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In the past several years, wind veer -- sometimes called "directional shear" -- has begun to attract attention due to its effects on wind turbines and their production, particularly as the length of manufactured turbine blades has increased. Meanwhile, applicable meteorological theory has not progressed significantly beyond idealized cases for decades, though veer's effect on the wind speed profile has been recently revisited. On the other hand the shear exponent (α) is commonly used in wind energy for vertical extrapolation of mean wind speeds, as well as being a key parameter for wind turbine load calculations and design standards. In this work we connect the oft-used shear exponent with veer, both theoretically and for practical use. We derive relations for wind veer from the equations of motion, finding the veer to be composed of separate contributions from shear and vertical gradients of crosswind stress. Following from the theoretical derivations, which are neither limited to the surface layer nor constrained by assumptions about mixing length or turbulent diffusivities, we establish simplified relations between the wind veer and shear exponent for practical use in wind energy. We also elucidate the source of commonly observed stress--shear misalignment and its contribution to veer, noting that our new forms allow for such misalignment. The connection between shear and veer is further explored through analysis of one-dimensional (single-column) Reynolds-averaged Navier--Stokes solutions, where we confirm our theoretical derivations as well as the dependence of mean shear and veer on surface roughness and atmospheric boundary layer depth in terms of respective Rossby numbers. Finally we investigate the observed behavior of shear and veer across different sites and flow regimes (including forested, offshore, and hilly terrain cases) over heights corresponding to multi-megawatt wind turbine rotors, also considering the effects of atmospheric stability. From this we find empirical forms for the probability distribution of veer during high-veer (stable) conditions and for the variability in veer conditioned on wind speed. Analyzing observed joint probability distributions of α and veer, we compare the two simplified forms we derived earlier and adapt them to ultimately arrive at more universally applicable equations to predict the mean veer in terms of observed (i.e., conditioned on) shear exponent; lastly, the limitations, applicability, and behavior of these forms are discussed along with their use and further developments for both meteorology and wind energy. [ABSTRACT FROM AUTHOR]

The planning of offshore wind energy projects requires wind observations over long periods for the establishment of wind speed distributions. In the marine environment, high-quality in situ observations are sparse and restricted to point locations. Numerical modeling is typically used to determine the spatial variability of the wind resource. Synthetic Aperture Radar (SAR) observations from satellites can be used for retrieval of wind fields over the ocean at a high spatial resolution. The recent launch of constellations of small SAR satellites by private companies will improve the sampling of SAR scenes significantly over the coming years compared with the current sampling rates offered by multi-purpose SAR missions operated by public space agencies. For the first time, wind fields are retrieved from a series of StriX SAR scenes delivered by Synspective (Japan) and also from Sentinel-1 scenes delivered by the European Space Agency. The satellite winds are compared with wind speed observations from the FINO3 mast in the North Sea. This leads to root-mean-square errors of 1.4–1.8 m s − 1 and negative biases of −0.4 m s − 1 and −1.0 m s − 1 , respectively. Although the Geophysical Model Functions (GMF) applied for wind retrievals have not yet been tuned for StriX SAR observations, the wind speed accuracy is satisfactory. Through conditional sampling, we estimate the wind resource from current and future SAR sampling scenarios where the number of SAR satellites in orbit is increasing over time. We find that hourly samples are needed to fully capture the diurnal wind speed variability at the site investigated. A combination of SAR samples from current missions with samples from clusters of small SAR satellites can yield the necessary number of wind speed samples for accurate wind resource estimation. This is particularly important for sites with pronounced diurnal wind speed variability. An additional benefit of small SAR satellites is that wind speed variability can be mapped at the sub-km scale. The very high spatial resolution is valuable for characterizing the wind conditions in the vicinity of existing offshore wind farms. [ABSTRACT FROM AUTHOR]

We investigate characteristics of large-scale coherent motions in the atmospheric boundary layer using field measurements made with two long-range scanning wind lidars. The joint scans provide quasi-instantaneous wind fields over a domain of ∼50 km2, at two heights above flat but partially forested terrain. Along with the two-dimensional wind fields, two-point statistics and spectra are used to identify and characterize the scales, shape, and anisotropy of coherent structures—as well as their influence on wind field homogeneity. For moderate to high wind speeds in near-neutral conditions, most of the observed structures correspond to narrow streaks of low streamwise momentum near the surface, extending several hundred meters in the streamwise direction; these are associated with positive vertical velocity ejections. For unstable conditions and moderate winds, these structures become large-scale rolls, with longitudinal extent exceeding the measuring domain (>∼5 km); they dominate the conventional surface-layer structures in terms of both physical scale and relative size of velocity-component variances, appearing as quasi-two-dimensional structures throughout the entire boundary layer. The observations shown here are consistent with numerical simulations of atmospheric flows, field observations, and laboratory experiments under similar conditions. Significance Statement: Coherent structures have attracted the interest of researchers for decades, being viewed as the closest to "order" that we can find within the chaos of turbulence. In the turbulent atmospheric boundary layer, micro- and mesoscale coherent structures come in many shapes and sizes, such as convective cells, rolls, or streaks. In this study we used dual lidars (remote sensing measurements), developing analysis of their tandem usage to characterize in detail some of the large-scale coherent structures generated over flat terrain. This allowed us to better understand the mechanisms that generate such structures and describe their influence on the morphology of the turbulent atmospheric boundary layer across a good deal of its depth. [ABSTRACT FROM AUTHOR]

Via 11 years of high-frequency measurements, we calculated the probability space of expected offshore wind-speed ramps, recasting it compactly in terms of relevant load-driving quantities for horizontal-axis wind turbines. A statistical ensemble of events in reduced ramp-parameter space (ramp acceleration, mean speed after ramp, upper-level shear) was created to capture the variability of ramp parameters and also allow connection of such to ramp-driven loads. Constrained Mann-model (CMM) turbulence simulations coupled to an aeroelastic model were made for each ensemble member, for a single turbine. Ramp acceleration was found to dominate the maxima of thrust-associated loads, with a ramp-induced increase of 45 %-50% for blade-root flap-wise bending moment and tower-base fore-aft moment, plus ~3% per 0.1 m/s2 of bulk ramp-acceleration magnitude. The ensemble of ramp events from the CMM was also embedded in large-eddy simulation (LES) of a wind farm consisting of rows of nine turbines. The LES uses actuator-line modeling for the turbines and is coupled to the aeroelastic model. The LES results indicate that the ramps, and the mean acceleration associated with them, tend to persist through the farm. Depending on the ramp acceleration, ramps crossing rated speed lead to maximum loads, which are nearly constant for the third row and further downwind. Where rated power is not achieved, the loads primarily depend on wind speed; as mean winds weaken within the farm, ramps can again have U rated. This leads to higher loads than pre-ramp conditions, with the distance where loads begin to increase depending on inflow Umax relative to Vrated. For the ramps considered here, the effect of turbulence on loads is found to be small relative to ramp amplitude that causes Vrated to be exceeded, but for ramps with Uafter rated, the combination of ramp and turbulence can cause load maxima. The same sensitivity of loads to acceleration is found in both the CMM-aeroelastic simulations and the coupled LES. [ABSTRACT FROM AUTHOR]

Parameterizing the effect of vertically-distributed vegetation through an effective roughness (z0,eff) – whereby momentum loss through a three-dimensional foliage volume is represented as momentum loss over an area at one vertical level – can facilitate the use of forest data in flow models, to any level of detail, and simultaneously reduce computational cost. Results of numerical experiments and comparison with observations show that a modelling approach based on z0,eff can estimate wind speed and turbulence levels over forested areas, at heights of interest for wind energy applications (∼60 m and higher), but only above flat terrain. Caution must be exercised in the application of such a model to zones of forest edges. Advanced flow models capable of incorporating local (distributed) drag forces are recommended for complex terrain covered by forest. [ABSTRACT FROM AUTHOR]

The design of wind turbines and wind farms can be improved by increasing the accuracy of the inflow models representing the atmospheric boundary layer. In this work we employ one-dimensional Reynoldsaveraged Navier-Stokes (RANS) simulations of the idealized atmospheric boundary layer (ABL), using turbulence closures with a length-scale limiter. These models can represent the mean effects of surface roughness, Coriolis force, limited ABL depth, and neutral and stable atmospheric conditions using four input parameters: the roughness length, the Coriolis parameter, a maximum turbulence length, and the geostrophic wind speed. We find a new model-based Rossby similarity, which reduces the four input parameters to two Rossby numbers with different length scales. In addition, we extend the limited-length-scale turbulence models to treat the mean effect of unstable stratification in steady-state simulations. The original and extended turbulence models are compared with historical measurements of meteorological quantities and profiles of the atmospheric boundary layer for different atmospheric stabilities. [ABSTRACT FROM AUTHOR]

A coupledwind‐wave modeling system is used to simulate 23 years of storms and estimate offshore extreme wind statistics. In this system, the atmospheric Weather Research and Forecasting (WRF) model and Spectral Wave model for Near shore (SWAN) are coupled, through a wave boundary layer model (WBLM) that is implemented in SWAN. The WBLM calculates momentum and turbulence kinetic energy budgets, using them to transfer wave‐induced stress to the atmospheric modeling. While such coupling has a trivial impact on the wind modeling for 10‐m wind speeds less than 20 ms−1, the effect becomes appreciable for stronger winds—both compared with uncoupled WRF modeling and with standard parameterization schemes for roughness length. The coupled modeling output is shown to be satisfactory compared with measurements, in terms of the distribution of surface‐drag coefficient with wind speed. The coupling is also shown to be important for estimation of extreme winds offshore, where the WBLM‐coupled results match observations better than results from noncoupled modeling, as supported by measurements from a number of stations. [ABSTRACT FROM AUTHOR]

The present study introduces a new method to characterize ramp-like wind speed fluctuations, including coherent gusts. This method combines two well-known methods: the continuous wavelet transform and the fitting of an analytical form based on the error function. The method provides estimation of ramp amplitude and rise time, and is herein used to statistically characterize ramp-like fluctuations at three different measurement sites. Together with the corresponding amplitude of wind direction change, the ramp amplitude and rise time variables are compared to the extreme coherent gust with direction change from the IEC wind turbine safety standard. From the comparison we find that the observed amplitudes of the estimated fluctuations do not exceed the one prescribed in the standard, but the rise time is generally much longer, on average around 200 s. The direction change does however exceed the one prescribed in the standard several times, but for those events the rise time is a minute or more. We also demonstrate a general pattern in the statistical behaviour of the characteristic ramp variables, noting their wind speed dependence, or lack thereof, at the different sites. [ABSTRACT FROM AUTHOR]

Wind profiles above the atmospheric surface layer are not accurately described by classic similarity theories. Far from the surface, the underlying assumptions of such surface‐layer theories break down due to the stronger influence of buoyancy forces induced by the temperature inversion that caps the atmospheric boundary layer (ABL), as well as the Coriolis force. This paper examines the influence of these forces on the mean flow and presents a new similarity theory to predict mean wind profiles in and above the surface layer for an ABL with zero surface heat flux and capped by an inversion of potential temperature, that is, the conditionally neutral ABL. The analysis here is based on the results of 17 large‐eddy simulations (LES) over a flat homogeneous rough surface, which leads to and supports the new similarity theory. The development is based on two applications of the Buckingham Π theorem. A first application allows determination of the entrainment‐induced heat flux profile through the ABL and into the surface layer, which is then used within a second dimensional argument for the vertical shear of mean wind speed. We subsequently find a new dimensionless group (Π2) depending on the capping inversion strength, the Coriolis parameter, the surface stress and the ABL depth, which is correlated to the dimensionless shear (Π1) through a universal function β. Integrating the functional relation between Π1 and Π2 produces an equation for the mean wind speed profile; it effectively includes an additive "correction" to the log‐law in terms of Π2, analogous to the Monin–Obukhov profile correction function. Unlike surface‐layer similarity, the new form accounts for the influences of both the surface and the ABL top. Relative to the LES, the new profile form exhibits errors in mean wind speed below 5% for heights below 90% of the ABL depth; this is relevant for applications above the surface layer (e.g., wind energy). [ABSTRACT FROM AUTHOR]

For measurements taken over a decade at the coastal Danish site Høvsøre, we find the variance associated with wind speed events from the offshore direction to exceed the prescribed extreme turbulence model (ETM) of the International Electrotechnical Commission (IEC) 61400-1 Edition 3 standard for wind turbine safety. The variance of wind velocity fluctuations manifested during these events is not due to extreme turbulence; rather, it is primarily caused by ramp-like increases in wind speed associated with larger-scale meteorological processes. The measurements are both linearly detrended and high-pass filtered in order to investigate how these events - and such commonly used filtering - affect the estimated 50-year return period of turbulence levels. High-pass filtering the measurements with a cutoff frequency of 1=300 Hz reduces the 50-year turbulence levels below that of IEC ETM class C, whereas linear detrending does not. This is seen as the high-pass filtering more effectively removes variance associated with the ramp-like events. The impact of the observed events on a wind turbine are investigated using aeroelastic simulations that are driven by constrained turbulence simulation fields. Relevant wind turbine component loads from the simulations are compared with the extreme turbulence load case prescribed by the IEC standard. The loads from the event simulations are on average lower for all considered load components, with one exception: ramp-like events at wind speeds between 8 and 16ms-1, at which the wind speed rises to exceed rated wind speed, can lead to high thrust on the rotor, resulting in extreme tower-base fore-aft loads that exceed the extreme turbulence load case of the IEC standard. [ABSTRACT FROM AUTHOR]

Numerical simulations of the Vestas multi-rotor demonstrator (4R-V29) are compared with field measurements of power performance and remote sensing measurements of the wake deficit from a short-range WindScanner lidar system. The simulations predict a gain of 0%-2% in power due to the rotor interaction at below rated wind speeds. The power curve measurements also show that the rotor interaction increases the power performance below the rated wind speed by 1.8%, which can result in a 1.5% increase in the annual energy production. The wake measurements and numerical simulations show four distinct wake deficits in the near wake, which merge into a single-wake structure further downstream. Numerical simulations also show that the wake recovery distance of a simplified 4R-V29 wind turbine is 1.03-1.44Deq shorter than for an equivalent singlerotor wind turbine with a rotor diameter Deq. In addition, the numerical simulations show that the added wake turbulence of the simplified 4R-V29 wind turbine is lower in the far wake compared with the equivalent singlerotor wind turbine. The faster wake recovery and lower far-wake turbulence of such a multi-rotor wind turbine has the potential to reduce the wind turbine spacing within a wind farm while providing the same production output. [ABSTRACT FROM AUTHOR]

In this study, we extend the work presented in to make the wave boundary layer model (WBLM) applicable for real cases by improving the wind-input and white-capping dissipation source functions. Improvement via the new source terms includes three aspects. First, the WBLM wind-input source function is developed by considering the impact of wave-induced wind profile variation on the estimation of wave growth rate. Second, the white-capping dissipation source function is revised to be not explicitly dependent on wind speed for real wave simulations. Third, several improvements are made to the numerical WBLM algorithm, which increase the model's numerical stability and computational efficiency. The improved WBLM wind-input and white-capping dissipation source functions are calibrated through idealized fetch-limited and depth-limited studies, and validated in real wave simulations during two North Sea storms. The new WBLM source terms show better performance in the simulation of significant wave height and mean wave period than the original source terms. [ABSTRACT FROM AUTHOR]

Displacement height ( d) is an important parameter in the simple modelling of wind speed and vertical fluxes above vegetative canopies, such as forests. Here we show that, aside from implicit definition through a (displaced) logarithmic profile, accepted formulations for d do not consistently predict flow properties above a forest. Turbulent transport can affect the displacement height, and is an integral part of what is called the roughness sublayer. We develop a more general approach for estimation of d, through production of turbulent kinetic energy and turbulent transport, and show how previous stress-based formulations for displacement height can be seen as simplified cases of a more general definition including turbulent transport. Further, we also give a simplified and practical form for d that is in agreement with the general approach, exploiting the concept of vortex thickness scale from mixing-layer theory. We assess the new and previous displacement height formulations by using flow statistics derived from the atmospheric boundary-layer Reynolds-averaged Navier-Stokes model SCADIS as well as from wind-tunnel observations, for different vegetation types and flow regimes in neutral conditions. The new formulations tend to produce smaller d than stress-based forms, falling closer to the classic logarithmically-defined displacement height. The new, more generally defined, displacement height appears to be more compatible with profiles of components of the turbulent kinetic energy budget, accounting for the combined effects of turbulent transport and shear production. The Coriolis force also plays a role, introducing wind-speed dependence into the behaviour of the roughness sublayer; this affects the turbulent transport, shear production, stress, and wind speed, as well as the displacement height, depending on the character of the forest. We further show how our practical ('mixing-layer') form for d matches the new turbulence-based relation, as well as correspondence to previous (stress-based) formulations. [ABSTRACT FROM AUTHOR]

A model has been derived for calculating the aggregate effects of stability and the finite height of the planetary boundary layer upon the long-term mean wind profile. A practical implementation of this probabilistic extended similarity-theory model is made, including its incorporation within the European Wind Atlas (EWA) methodology for site-to-site application. Theoretical and practical implications of the EWA methodology are also derived and described, including unprecedented documentation of the theoretical framework encompassing vertical extrapolation, as well as some improvement to the methodology. Results of the modeling are shown for a number of sites, with discussion of the models' efficacy and the relative improvement shown by the new model, for situations where a user lacks local heat flux information, as well as performance of the new model using measured flux statistics. Further, the uncertainty in vertical extrapolation is characterized for the EWA model contained in standard (i.e., WAs P) wind resource assessment, as well as for the new model. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A range of large-eddy simulations, with differing free atmosphere stratification and zero or slightly positive surface heat flux, is investigated to improve understanding of the neutral and near-neutral, inversion-capped, horizontally homogeneous, barotropic atmospheric boundary layer with emphasis on the upper region. We find that an adjustment time of at least 16 h is needed for the simulated flow to reach a quasi-steady state. The boundary layer continues to grow, but at a slow rate that changes little after 8 h of simulation time. A common feature of the neutral simulations is the development of a super-geostrophic jet near the top of the boundary layer. The analytical wind-shear models included do not account for such a jet, and the best agreement with simulated wind shear is seen in cases with weak stratification above the boundary layer. Increasing the surface heat flux decreases the magnitude and vertical extent of the jet and leads to better agreement between analytical and simulated wind-speed profiles. Over a range of different inversion strengths and surface heat fluxes, we also find good agreement between the performed simulations and models of the equilibrium boundary-layer height, and of the budget of turbulent kinetic energy integrated across the boundary layer. [ABSTRACT FROM AUTHOR]

The Weibull distribution is commonly used to describe climatological wind-speed distributions in the atmospheric boundary layer. While vertical profiles of mean wind speed in the atmospheric boundary layer have received significant attention, the variation of the shape of the wind distribution with height is less understood. Previously we derived a probabilistic model based on similarity theory for calculating the effects of stability and planetary boundary-layer depth upon long-term mean wind profiles. However, some applications (e.g. wind energy estimation) require the Weibull shape parameter ( k), as well as mean wind speed. Towards the aim of improving predictions of the Weibull- $$k$$ profile, we develop expressions for the profile of long-term variance of wind speed, including a method extending our probabilistic wind-profile theory; together these two profiles lead to a profile of Weibull-shape parameter. Further, an alternate model for the vertical profile of Weibull shape parameter is made, improving upon a basis set forth by Wieringa (Boundary-Layer Meteorol, , Vol. 47, 85-110), and connecting with a newly-corrected corollary of the perturbed geostrophic-drag theory of Troen and Petersen (European Wind Atlas, , Risø National Laboratory, Roskilde). Comparing the models for Weibull- k profiles, a new interpretation and explanation is given for the vertical variation of the shape of wind-speed distributions. Results of the modelling are shown for a number of sites, with a discussion of the models' efficacy and applicability. The latter includes a comparative evaluation of Wieringa-type empirical models and perturbed-geostrophic forms with regard to surface-layer behaviour, as well as for heights where climatological wind-speed variability is not dominated by surface effects. [ABSTRACT FROM AUTHOR]

In this study we extend the work presented in Du et al. (2017) to make the WBLM applicable for real cases by improving the wind input and white-capping dissipation source functions. Improvement via the new source terms includes three aspects. First, the WBLM wind-input source function is developed by considering the impact of wave-induced wind profile variation on the estimation of wave growth rate. Second, the white-capping dissipation source function is revised to be not explicitly dependent on wind speed for real wave simulations. Third, several improvements are made to the numerical WBLM algorithm, which increase the model's numerical stability and computational efficiency. The improved WBLM wind-input and white-capping dissipation source functions are calibrated through idealized fetch-limited and depth-limited studies, and validated in real wave simulations during two North Sea storms. The new WBLM source terms show better performance in the simulation of significant wave height and mean wave period than the original source terms. [ABSTRACT FROM AUTHOR]