constant turbulence intensity, the lateral coherence decay becomes independent of the mean wind speed.     

A Simple Model for the Afternoon and Early Evening Decay of Convective Turbulence Over Different Land Surfaces

A simple model to study the decay of turbulent kinetic energy (TKE) in the convective surface layer is presented. In this model, the TKE is dependent upon two terms, the turbulent dissipation rate and the surface buoyancy fluctuations. The time evolution of the surface sensible heat flux is modelled based on fitting functions of actual measurements from the LITFASS-2003 field campaign. These fitting functions carry an amplitude and a time scale. With this approach, the sensible heat flux can be estimated without having to solve the entire surface energy balance. The period of interest covers two characteristic transition sub-periods involved in the decay of convective boundary-layer turbulence. The first sub-period is the afternoon transition, when the sensible heat flux starts to decrease in response to the reduction in solar radiation. It is typically associated with a decay rate of TKE of approximately t ⁻² (t is time following the start of the decay) after several convective eddy turnover times. The early evening transition is the second sub-period, typically just before sunset when the surface sensible heat flux becomes negative. This sub-period is characterized by an abrupt decay in TKE associated with the rapid collapse of turbulence. Overall, the results presented show a significant improvement of the modelled TKE decay when compared to the often applied assumption of a sensible heat flux decreasing instantaneously or with a very short forcing time scale. In addition, for atmospheric modelling studies, it is suggested that the afternoon and early evening decay of sensible heat flux be modelled as a complementary error function.     

On the Turbulence in the Upper Part of the Low-Level Jet: An Experimental and Numerical Study

The characteristics of low-level jets (LLJ) observed at the “Centro de Investigacion de la Baja Atmósfera” (CIBA) site in Spain are analysed, focussing on the turbulence generated in the upper part of the jet, a feature that is still to be thoroughly understood. During the Stable Boundary Layer Experiment in Spain (SABLES) 1998, captive balloon soundings were taken intensively, and their analyses have highlighted the main characteristics of the jet’s wind and temperature structure, leading to a composite profile. There are indications that the turbulence has a minimum at the level of the wind maximum, with elevated turbulence in a layer at a height between two and three times that of the LLJ maximum, but no direct measurements of turbulence were available at these heights. In September 2001, a 100-m tower at the same site was re-instrumented to give turbulence measurements up to 96.6 m above ground level. All occurrences of LLJ below this height between September 2002 and June 2003 have been selected and significant turbulence above the LLJ has been found. Simulations with a single-column turbulence kinetic energy model have been made in order to further investigate the generation of elevated turbulence. The results correlate well with the measurements, showing that in the layer above the LLJ, where there is significant shear and weakly stable stratification, conditions are conducive to the development of turbulence.     

Wind Tunnel And Field Measurements Of Turbulent Flow In Forests. Part I: Uniformly Thinned Stands

Many forest management methods alterstand density uniformly. The effectsof such a change on the wind andturbulence regimes in the forest arecritical to a number of processes governingthe stability of the stand and itsmicroclimate. We measured wind speed andturbulence statistics with a Dantec tri-axialhot-film probe in model forests of variousdensities (31–333 trees m^-2), created byremoving whole trees in a regular pattern in awind tunnel, and compared them with similarmeasurements made with propeller anemometers insimilarly thinned plots (156–625 trees ha^-1)within a Sitka spruce stand in Scotland. The results agree well, in general, with measurements made inother such studies with diverse canopy types.The systematic variations with density and verticalleaf-area distribution (which differed betweenwind-tunnel and field trees) in our work can explainmuch of the variability shown in scaled profiles ofbasic turbulence statistics reported in theliterature. The wind tunnel and field results are shown to be in good agreement overalldespite the difference in vertical leaf-areadistribution. Within-canopy and isolated-treedrag coefficients in the wind tunnel showthat tree-scale shelter effects increase astree density increases. The measurements indicatethat turbulence in the canopy is dominated bylarge-scale structures with dimensions of the sameorder as the height of the canopy as found inother studies but suggest that inter-tree spacing also modulates the size of these structures. These structures are associated with the sweeps that dominatemomentum exchange in the canopy and it is thisfact that allows the tri-axial probe to operate sowell despite the relatively narrow range of anglesin which the wind vector is correctly measured. Theratio of streamwise periodicity of these structuresto vorticity thickness varies systematically withtree density in the range 2.7–5.1, which spans theexpected range of 3.5–5 found in a laboratorymixing-layer, suggesting that tree spacing imposes another relevant length scale. This test andothers show that the results are in agreement withthe idea that canopy turbulence resembles that of a mixing layer even though they disagree with, and challenge the linear relationship between, streamwise periodicity andshear length scale presented recently in theliterature. The measurements are also in goodoverall agreement with simple drag models presented recently by other researchers.     

Cross‐shore variations of near‐surface wind velocity and atmospheric turbulence at the land‐sea boundary during CASP

Abstract

Airborne measurements of mean wind velocity and turbulence in the atmospheric boundary layer under wintertime conditions of cold offshore advection suggest that at a height of 50 m the mean wind speed increases with offshore distance by roughly 20% over a horizontal scale of order 10 km. Similarly, the vertical gust velocity and turbulent kinetic energy decay on scales of order 3.5 km by factors of 1.5 and 3.2, respectively. The scale of cross‐shore variations in the vertical fluxes of heat and downwind momentum is also 10 km, and the momentum flux is found to be roughly constant to 300 m, whereas the heat flux decreases with height. The stability parameter, z/L (where z = 50 m and L is the local Monin‐Obukhov length), is generally small over land but may reach order one over the warm ocean. The magnitude and horizontal length scales associated with the offshore variations in wind speed and turbulence are reasonably consistent with model results for a simple roughness change, but a more sophisticated model is required to interpret the combined effects of surface roughness and heat flux contrasts between land and sea.

Comparisons between aircraft and profile‐adjusted surface measurements of wind speed indicate that Doppler biases of 1–2 m s^?1 in the aircraft data caused by surface motions must be accounted for. In addition, the wind direction measurements of the Minimet anemometer buoy deployed in CASP are found to be in error by 25 ± 5°, possibly due to a misalignment of the anemometer vane. The vertical fluxes of heat and momentum show reasonably good agreement with surface estimates based on the Minimet data.     

A wind tunnel study of turbulent flow over model hills

Detailed wind tunnel measurements have been made of mean flow and turbulence over a two-dimensional ridge and a circular hill, both having cosine-squared cross-section and maximum slope about 15 °. The measurements were made in an artificially thickened neutrally stratified boundary layer, and have been compared with results from linear models and rapid distortion theory as appropriate.Our study shows that linear theory gives generally good predictions of the mean flow on the upwind side of the hills, and especially of the flow speedup at the hill top, but that the turbulence is less well predicted. In particular, the measurements show a major increase in the vertical component of turbulence and in the shear stress on the upwind slope of both the two- and three-dimensional hills which is not predicted by either equilibrium or isotropic rapid-distortion theories, although this may be partly due to the effect of streamline curvature. Rapid-distortion theory is successful only in describing the streamwise component of turbulence in the outer region of the flow, while in the upper part of the inner region of the flow, the turbulence measurements show disagreement with both the equilibrium and the rapid-distortion theories. Our experiments also confirm that the equilibrium region is a very thin layer close to the surface, while above this region and below the outer region, there is a transitional region where all terms in the stress equation are important.The measurements over the three-dimensional hill suggest that the mean flow and turbulence are broadly similar to those over the two-dimensional ridge, but with reduced perturbation amplitudes. The major differences between the two cases are found on the upwind slope and in the wake where, respectively, horizontal divergence and convergence of the three-dimensional flow are most pronounced.     

Hurricane Wind Power Spectra, Cospectra, and Integral Length Scales

Atmospheric turbulence is an important factor in the modelling of wind forces on structures and the losses they produce in extreme wind events. However, while turbulence in non-hurricane winds has been thoroughly researched, turbulence in tropical cyclones and hurricanes that affect the Gulf and Atlantic coasts has only recently been the object of systematic study. In this paper, Florida Coastal Monitoring Program surface wind measurements over the sea surface and open flat terrain are used to estimate tropical cyclone and hurricane wind spectra and cospectra as well as integral length scales. From the analyses of wind speeds obtained from five towers in four hurricanes it can be concluded with high confidence that the turbulent energy at lower frequencies is considerably higher in hurricane than in non-hurricane winds. Estimates of turbulence spectra, cospectra, and integral turbulence scales presented can be used for the development in experimental facilities of hurricane wind flows and the forces they induce on structures.     

Stability Dependence of Canopy Flows over a Flat Larch Forest

The dependence on atmospheric stability of flow characteristics adjacent to a very rough surface was investigated in a larch forest in Japan. Micrometeorological measurements of three-dimensional wind velocity and air temperature were taken at two heights above the forest, namely 1.7 and 1.2 times the mean canopy height h. Under near-neutral and stable conditions, the observed turbulence statistics suggest that the flow was likely to be that of the atmospheric surface layer (ASL) at 1.7h, and of the roughness sublayer (RSL) at 1.2h. However, in turbulence spectra, canopy-induced large coherent motions appeared clearly at both heights. Even under strongly stable conditions, the large-scale motions were retained at 1.2h, whereas they were overwhelmed by small-scale motions at 1.7h. This phenomenon was probably due to the enhanced contribution of the ASL turbulence associated with nocturnal decay of the RSL depth, because the small-scale motions appeared at frequencies close to the peak frequencies of well-known ASL spectra. This result supports the relatively recent concept that canopy flow is a superimposition of coherent motions and the ASL turbulence. The large-scale motions were retained in temperature spectra over a wider region of stability compared to streamwise wind spectra, suggesting that a canopy effect extended higher up for temperature than wind. The streamwise spacing of dominant eddies according to the plane mixing-layer analogy was only valid in a narrow range at near neutral, and it was stabilised at nearly half its value under stable conditions.     

The partitioning of attached and detached eddy motion in the atmospheric surface layer using Lorentz wavelet filtering

Townsend's attached eddy hypothesis states that the turbulent structure in the constant stress layer can be decomposed into attached and detached eddy motion. This paper proposes and tests a methodology for separating the attached and detached eddy motion from time series measurements of velocity and temperature. The proposed methodology is based on the time-frequency localization and filtering capabilities of the orthonormal wavelet transforms. Using a relative entropy statistical measure, the optimal wavelet basis is identified first. The turbulence time series measurements are then transformed into the wavelet domain where the contribution of specific events in the time-frequency domain is identified. The filtering scheme utilizes a recently constructed Lorentz thresholding methodology that successfully eliminates all wavelet coefficients associated with the detached eddy motion. While this filtering scheme lacks the compression efficiency of the classical Donoho and Johnstone's universal thresholding model, it conserves the higher-order statistics and important turbulence interactions related to the Reynolds stresses. Following the filtering scheme, the attached eddy motion time series is re-constructed by an inverse wavelet transform of the non-zero wavelet coefficients. The proposed partitioning methodology for attached and detached eddy motion is tested using 56 Hz triaxial sonic anemometer velocity and temperature measurements above a uniform dry lake bed in Owens valley, California, for a wide range of atmospheric stability conditions. Validation that the wavelet filtered time series represents the attached eddy motion is also discussed in the context of conservation of turbulence energy and surface fluxes.     

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.     

Some similarity states of stably stratified homogeneous turbulence

The decay of statistically homogeneous velocity and density fluctuations in a stably stratified fluid is considered. Over decay times long compared with the turbulence time scale but short compared with the period of internal gravity waves, three distinct high Reynolds number similarity states may develop. These. similarity states are a consequence of the invariance of the low wavenumber coefficients of the three-dimensional kinetic or potential energy spectrum, and their preferential development depends on the relative magnitudes of the initial kinetic and potential energy per unit mass of the fluid. When the turbulence has decayed over a time comparable with the period of the gravity waves, the three similarity states mentioned above are disrupted. Evidence will be presented of a new similarity state which then develops asymptotically. In this similarity state, the time decay exponent of the total energy per unit mass of the turbulence is reduced by a factor of two from its value for decaying isotropic turbulence, and the associated vertical integral scale approaches a constant independent of time.     

Using a Sodar to Measure Optical Turbulence and Wind Speed for the Thirty Meter Telescope Site Testing. Part II: Comparison with Independent Instruments

In the second part of this study, we compare both the wind speed and turbulence given by the Sodars with independent sets of measurements. In the case of the wind speed we compare the lowest Sodar data bin with a sonic anemometer located on a 7-m tower. The agreement between the two instruments was convincing with a regression slope near unity. The integrated turbulence measurements of the Sodars are compared with those obtained with a combined multi-aperture scintillation sensor and differential image motion monitor (MASS/DIMM) unit. It was found that the Sodars are indeed capable of quantitatively measuring optical turbulence, and agree with the MASS/DIMM measurements with a correlation coefficient of approximately 80% and a regression slope within 10% of unity. Additional acoustic noise in the Sodar data was identified using this comparison and removed from the data.     

Subgrid-Scale Dynamics of Water Vapour, Heat, and Momentum over a Lake

We examine the dynamics of turbulence subgrid (or sub-filter) scales over a lake surface and the implications for large-eddy simulations (LES) of the atmospheric boundary layer. The analysis is based on measurements obtained during the Lake-Atmosphere Turbulent EXchange (LATEX) field campaign (August–October, 2006) over Lake Geneva, Switzerland. Wind velocity, temperature and humidity profiles were measured at 20 Hz using a vertical array of four sonic anemometers and open-path gas analyzers. The results indicate that the observed subgrid-scale statistics are very similar to those observed over land surfaces, suggesting that the effect of the lake waves on surface-layer turbulence during LATEX is small. The measurements allowed, for the first time, the study of subgrid-scale turbulent transport of water vapour, which is found to be well correlated with the transport of heat, suggesting that the subgrid-scale modelling of the two scalars may be coupled to save computational resources during LES.     

Two-dimensional field of thermal turbulence at the edge of an escarpment

Acoustic sounder measurements of the temperature structure parameter were obtained at the edge of an escarpment which is part of a ridge of mountains. These measurements indicate that in mountainous terrain, the daytime two-dimensional field of thermal turbulence is strongly affected by relative sun-slope orientation and wind direction out to ranges of at least 200–300 m. For the geometry of this site, westerly flow results in a field which tends to decrease rapidly to the west in the morning with a much less rapid decrease in the afternoon. At night, easterly flow results in significantly higher thermal turbulence compared to that obtained during westerly flow.These measurements show an increase in thermal turbulence at horizontal ranges of 100–200 m to the west of the escarpment during early afternoon on days with deep mixed layers. It is conjectured that this is due to the mountain upslope wind.     

The depth of the internal boundary layer over an urban area under sea-breeze conditions

Field data are analyzed in order to study the development of the Thermal Internal Boundary Layer (TIBL) under sea breeze conditions. The measurements were carried out by the National Observatory of Athens (NOA) during ATHens Internal Boundary Layer Experiment (ATHIBLEX) in summer 1989 and 1990.Several formulations found in the literature are tested against the measurements in order to investigate whether they are capable of predicting the depth of the TIBL. It is found that a slab model including mechanical production of turbulence gives overall good agreement with the measurements.Finally, the concept of local equilibrium is used to explain the discrepancies found between small-and meso-scale observations and models; a formula is proposed which is intended for use over a wide range of downwind fetches.