Stratified Atmospheric Boundary Layer Research Articles

The multi-scale coupled model: a new framework capturing wind farm–atmosphere interaction and global blockage effects

Abstract. The growth in the number and size of wind energy projects in the last decade has revealed structural limitations in the current approach adopted by the wind industry to assess potential wind farm sites. These limitations are the result of neglecting the mutual interaction of large wind farms and the thermally stratified atmospheric boundary layer. While currently available analytical models are sufficiently accurate to conduct site assessments for isolated rotors or small wind turbine clusters, the wind farm's interaction with the atmosphere cannot be neglected for large-size arrays. Specifically, the wind farm displaces the boundary layer vertically, triggering atmospheric gravity waves that induce large-scale horizontal pressure gradients. These perturbations in pressure alter the velocity field at the turbine locations, ultimately affecting global wind farm power production. The implication of such dynamics can also produce an extended blockage region upstream of the first turbines and a favorable pressure gradient inside the wind farm. In this paper, we present the multi-scale coupled (MSC) model, a novel approach that allows the simultaneous prediction of micro-scale effects occurring at the wind turbine scale, such as individual wake interactions and rotor induction, and meso-scale phenomena occurring at the wind farm scale and larger, such as atmospheric gravity waves. This is achieved by evaluating wake models on a spatially heterogeneous background velocity field obtained from a reduced-order meso-scale model. Verification of the MSC model is performed against two large-eddy simulations (LESs) with similar average inflow velocity profiles and a different capping inversion strength, so that two distinct interfacial gravity wave regimes are produced, i.e. subcritical and supercritical. Interfacial waves can produce high blockage in the first case, as they are allowed to propagate upstream. On the other hand, in the supercritical regime their propagation speed is less than their advection velocity, and upstream blockage is only operated by internal waves. The MSC model not only proves to successfully capture both local induction and global blockage effects in the two analyzed regimes, but also captures the interaction between the wind farm and gravity waves, underestimating wind farm power by about only 2 % compared with the LES results. Conversely, wake models alone cannot distinguish between differences in thermal stratification, even if combined with a local induction model. Specifically, they are affected by a first-row overprediction bias that leads to an overestimation of the wind farm power by 13 % to 20 % for the modeled regimes.

Lagrangian Stochastic Modeling of Stratified Atmospheric Boundary Layer

A single-column turbulence model for stratified atmospheric boundary layer (ABL), which solves the transport equations of turbulence probability density function (PDF) using a Lagrangian stochastic modeling (LSM) approach, is proposed in this study. This study adopts previously developed stochastic differential equations (SDEs) for particle velocity and temperature and extends the LSM to simulate inhomogeneous turbulence. The proposed LSM is tested for its ability to fully simulate statistics of inhomogeneous stratified turbulence. In the model, particles evolve by SDEs, and turbulence statistics are calculated by averaging the properties of particles. The model provides a full representation of turbulence PDF and simulates turbulent transport without any modeling assumption. The model performance is evaluated against large-eddy simulation (LES) results in the simulations of convective and stable ABL cases. For the convective ABL, LSM realistically simulates the entrainment process with the temperature and heat flux profiles that closely match with LES. The joint PDF simulated by LSM reproduces a curved and highly skewed shape, and some distinct features, like the asymmetric distribution of vertical velocity and the separation of the PDF in the entrainment zone, are simulated. LSM also reproduces the entrainment enhancement by wind shear in the simulation of sheared convective ABL. The LSM simulation of stable ABL predicts realistic turbulence intensity and mean field profiles, where Gaussian-like PDFs are simulated both in LSM and LES.

Large-eddy simulation-based reconstruction of turbulence in a neutral boundary layer using spectral-tensor regularization

We propose an efficient method to reconstruct the turbulent flow field in a neutrally stratified atmospheric boundary layer using large-eddy simulation (LES) and a series of lidar measurements. The reconstruction is formulated as a strong four-dimensional variational data assimilation problem, which involves optimizing two competing terms that contribute in the objective functional. The first term is a likelihood term, while the second contains the initial background distribution of turbulent velocity fluctuations and works as a regularization term. However, computing and storing the full background covariance tensor in turbulent flows is time consuming and resource intensive. In the current work, we investigate the possibility of replacing the complex background tensor by simple analytical approximations based on spectral tensors such as the Hunt–Graham–Wilson (HGW) model (Boundary-Layer Meteorol., vol. 85, 1997, pp. 35–52) or the Mann model (J. Fluid Mech., vol. 273, 1994, pp. 141–168). Afterwards, the problem is solved using a quasi-Newton algorithm and preconditioned to enhance the convergence rate. We test the method using virtual lidar measurements collected on a fine reference LES. Results show a super-linear convergence rate of the optimization algorithm to a local minimum and very good agreement between virtual lidar measurements and reconstruction in the scanning region. Furthermore, we demonstrate that incorporating the Saffman energy spectrum ( $E(k) \sim k^2$ where E is the energy spectrum and k is the magnitude of the wavenumber vector) at low wavenumbers into the Mann spectral tensor yields a longer streamwise correlation length, resulting in reduced reconstruction error when compared with the Batchelor spectrum ( $E(k) \sim k^4$ ). Finally, we observe that using the HGW model or Mann model with a Saffman spectrum yields similar results.

Sensitivity of the polar boundary layer to transient phenomena

Abstract. Numerical weather prediction and climate models encounter challenges in accurately representing flow regimes in the stably stratified atmospheric boundary layer and the transitions between them, leading to an inadequate depiction of regime occupation statistics. As a consequence, existing models exhibit significant biases in near-surface temperatures at high latitudes. To explore inherent uncertainties in modeling regime transitions, the response of the near-surface temperature inversion to transient small-scale phenomena is analyzed based on a stochastic modeling approach. A sensitivity analysis is conducted by augmenting a conceptual model for near-surface temperature inversions with randomizations that account for different types of model uncertainty. The stochastic conceptual model serves as a tool to systematically investigate which types of unsteady flow features may trigger abrupt transitions in the mean boundary layer state. The findings show that the incorporation of enhanced mixing, a common practice in numerical weather prediction models, blurs the two regime characteristic of the stably stratified atmospheric boundary layer. Simulating intermittent turbulence is shown to provide a potential workaround for this issue. Including key uncertainty in models could lead to a better statistical representation of the regimes in long-term climate simulation. This would help to improve our understanding and the forecasting of climate change in high-latitude regions.

The role of a low-level jet for stirring the stable atmospheric surface layer in the Arctic

Abstract. In this study, we analyze the transition of a stable atmospheric boundary layer (ABL) with a low-level jet (LLJ) to a traditional stable ABL with a classic Ekman helix in the late-winter central Arctic. Vertical profiles in the ABL were measured with a hot-wire anemometer on a tethered balloon during a 15 h period in March 2018 in northeast Greenland. The tethered balloon allows high-resolution turbulence observations from the ground to the top of the ABL. The core of the LLJ was observed at about 150 m altitude, and its height and strength were associated with the temperature inversion. Increased turbulence was observed in the vicinity of the LLJ, but most of the turbulence does not reach down to the surface, thus decoupling the LLJ from the surface. Only when the LLJ collapses and the ABL again exhibits a more classical Ekman spiral is a coupling to the surface re-established. The LLJ might enhance both advective and turbulent vertical transport of passive tracers such as aerosol particles or moisture in the often stably stratified Arctic ABL.

Logarithmic profiles of velocity in stably stratified atmospheric boundary layers

Logarithmic profiles of velocity in stably stratified atmospheric boundary layers

Comparison of the wake characteristics and aerodynamic response of a wind turbine under varying atmospheric conditions using WRF-LES-GAD and WRF-LES-GAL wind turbine models

A generalized actuator line model (GAL) is implemented in the Weather Research and Forecasting (WRF) (Skamarock and Klemp, 2008) model to carry out high-fidelity large-eddy simulations (LESs) of turbulent wind fields in stratified atmospheric boundary layer (ABL) flows and study the effects of atmospheric stability on the wake characteristics and aerodynamic response of a wind turbine (WT). The performance of Vestas V27 WT has been evaluated paying attention to the wind turbine wake behavior and the aerodynamic performance using the already available generalized actuator disk (GAD) and the recently implemented GAL model. Spatial distributions of mean velocity components, their variances and instantaneous vorticity in the wake of the wind turbine are analyzed by comparing the results from GAD and GAL approaches. Results of the wake velocity deficit profiles and wind turbine aerodynamic response have been compared with the experimental ones obtained in the Scaled Wind Farm Technology campaign and available LES data reported in the works of Doubrawa et al. (2020) and Jézéquel et al. (2021). The results from the GAD and GAL models, including the aerodynamic effects of nacelle and tower, agree reasonably well with the results from other LES codes and experimental data, with minor differences between these two models regarding velocity deficits in the near-wake region and wind turbine response under varying atmospheric stability conditions. Overall, the GAL model is able to reproduce the observed wake behavior and the aerodynamic response of the Vestas V27 for the atmospheric conditions tested.

On the motion of hairpin filaments in the atmospheric boundary layer

On the motion of hairpin filaments in the atmospheric boundary layer

Wake interactions behind individual-tower multi-rotor wind turbine configurations

Multiple rotors on single structures have long been proposed to increase wind turbine energy capture with no increase in rotor size, but at the cost of additional mechanical complexity in the yaw and tower designs. Standard turbines on their own very-closely-spaced towers avoid these disadvantages but create a significant disadvantage; for some wind directions the wake turbulence of a rotor enters the swept area of a very close downwind rotor causing low output, fatigue stress, and changes in wake recovery. Knowing how the performance of pairs of closely spaced rotors varies with wind direction is essential to design a layout that maximizes the useful directions and minimizes the losses and stress at other directions. In the current work, the high-fidelity large-eddy simulation (LES) code Exa-Wind/Nalu-Wind is used to simulate the wake interactions from paired-rotor configurations in a neutrally stratified atmospheric boundary layer to investigate performance and feasibility. Each rotor pair consists of two Vestas V27 turbines with hub-to-hub separation distances of 1.5 rotor diameters. The on-design wind direction results are consistent with previous literature. For an off-design wind direction of 26.6°, results indicate little change in power and far-wake recovery relative to the on-design case. At a direction of 45.0°, significant rotor-wake interactions produce an increase in power but also in far-wake velocity deficit and turbulence intensity. A severely off-design case is also considered.

Submeso Wave-Like Structures in the Atmospheric Boundary Layer and Their Parameters Measured with the Help of Sodar in Moscow Region

The paper presents study of the parameters of wave-like structures based on the data of long-term continuous sodar monitoring of the atmospheric boundary layer (ABL). Submesoscale internal gravity waves (IGWs) of non-orographic origin trapped in a stably stratified ABL (SBL) are considered. Statistical data on the parameters of two classes of IGWs are presented: internal gravity-shear waves (IGSWs) of the Kelvin-Helmholtz billow (KHB) type and buoyancy waves (BW). Identification and classification of IGWs was carried out by the visual analysis of sodar echograms. The measurements carried out in the Moscow region were used. The seasonal and diurnal variability of the frequency of registration of waves of both classes were studied, the values of the parameters of the observed waves were analyzed, and the ranges and average values of these quantities were compared.

Comparison of turbulent inflow conditions for neutral stratified atmospheric boundary layer flow

In the present work, measurements of the atmospheric boundary layer (ABL) flow, reproduced in a boundary layer wind tunnel, and large eddy simulation (LES) of the full scale ABL are presented for two ground roughness lengths. In the numerical part the ABL is simulated by utilizing the cyclic boundary conditions in downstream direction and artificial turbulence specified at the inlet. Five synthetic turbulence generation techniques are used with reviewing two input methods for the Reynolds stress. Convergence of mean velocity and second order moments is discussed for various horizontal and vertical grid refinement as well as for different roughness and wall boundary conditions of the ground. The transition of mean velocity, second order moments, stream-wise velocity spectrum and longitudinal turbulent length scale in downstream direction is analyzed. The applicability of the synthetic turbulence condition was confirmed for the LES of ABL simulations. In this way, the inflow domain length for simulations can significantly be reduced.

Wind farm blockage in a stable atmospheric boundary layer

Wind farm blockage is the flow deceleration in front of a large turbine array, due to which the first wind farm row produces less power than a corresponding solitary row. Understanding wind farm blockage is crucial as a failure to accurately model the effect leads to a systematic difference between the modeled and actual wind farm performance. While stable atmospheric conditions are known to impact wind farm performance, the effect on wind farm blockage is not well understood. We use large eddy simulations to investigate blockage in a stably stratified atmospheric boundary layer without capping inversion by systematically varying the streamwise turbine spacing and the surface cooling rate. We consider stable boundary layers without capping inversion as it allows us to isolate the effect of surface stability. Primarily, we demonstrate that wind farm blockage increases with atmospheric stability due to the deflection of relatively cold flow over the wind farm. Displacement of this high-density colder air creates a high-pressure region at the wind farm entrance. The formation of the high-pressure region enhances the adverse pressure gradient and increases the flow deceleration in front of the wind farm under stable atmospheric conditions.

On the influence of internal gravity waves on the intensity of turbulence in the atmospheric boundary layer

To date experimental data concerning the impact of internal gravity waves on the intensity of turbulence in a stably stratified atmospheric boundary layer are scarce. The paper presents the results of the analysis of the degree of influence on turbulence characteristics of wave-like motions of two classes: Kelvin-Helmholtz billows (KHBs) and horizontally propagating buoyancy waves (BWs). For this purpose the data of long-term sodar measurements carried out in the suburban area of Moscow were used. The passage of 30% of KHB trains and 90% of BW trains was accompanied with increase of turbulent kinetic energy and both heat and momentum fluxes. The relative increase in values of these characteristics was higher during BWs passage. Nevertheless the magnitude of turbulence characteristics were similar for both IGWs classes. In general the difference between characteristics calculated in the presence and in the absence of wavelike motions was smaller than between those in strongly and weakly stable boundary layers.

A scale-wise analysis of intermittent momentum transport in dense canopy flows

We investigate the intermittent dynamics of momentum transport and its underlying time scales in the near-wall region of the neutrally stratified atmospheric boundary layer in the presence of a vegetation canopy. This is achieved through an empirical analysis of the persistence time scales (periods between successive zero-crossings) of momentum flux events, and their connection to the ejection–sweep cycle. Using high-frequency measurements from the GoAmazon campaign, spanning multiple heights within and above a dense canopy, the analysis suggests that, when the persistence time scales ( $t_p$ ) of momentum flux events from four different quadrants are separately normalized by $\varGamma _{w}$ (integral time scale of the vertical velocity), their distributions $P(t_p/\varGamma _{w})$ remain height-invariant. This result points to a persistent memory imposed by canopy-induced coherent structures, and to their role as an efficient momentum-transporting mechanism between the canopy airspace and the region immediately above. Moreover, $P(t_p/\varGamma _{w})$ exhibits a power-law scaling at times $t_{p}<\varGamma _{w}$ , with an exponential tail appearing for $t_{p} \geq \varGamma _{w}$ . By separating the flux events based on $t_p$ , we discover that around 80 % of the momentum is transported through the long-lived events ( $t_{p} \geq \varGamma _{w}$ ) at heights immediately above the canopy, while the short-lived ones ( $t_{p} < \varGamma _{w}$ ) only contribute marginally ( $\approx 20\,\%$ ). To explain the role of instantaneous flux amplitudes in momentum transport, we compare the measurements with newly developed surrogate data and establish that the range of time scales involved with amplitude variations in the fluxes tends to increase as one transitions from within to above the canopy.

Wind tunnel experiments for investigating wake effects in atmospheric boundary layers using a simplified miniature model wind turbine

The clustering of wind turbines within a prospective site is prone to significant wake interactions, which have a negative impact in terms of loads and plant performance. Further improvements in the design and control of wind farms can be achieved through a detailed assessment of wake effects under site-specific conditions. The aim of this paper was to investigate wake effects in atmospheric boundary layer (ABL) flows using a simplified model wind turbine. First, we performed experiments under smooth- and turbulent-uniform inflows to highlight the wake features of the model. Second, we evaluated the interactions with two different neutrally stratified ABL: i) ABL Type-I (α = 0.11, TI = 6 %), ii) ABL Type-II (α = 0.23, TI = 13 %), where α is the incident wind shear and TI is the turbulence intensity. For each case, hot-wire anemometry was used to obtain wake mean velocity, turbulence intensity and power spectrum profiles at four different downstream positions. We also included a comparison with three analytical wake models to get further indications on the experimental measurements. First results showed that the simplified model is well-suited for its intended purpose. The largest discrepancies between experiments and model predictions were in the near-wake region and in cases with lower background turbulence. We also corroborated a strong influence of the incoming wind profile on how fast the wake recovers to the undisturbed conditions. Furthermore, this study provided an initial framework to explore the ABL wind tunnel at Universidade Federal do Rio Grande do Sul (UFRGS) as a viable tool for research in wind energy.

Large Eddy Simulation of wind turbine fatigue loading and yaw dynamics induced by wake turbulence

A coupled Large Eddy Simulation (LES) and aeroelastic code was used to evaluate control responses and fatigue loading of a four-inline wind turbine array. Neutral and unstably stratified atmospheric boundary layers with hub-height wind speeds of 7 and 15 m/s were used for wind farm inflows. These cases operate in different control regions. It was found that for both incoming wind speeds, atmospheric stability has no significant impact on the fatigue loads of the front-row wind turbines. However, stability affected wake characteristics which caused differences in control response and fatigue experienced by downstream turbines. The most distinctive difference was observed at a downstream turbine in the above-rated condition where the shaft torsional load in neutral stability condition was up to 50% higher than the unstable case. A baseline active yaw controller was implemented in the below-rated condition, which caused higher fatigue on turbines in the wake compared to the fixed yaw turbine case, without any power output gain.

Coupling of Wind and Potential Temperature in an Ekman Model in the Stratified Atmospheric Boundary Layer

Abstract A linear Ekman model in the stratified atmospheric boundary layer (ABL) is proposed based on the steady-state version of the linearized three-dimensional primitive equations with the inclusion of the vertical diffusivity. Due to the inclusion of the potential temperature equation and hydrostatic equation, pressure and potential temperature couple with wind in the proposed model, and thus are not arbitrarily specified variables as in previous studies on the baroclinicity in the Ekman model. The extended thermal wind balance equation and the Ekman potential vorticity equation are derived to describe the coupling. The two equations, along with the equation describing the constraint on potential temperature, are employed to derive the analytical solutions of the proposed Ekman model. Because potential temperature is not a specified variable but part of the solution, the derived analytical solutions have very different forms from those derived in previous studies. The differences illustrate the impact of the inclusion of the potential temperature equation and hydrostatic equation on wind, pressure, and potential temperature in the proposed Ekman model. It is found that the computed wind profiles based on the proposed model can capture some important features of the observed wind profiles.

Baroclinicity in stable atmospheric boundary layers: Characterizing turbulence structures and collapsing wind profiles via reduced models and large‐eddy simulations

AbstractBaroclinicity is a common, while often overlooked, phenomenon in the atmospheric boundary layer (ABL) that significantly impacts mean wind and turbulence structures. It adds another layer of complexity to the much‐studied stable barotropic ABLs by modulating the pressure gradient in height. Despite the prevalence of baroclinic and stable conditions in nature, our knowledge of their interacting effects on stratified ABL features is limited. The article aims to bridge this knowledge gap by systematically varying baroclinicity and stability using the large‐eddy simulation (LES) technique. The results of 15 conducted LESs indicate that baroclinicity alters the Ekman spiral shape and the low‐level jet's height in stable ABLs. Friction velocity, Obukhov length, shear production and the ABL height are highly influenced by baroclinicity in weakly stable ABLs, whereas they converge to a constant asymptote as the stability increases, independent of the baroclinicity regime. This is attributed to the strong turbulence destruction in very stable ABLs that decouples the surface from higher elevations where the baroclinicity effect is more significant. A reduced model for baroclinic wind profiles is developed and an analytical estimation of that for weakly baroclinic regimes is tested against LES results. Two rescaling methods in the inner and outer layers of stable baroclinic ABLs are used in a novel way to non‐dimensionalize the wind profiles. The suggested approaches reasonably collapse baroclinic/barotropic stable wind profiles in all considered LES cases. This study's findings elucidate the underlying physics of baroclinic stable ABLs and are useful for characterizing the wind profiles in weather/climate models, field measurements, and various industrial applications.

Thrust force and base bending moment acting on a horizontal axis wind turbine with a high tip speed ratio at high yaw angles

Onshore wind turbines may experience substantially different wind loads depending on their working conditions, i.e., rotation velocity of rotor blades, incoming freestream wind velocity, pitch angle of rotor blades, and yaw angle of the wind-turbine tower. In the present study, aerodynamic loads acting on a horizontal axis wind turbine were accordingly quantified for the high tip speed ratio (TSR) at high yaw angles because these conditions have previously not been adequately addressed. This was analyzed experimentally on a small-scale wind-turbine model in a boundary layer wind tunnel. The wind-tunnel simulation of the neutrally stratified atmospheric boundary layer (ABL) developing above a flat terrain was generated using the Counihan approach. The ABL was simulated to achieve the conditions of a wind-turbine model operating in similar inflow conditions to those of a prototype wind turbine situated in the lower atmosphere, which is another important aspect of the present work. The ABL and wind-turbine simulation length scale factors were the same (S=300) in order to satisfy the Jensen similarity criterion. Aerodynamic loads experienced by the wind-turbine model subjected to the ABL simulation were studied based on the high frequency force balance (HFFB) measurements. Emphasis was put on the thrust force and the bending moment because these two load components have previously proven to be dominant compared to other load components. The results indicate several important findings. The loads were substantially higher for TSR=10 compared to TSR=5.6. In these conditions, a considerable load reduction was achieved by pitching the rotor blades. For the blade pitch angle at 90°, the loads were ten times lower than the loads of the rotating wind-turbine model. For the blade pitch angle at 12°, the loads were at 50% of the rotating wind-turbine model. The loads were reduced by up to 40% through the yawing of the wind-turbine model, which was observed both for the rotating and the parked wind-turbine model.

The resistance law for stably stratified atmospheric planetary boundary layers

AbstractThe resistance law for stably and neutrally stratified atmospheric planetary boundary layers (PBL) entered textbooks on boundary‐layer meteorology but, until now, remains practically unused in modelling applications. This is not surprising. The law has been formulated and validated only for idealised cases, such as truly neutral PBL – implying neutral stratification across the entire atmosphere, nocturnal stable PBL – stably stratified near the surface but developed against the neutrally stratified free flow, and (more recently) conventionally neutral PBLs – neutrally stratified near the surface but developed against stable stratification in the free flow. We derive and validate the general formulation of the resistance law accounting for the integral effect on PBL of stable stratifications at the surface and in the free atmosphere. Such long‐lived stable PBLs, typical of wintertime at high latitudes, were until recently overlooked in boundary‐layer meteorology, not to mention weather and climate models. The proposed general formulation of the resistance law covers long‐lived stable PBLs and opens up prospects for their improved modelling.