To achieve decarbonization targets, wind turbines are growing in hub height and rotor diameter, and they are being deployed in new locations with diverse atmospheric conditions not previously seen, such as offshore. Physics-based analytical wake models commonly used for design and control of wind farms simplify atmospheric boundary layer (ABL) and wake physics to achieve computational efficiency. This is accomplished primarily through a simplified model form that neglects certain flow processes, such as atmospheric stability, and through the parametrization of ABL and wake turbulence through a wake spreading rate. In this study, we systematically analyze the physical mechanisms that govern momentum and turbulence within a wind turbine wake in the stratified ABL. We use large-eddy simulation and analysis of the streamwise momentum deficit and wake-added turbulence kinetic energy (TKE) budgets to study wind turbine wakes under neutral and stable conditions. To parse the turbulence in the wake from the turbulent, incident ABL flow, we decompose the flow into the base ABL flow and the deficit flow produced by the presence of a turbine. We then analyze the decomposed flow field budgets to study the effects of changing stability on the streamwise momentum deficit and wake-added TKE. The results demonstrate that stability changes the relative balance of turbulence and advection for both the streamwise momentum deficit and wake-added TKE primarily through the nonlinear interactions of the base flow with the deficit flow. The stable cases are most affected by increased shear and veer in the base flow and the neutral case is most affected by the increased ambient turbulence intensity. These differences in the base flow that arise from stratification are relatively more important than the buoyancy forcing terms in the wake-added TKE budget. The wake-added TKE depends on the ABL stability. An existing wake-added TKE model that neglects the effects of ABL stability yieldserror compared to large-eddy simulation, with errors that are higher in stable conditions than neutral. These results motivate future research to develop fast-running models of wake-added TKE that account for stability effects.
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Published by the American Physical Society 2024 Free, publicly-accessible full text available November 1, 2025 -
Wind turbine control via concurrent yaw misalignment and axial induction control has demonstrated potential for improving wind farm power output and mitigating structural loads. However, the complex aerodynamic interplay between these two effects requires deeper investigation. This study presents a modified blade element momentum (BEM) model that matches rotor-averaged quantities to an actuator disk model of yawed rotor induction, enabling analysis of joint yaw-induction control using realistic turbine control inputs. The BEM approach reveals that common torque control strategies such as K−Ω^2 exhibit sub-optimal performance under yawed conditions. Notably, the power-yaw and thrust-yaw sensitivities vary significantly depending on the chosen control strategy, contrary to common modeling assumptions. In the context of wind farm control, employing induction control which minimizes the thrust coefficient proves most effective at reducing wake strength for a given power output across all yaw angles. Results indicate that while yaw control deflects wakes effectively, induction control more directly influences wake velocity magnitude, underscoring their complementary effects. This study advances a fundamental understanding of turbine aerodynamic responses in yawed operation and sets the stage for modeling joint yaw and induction control in wind farms.more » « lessFree, publicly-accessible full text available June 1, 2025
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Combined wake steering and induction control is a promising strategy for increasing collective wind farm power production over standard turbine control. However, computationally efficient models for predicting optimal control set points still need to be tested against high-fidelity simulations, particularly in regimes of high rotor thrust. In this study, large eddy simulations (LES) are used to investigate a two-turbine array using actuator disk modeling in conventionally neutral atmospheric conditions. The thrust coefficient and yaw-misalignment angle are independently prescribed to the upwind turbine in each simulation while downwind turbine operation is fixed. Analyzing the LES velocity fields shows that near-wake length decreases and wake recovery rate increases with increasing thrust. We model the wake behavior with a physics-based near-wake and induction model coupled with a Gaussian far-wake model. The near-wake model predicts the turbine thrust and power depending on the wake steering and induction control set point. The initial wake velocities predicted by the near-wake model are validated against LES data, and a calibrated far-wake model is used to estimate the power maximizing control set point and power gain. Both model-predicted and LES optimal set points exhibit increases in yaw angle and thrust coefficient for the leading turbine relative to standard control. The model-optimal set point predicts a power gain of 18.1% while the LES optimal set point results in a power gain of 20.7%. In contrast, using a tuned cosine model for the power-yaw relationship results in a set point with a lower magnitude of yaw, a thrust coefficient lower than in standard control, and predicts a power gain of 13.7%. Using the physics-based, model-predicted set points in LES results in a power within 1.5% of optimal, showing potential for joint yaw-induction control as a method for predictably increasing wind farm power output.more » « lessFree, publicly-accessible full text available June 1, 2025
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Modeling the effect of wind speed and direction shear on utility‐scale wind turbine power productionWind speed and direction variations across the rotor affect power production. As utility‐scale turbines extend higher into the atmospheric boundary layer (ABL) with larger rotor diameters and hub heights, they increasingly encounter more complex wind speed and direction variations. We assess three models for power production that account for wind speed and direction shear. Two are based on actuator disc representations, and the third is a blade element representation. We also evaluate the predictions from a standard power curve model that has no knowledge of wind shear. The predictions from each model, driven by wind profile measurements from a profiling LiDAR, are compared to concurrent power measurements from an adjacent utility‐scale wind turbine. In the field measurements of the utility‐scale turbine, discrete combinations of speed and direction shear induce changes in power production of −19% to +34% relative to the turbine power curve for a given hub height wind speed. Positive speed shear generally corresponds to over‐performance and increasing magnitudes of direction shear to greater under‐performance, relative to the power curve. Overall, the blade element model produces both higher correlation and lower error relative to the other models, but its quantitative accuracy depends on induction and controller sub‐models. To further assess the influence of complex, non‐monotonic wind profiles, we also drive the models with best‐fit power law wind speed profiles and linear wind direction profiles. These idealized inputs produce qualitative and quantitative differences in power predictions from each model, demonstrating that time‐varying, non‐monotonic wind shear affects wind power production.more » « lessFree, publicly-accessible full text available June 1, 2025
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Wind farm design generally relies on the use of historical data and analytical wake models to predict farm quantities, such as annual energy production (AEP). Uncertainty in input wind data that drive these predictions can translate to significant uncertainty in output quantities. We examine two sources of uncertainty stemming from the level of description of the relevant meteorological variables and the source of the data. The former comes from a standard practice of simplifying the representation of the wind conditions in wake models, such as AEP estimates based on averaged turbulence intensity (TI), as opposed to instantaneous. Uncertainty from the data source arises from practical considerations related to the high cost of in situ measurements, especially for offshore wind farms. Instead, numerical weather prediction (NWP) modeling can be used to characterize the more exact location of the proposed site, with the trade-off of an imperfect model form. In the present work, both sources of input uncertainty are analyzed through a study of the site of the future Vineyard Wind 1 offshore wind farm. This site is analyzed using wind data from LiDAR measurements located 25 km from the farm and NWP data located within the farm. Error and uncertainty from the TI and data sources are quantified through forward analysis using an analytical wake model. We find that the impact of TI error on AEP predictions is negligible, while data source uncertainty results in 0.4%–3.7% uncertainty over feasible candidate hub heights for offshore wind farms, which can exceed interannual variability.
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null (Ed.)To design and optimize arrays of vertical-axis wind turbines (VAWTs) for maximal power density and minimal wake losses, a careful consideration of the inherently three-dimensional structure of the wakes of these turbines in real operating conditions is needed. Accordingly, a new volumetric particle-tracking velocimetry method was developed to measure three-dimensional flow fields around full-scale VAWTs in field conditions. Experiments were conducted at the Field Laboratory for Optimized Wind Energy (FLOWE) in Lancaster, CA, using six cameras and artificial snow as tracer particles. Velocity and vorticity measurements were obtained for a 2 kW turbine with five straight blades and a 1 kW turbine with three helical blades, each at two distinct tip-speed ratios and at Reynolds numbers based on the rotor diameter $D$ between $1.26 \times 10^{6}$ and $1.81 \times 10^{6}$ . A tilted wake was observed to be induced by the helical-bladed turbine. By considering the dynamics of vortex lines shed from the rotating blades, the tilted wake was connected to the geometry of the helical blades. Furthermore, the effects of the tilted wake on a streamwise horseshoe vortex induced by the rotation of the turbine were quantified. Lastly, the implications of this dynamics for the recovery of the wake were examined. This study thus establishes a fluid-mechanical connection between the geometric features of a VAWT and the salient three-dimensional flow characteristics of its near-wake region, which can potentially inform both the design of turbines and the arrangement of turbines into highly efficient arrays.more » « less
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Abstract Data required to calibrate uncertain general circulation model (GCM) parameterizations are often only available in limited regions or time periods, for example, observational data from field campaigns, or data generated in local high‐resolution simulations. This raises the question of where and when to acquire additional data to be maximally informative about parameterizations in a GCM. Here we construct a new ensemble‐based parallel algorithm to automatically target data acquisition to regions and times that maximize the uncertainty reduction, or information gain, about GCM parameters. The algorithm uses a Bayesian framework that exploits a quantified distribution of GCM parameters as a measure of uncertainty. This distribution is informed by time‐averaged climate statistics restricted to local regions and times. The algorithm is embedded in the recently developed calibrate‐emulate‐sample framework, which performs efficient model calibration and uncertainty quantification with only
model evaluations, compared with evaluations typically needed for traditional approaches to Bayesian calibration. We demonstrate the algorithm with an idealized GCM, with which we generate surrogates of local data. In this perfect‐model setting, we calibrate parameters and quantify uncertainties in a quasi‐equilibrium convection scheme in the GCM. We consider targeted data that are (a) localized in space for statistically stationary simulations, and (b) localized in space and time for seasonally varying simulations. In these proof‐of‐concept applications, the calculated information gain reflects the reduction in parametric uncertainty obtained from Bayesian inference when harnessing a targeted sample of data. The largest information gain typically, but not always, results from regions near the intertropical convergence zone. -
Abstract Climate models are generally calibrated manually by comparing selected climate statistics, such as the global top‐of‐atmosphere energy balance, to observations. The manual tuning only targets a limited subset of observational data and parameters. Bayesian calibration can estimate climate model parameters and their uncertainty using a larger fraction of the available data and automatically exploring the parameter space more broadly. In Bayesian learning, it is natural to exploit the seasonal cycle, which has large amplitude compared with anthropogenic climate change in many climate statistics. In this study, we develop methods for the calibration and uncertainty quantification (UQ) of model parameters exploiting the seasonal cycle, and we demonstrate a proof‐of‐concept with an idealized general circulation model (GCM). UQ is performed using the calibrate‐emulate‐sample approach, which combines stochastic optimization and machine learning emulation to speed up Bayesian learning. The methods are demonstrated in a perfect‐model setting through the calibration and UQ of a convective parameterization in an idealized GCM with a seasonal cycle. Calibration and UQ based on seasonally averaged climate statistics, compared to annually averaged, reduces the calibration error by up to an order of magnitude and narrows the spread of the non‐Gaussian posterior distributions by factors between two and five, depending on the variables used for UQ. The reduction in the spread of the parameter posterior distribution leads to a reduction in the uncertainty of climate model predictions.