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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Thermodynamic and electrical transport properties of UTe 2 under uniaxial stress

Despite intense experimental efforts, the nature of the unconventional superconducting order parameter of UTe 2 remains elusive. This puzzle stems from reports of either a single or a double superconducting transition at ambient pressure as well as a complex pressure-temperature phase diagram. To address this issue, we measured the heat capacity and electrical resistivity of UTe 2 under compressive uniaxial stress σ applied along different crystallographic directions. We find that the critical temperature T c of the single observed bulk superconducting transition decreases with σ along [100] and [110] but increases with σ along [001]. Aside from its effect on T c , c-axis stress leads to a significant piezoresistivity. Importantly, an in-plane shear stress σ xy does not induce any observable splitting of the superconducting transition over a stress range of σ xy ≈ 0.17GPa. Furthermore, this result suggests that the superconducting order parameter of UTe 2 may be single component at ambient pressure.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Minijet quenching in a concurrent jet + hydro evolution and the nonequilibrium quark-gluon plasma

Minijets, created by perturbative hard QCD collisions at moderate energies, can represent a significant portion of the total multiplicity of a heavy-ion collision event. Since their transverse momenta are initially larger than the typical saturation scale describing the bulk of the equilibrating quark-gluon plasma (QGP), they ought to be described through the physics of parton energy loss. Indeed, their typical stopping distances are larger than the usual hydrodynamization time, so they do not in general hydrodynamize at the same pace than the bulk of the collision. Therefore, in general minijets cannot be described solely by a unique preequilibrium stage that bridges the initial, overoccupied glasma state, with the hydrodynamical evolution. In this work we make use of a new concurrent minijet+hydrodynamic framework in which the properties of the hydrodynamically evolving QGP are modified due to the injection of energy and momentum from the minijets. We study the system for different choices of the minimum transverse momentum associated with minijet production. In order to achieve a realistic description of charged particle multiplicity, the amount of entropy associated to the low- x initial state needs to be reduced. Moreover, the fact that the injected momentum from the randomly oriented minijets is not correlated with the spatial gradients of the system reduces overall flow, and the value of the QGP transport coefficients needs to be reduced accordingly in order to describe the measured flow coefficients in experiments. They are, in effect, an important new source of fluctuations, resulting in a spikier, notably modified hydrodynamical evolution when compared to the scenario in which the presence of minijets is ignored. We avow that their abundance makes it necessary to include their physics in holistic descriptions of heavy-ion collisions. We discuss the impact of the minijets on a number of observables, such as p T spectra and p T -differential flow v n for a wide range of centrality classes. In contrast to elliptic, triangular or quadrangular flow, here we find that directed flow, v 1 , has the strongest potential to discriminate between different minijet production rates.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Directional locking and hysteresis in stripe- and bubble-forming systems on one-dimensional periodic substrates with a rotating drive

We examine the dynamics of a two-dimensional stripe, bubble, and crystal forming system interacting with a periodic one-dimensional substrate under an applied drive that is rotated with respect to the substrate periodicity direction 𝑥. We find that the stripes remain strongly directionally locked to the 𝑥 direction for an extended range of drives before undergoing motion parallel to the drive. In some cases, the stripes break apart at the unlocking transition, but they can dynamically reform into stripes aligned perpendicular to the 𝑥 direction, producing hysteresis in the directional locking and unlocking transitions. In contrast, moving anisotropic crystal and bubble phases exhibit weaker directional locking and reduced or no hysteresis. The hysteresis occurs in regimes where the particle rearrangements occur and is most pronounced near the stripe phase. In conclusion, we also show that for varied substrate strength, substrate spacing, and particle density, a number of novel dynamical patterns can form that include a combination of stripe, bubble, and crystal morphologies.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Unveiling the mechanism of phase and morphology selections during the devitrification of Al-Sm amorphous ribbon

The complex interplay between energetic and kinetic factors that governs the phase and morphology selections can originate at the earliest stage of crystallization in the amorphous parent phases. Because of the extreme difficulties in capturing the microscopic nucleation process, a detailed picture of how initial disordered structures affect the transformation pathway remains unclear. Here, we report the experimental observation of widely varying phase selection and grain size evolution during the devitrification of a homogeneous melt-spun glassy ribbon. Two different crystalline phases, θ-Al 5 Sm and ε-Al 60 Sm 11 , are found to form in the different regions of the same metallic glass ribbon during the devitrification. The grain size of ε-Al 60 Sm 11 phase shows a strong spatial heterogeneity. Coarse-grained ε-Al 60 Sm 11 phase coupled with the small volume fraction of θ-Al 5 Sm phase is preferably formed close to wheel side of the melt-spun ribbon. Combining experimental characterization and computational simulations, we show that phase selection and microstructure evolution can be traced back to different types and populations of atomic clusters that serve as precursors for the nucleation of different crystalline phases. Inhomogeneous cooling rates cause different structure orders across the glass sample during the quenching process. Our findings provide direct insight into the effect of structural order on the crystallization pathways during the devitrification of metallic glass. It also opens an avenue to study the detailed nucleation process at the atomic level using the metallic glass as a platform and suggests the opportunity of microstructure and property design via controlling the cooling process.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Effect of interfacial structures on phonon transport across atomically precise Si/Al heterojunctions

Phonons are important carriers of energy and information in many cryogenic devices used for quantum information science and in fundamental physics experiments such as dark matter detectors. In these systems phonon behavior can be dominated by interfaces, hence there is increasing demand for a more detailed understanding of interfacial phonon transport in relevant material systems. Previous studies have focused on understanding thermal transport over the entire phonon spectrum at and above room temperature. At ultra-low temperatures, however, knowledge is missing regarding athermal phonon behavior due to the challenge in modeling the extreme conditions in micro-scale, heterogeneous cryogenic systems, as well as extracting single-phonon information from a large ensemble. In this work, we delineate interfacial phonon transport using a combination of classical molecular dynamics (MD) and phonon wave packet simulations, to illustrate the consistency and differences between the ensemble- and single-phonon dynamics. We consider three single-crystal Si surface reconstructions --- (1×1), (v3×v3) and (7×7) --- and model both experimentally observed Si(1×1)/Al interfaces and hypothesized Si(v3×v3)/Al and Si(7×7)/Al interfaces. The overall interfacial thermal conductance calculated from non-equilibrium MD shows that for the Si(1×1)/Al system, the presence of Al twin grain boundaries can hinder phonon transport and reduce thermal conductance by 2--12% relative to single-crystal Al; whereas the Si (v3×v3) and (7×7) reconstructions can enhance it by 6--19%. Normal mode decomposition reveals that both the increase and decrease in conductance are related to inelastic phonon scattering. Single-phonon wave packet simulations show results consistent with NEMD, while further suggesting that phonon polarization conversion is significant even when elastic transmission dominates, and that the interfacial structures have anisotropic impacts on atomic vibrations along different lattice directions. Our findings suggest alternative perspectives in achieving selective phonon transport through controlling interfacial structures of materials with atomically-precise fabrication techniques, and that the phonon wave packet formalism is a potentially powerful method for developing a detailed understanding of non-equilibrium phenomena in the low-temperature limit.

Lu, Zexi↗
DOE OSTI2024

Intrinsic Limits of Charge Carrier Mobilities in Layered Halide Perovskites

Layered halide perovskites have emerged as potential alternatives to three-dimensional (3D) halide perovskites due to their improved stability and larger material phase space, allowing fine tuning of structural, electronic, and optical properties. However, their charge carrier mobilities are significantly smaller than those of 3D halide perovskites, which has a considerable impact on their application in optoelectronic devices. Here, we employ state-of-the-art approaches to unveil the electron-phonon mechanisms responsible for the diminished transport properties of layered halide perovskites. Starting from a prototypical A M X 3 halide perovskite, we model the case of n = 1 and n = 2 layered structures and compare their electronic and transport properties to the 3D reference. The electronic and phononic properties are investigated within density functional theory (DFT) and density functional perturbation theory (DFPT), while transport properties are obtained via the Boltzmann transport equation. The vibrational modes contributing to charge carrier scattering are investigated and associated with polar-phonon scattering mechanisms arising from the long-range Fröhlich coupling and deformation-potential scattering processes. Our investigation reveals that the lower mobilities in layered systems primarily originate from the increased electronic density of states at the vicinity of the band edges, while the electron-phonon coupling strength remains similar. Such an increase is caused by the dimensionality reduction and the break in octahedra connectivity along the stacking direction. Our findings provide a fundamental understanding of the electron-phonon coupling mechanisms in layered perovskites and highlight the intrinsic limitations of the charge carrier transport in these materials. Published by the American Physical Society 2024

Cucco, Bruno (ORCID:0000000331564143)↗
DOE OSTI2021

Increasing temperatures reduce invertebrate abundance and slow decomposition

Decomposition is an essential ecosystem service driven by interacting biotic and abiotic factors. Increasing temperatures due to climate change can affect soil moisture, soil fauna, and subsequently, decomposition. Understanding how projected climate change scenarios will affect decomposition is of vital importance for predicting nutrient cycling and ecosystem health. In this study, we experimentally addressed the question of how the early stages of decomposition would vary along a gradient of projected climate change scenarios. Given the importance of biodiversity for ecosystem service provisioning, we measured the effect of invertebrate exclusion on red maple ( Acer rubrum ) leaf litter breakdown along a temperature gradient using litterbags in warming chambers over a period of five weeks. Leaf litter decomposed more slowly in the warmer chambers and in the litterbag treatment that minimized invertebrate access. Moreover, increasing air temperature reduced invertebrate abundance and richness, and altered the community composition, independent of exclusion treatment. Using structural equation models, we were able to disentangle the effects of average air temperature on leaf litter loss, finding a direct negative effect of warming on the early stages of decomposition, independent of invertebrate abundance. This result indicates that not only can climate change affect the invertebrate community, but may also directly influence how the remaining organisms interact with their environment and their effectiveness at provisioning ecosystem services. Overall, our study highlights the role of biodiversity in maintaining ecosystem services and contributes to our understanding of how climate change could disrupt nutrient cycling.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Theoretical Particle Physics in the Data-Driven Era (Final Report)

DOE award DE-SC0021447 supports theoretical research in high energy physics. PI and students are not a part of any experimental collaboration, even if some works were done in collaboration with experimental colleagues. All research products are in the form of research articles and they are publicly available under inspirehep.net and arxiv.org, which are typical publication methods in high energy physics. No invention or patent is involved with this research. No equipment or hardware is involved with the research under this award. Research outcomes are used by colleagues in high energy physics, including both theorists and experimentalists. Therefore the outcome of research topics under this award supported the High Energy Physics experimental research program, both in understanding the data and in finding new directions for experimental exploration. The research materials are used to train undergraduate students, graduate students and postdoctoral scholars. We summarize research activity under this award in the following section and major products are listed in section 3. Section 4 contains professional presentations given by PI. Other products developed during the award period are in section 5. Students’ activities are summarized in section 6.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Complete Initial Evaluation of Novel Complexants for Tc Holdback for Simplified Single Cycle Separations.

Management of technetium at the back end of nuclear fuel cycle is complicated by its unique physico-chemical character, but must be addressed to due to the environmental, storage and reprocessing challenges of this fission product. In a single-cycle scenario, the recovery and purification of uranium is particularly challenging due to the tendency of a pertechnetate anion to follow uranyl cation. This report summarizes initial studies directed towards finding the solution for technetium management. Two options for controlling technetium’s chemistry in solvent extraction scenarios were studied. Molecular recognition of pertechnetate by aqueous complexants based on guanidinium moieties was compared to redox manipulation of technetium using dihydrazide reagents. Solvent extraction, potentiometric and nuclear magnetic resonance spectroscopy studies were performed. The influence of guanidinium reagents on the liquid-liquid partitioning of technetium is less pronounced, relative to dihydrazides. Strong impact exerted by dihydrazides originates from the technetium-catalyzed decomposition of such compounds which reduces technetium to a tetravalent, non-extractable state. Although this route of technetium management is very effective the destruction of dihydrazides is undesirable. Guanidinium complexants show a more tempered influence on technetium. The effect on the liquid-liquid partitioning of pertechnetate is evident and likely guided by anion recognition due to ion-pair and hydrogen bond formation. Guanidiniums are stable in presence of technetium as evidenced by nuclear magnetic resonance studies. The steady state chemistry of guanidiniums identify this class of aqueous complexants as solid candidates for structure-function pertechnetate recognition studies.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Complete Initial Studies in Microstructural Studies of Nuclear Graphite

Nuclear graphite is a critical material for the performance and safety of high-temperature reactors, making its study essential for the successful deployment of next-generation reactors in the United States. During the past year, Oak Ridge National Laboratory (ORNL) has contributed extensively to advancing the understanding of nuclear graphite’s properties, behavior, and applications; particular focus has been given to irradiation effects, oxidation mechanisms, thermal and mechanical performance, and long-term stability under reactor conditions. This report provides an update on the ongoing publications being prepared at ORNL. These studies are collectively intended to build a comprehensive knowledge base on nuclear graphite. The studies focus on key aspects such as microstructural characterization, oxidation behavior, advanced analytical techniques, molten salt infiltration, technique development, and billet-to-billet variability. By summarizing the progress of these publications, this report outlines ORNL’s contributions to the field, identifies knowledge gaps, and proposes future research directions. The findings presented in these studies will help enhance the understanding of nuclear graphite’s behavior, support the qualification of nuclear graphite materials, further the development of new techniques and guidelines for using microscopy techniques, and improve reactor safety and performance.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Understanding the High-Temperature Deformation Behaviors in Additively Manufactured Al6061+TiC Composites via In Situ Neutron Diffraction

Aluminum matrix composites (AMCs) are designed to enhance the performance of conventional aluminum alloys for engineering applications at both room and elevated temperatures. However, the dynamic phase-specific deformation behavior and load-sharing mechanisms of AMCs at elevated temperatures have not been extensively studied and remain unclear. Here, in situ neutron diffraction experiments are employed to reveal the phase-specific structure evolution of additively manufactured Al6061+TiC composites under compressive loading at 250 °C. It is found that the addition of a small amount of nano-size TiC significantly alters the deformation behavior and increases the strength at 250 °C in comparison to the as-printed Al6061. Unlike the two-stage behavior observed in Al6061, the Al6061+TiC composites exhibit three stages during compression triggered by changes in the interphase stress states. Further analysis of Bragg peak intensity and broadening reveals that the presence of TiC alters the dislocation activity during deformation at 250 °C by influencing dislocation slip planes and promoting dislocation accumulation. These findings provide direct experimental observations of the phase-specific dynamic process in AMCs under deformation at an elevated temperature. The revealed mechanisms provide insights for the future design and optimization of high-performance AMCs.

36 MATERIALS SCIENCE↗
DOE OSTI2024

"Hall" transport of liquid crystal solitons in Couette flow

Topology establishes a unifying framework for a diverse range of scientific areas including particle physics, cosmology, and condensed matter physics. One of the most fascinating manifestations of topology in the context of condensed matter is the topological Hall effect, and its relative: the Skyrmion Hall effect. Skyrmions are stable vortex-like spin configurations in certain chiral magnets, and when subject to external electric currents can drift in the transverse direction to the current. These quasi-particles are characterised by a conserved topological charge which in the Skyrmion Hall effect plays the role of electric charges in the ordinary Hall effect. Recently, it has been shown that liquid crystals endowed with chiral properties serve as an ideal testbed for the fundamental investigation of topological solitons, including their two- and three-dimensional realisations. Here, we show experimentally and numerically that three-dimensional solitons aka "torons" exhibit a Hall-like effect when driven by shear flows: the torons are deflected in the direction perpendicular to the shear plane. The experimental results are rationalised in terms of the dynamic Ericksen-Leslie equations, which predict the emergence of the transverse component of the net mass flow, the magnitude of which scales as the 3rd power of the shear rate. The perturbation analysis highlights an interplay of the viscous and chiral elastic torques as the mechanism for the emergence of net transverse currents. Numerical simulations demonstrate, however, that torons are not merely dragged by the flow but move with their own transverse speed, much larger than the average flow velocity in the transverse direction. Our findings may enable responsive microfluidic applications relying on soft topological solitons.

FOS: Physical sciences↗
DOE OSTI2026

Identification of Differential Equations by Dynamics-Guided Weighted Weak Form with Voting

In the identification of differential equations from data, significant progresses have been made with the weak/integral formulation. In this paper, we explore the direction of finding more efficient and robust test functions adaptively given the observed data. While this is a difficult task, we propose weighting a collection of localized test functions for better identification of differential equations from a single trajectory of noisy observations on the differential equation. We find that using high dynamic regions is effective in finding the equation as well as the coefficients, and propose a dynamics indicator per differential term and weight the weak form accordingly. For stable identification against noise, we further introduce a voting strategy to identify the active features from an ensemble of recovered results by selecting the features that frequently occur in different weighting of test functions. Systematic numerical experiments are provided to demonstrate the robustness of our method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Moving from scientific research to consenting guidance for MRE environmental risk

Potential environmental effects from tidal and wave devices are of concern to regulators, advisors, and other stakeholders in many nations. Monitoring results from early deployments and the first commercial arrays, coupled with targeted research studies, are providing a growing base of knowledge of how components of tidal turbines and wave energy converters might interact with marine animals and habitats. Efforts are underway to organize and direct these findings towards facilitating consenting that allays concerns and allows the marine renewable energy (MRE) industry to move forward. The OES-Environmental international initiative has developed scientific evidence bases for several key interactions from MRE devices, organized around stressors (portions of MRE systems that may cause injury or stress to the marine ecosystem), and receptors (the animals, habitats, and ecosystem processes that may be affected). This paper summarizes the evidence bases for four stressors (underwater noise, electromagnetic fields, habitat change, and changes in oceanographic systems) and presents the process of moving from the scientific knowledge into guidance documents to support the regulatory process. The guidance documents will serve as a broad guide that can be used internationally to look at stressor-receptor interactions of interest within a regulatory context. The evidence bases and guidance documents aim to assist MRE developers, regulators, and advisors with project scoping, consenting, and licensing processes.

Copping, Andrea E.↗
DOE OSTI2021

Decreased growth of wild soil microbes after 15 years of transplant‐induced warming in a montane meadow

Abstract The carbon stored in soil exceeds that of plant biomass and atmospheric carbon and its stability can impact global climate. Growth of decomposer microorganisms mediates both the accrual and loss of soil carbon. Growth is sensitive to temperature and given the vast biological diversity of soil microorganisms, the response of decomposer growth rates to warming may be strongly idiosyncratic, varying among taxa, making ecosystem predictions difficult. Here, we show that 15 years of warming by transplanting plant–soil mesocosms down in elevation, strongly reduced the growth rates of soil microorganisms, measured in the field using undisturbed soil. The magnitude of the response to warming varied among microbial taxa. However, the direction of the response—reduced growth—was universal and warming explained twofold more variation than did the sum of taxonomic identity and its interaction with warming. For this ecosystem, most of the growth responses to warming could be explained without taxon‐specific information, suggesting that in some cases microbial responses measured in aggregate may be adequate for climate modeling. Long‐term experimental warming also reduced soil carbon content, likely a consequence of a warming‐induced increase in decomposition, as warming‐induced changes in plant productivity were negligible. The loss of soil carbon and decreased microbial biomass with warming may explain the reduced growth of the microbial community, more than the direct effects of temperature on growth. These findings show that direct and indirect effects of long‐term warming can reduce growth rates of soil microbes, which may have important feedbacks to global warming.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Algorithm to extract direction in 2D discrete distributions and a continuous Frobenius norm

In this study, we present a novel algorithm for determining directionality in 2D distributions of discrete data. We compare a reference dataset with a known direction to a measured dataset with an unknown direction by the Frobenius norm of the difference (FND) to find the unknown direction. To generalize this concept, we develop a continuous Frobenius norm of the difference (CFND) as a continuous analog of the FND and derive its analytical expression. By relating fitted and normalized 2D Gaussian distributions, we show that the CFND approximates the FND, and we validate this relationship with computer simulations. We find that a first-order approximation of the CFND between two similar Gaussian distributions takes the form of an absolute sine function, offering a simple analytical form with potential for specialized applications in segmented inverse beta decay (IBD) neutrino detectors, astronomy, machine learning, and more. Although this method may easily extend to 3D scalar fields, our focus here is on 2D real-valued fields as it directly applies to directionality. Our methodology consists of modeling a 2D Gaussian distribution, binning the data into a histogram, and encoding it as a square matrix. Rotating this matrix around its geometric center and comparing it to a measured dataset using the FND gives us rotational data that we fit with an absolute sine function. The location of the minimum of this fit is the angle closest to the true angle of the direction in the measured dataset. We present the derivation and discuss initial applications of the CFND in our novel algorithm, demonstrating its success in approximating directionality in 2D distributions.

Data Analysis, Statistics and Probability (physics↗
DOE OSTI2026

Algorithm to extract direction in 2D discrete distributions and a continuous Frobenius norm

In this study, we present a novel algorithm for determining directionality in 2D distributions of discrete data. We compare a reference dataset with a known direction to a measured dataset with an unknown direction by the Frobenius norm of the difference (FND) to find the unknown direction. To generalize this concept, we develop a continuous Frobenius norm of the difference (CFND) as a continuous analog of the FND and derive its analytical expression. By relating fitted and normalized 2D Gaussian distributions, we show that the CFND approximates the FND, and we validate this relationship with computer simulations. We find that a first-order approximation of the CFND between two similar Gaussian distributions takes the form of an absolute sine function, offering a simple analytical form with potential applications in specialized areas such as segmented inverse beta decay neutrino detectors, astronomy, machine learning, and more. Our methodology consists of modeling a 2D Gaussian distribution, binning the data into a histogram, and encoding it as a square matrix. Rotating this matrix around its geometric center and comparing it to a measured dataset using the FND gives us rotational data that we fit with an absolute sine function. The location of the minimum of this fit is the angle closest to the true angle of the direction in the measured dataset. We present the derivation and discuss initial applications of the CFND in our novel algorithm, demonstrating its success in approximating directionality in 2D distributions.

Physics↗
DOE OSTI2021

Results from a wake-steering experiment at a commercial wind plant: investigating the wind speed dependence of wake-steering performance

Wake steering is a wind farm control strategy in which upstream wind turbines are misaligned with the wind to redirect their wakes away from downstream turbines, thereby increasing the net wind plant power production and reducing fatigue loads generated by wake turbulence. In this paper, we present results from a wake-steering experiment at a commercial wind plant involving two wind turbines spaced 3.7 rotor diameters apart. During the 3-month experiment period, we estimate that wake steering reduced wake losses by 5.6% for the wind direction sector investigated. After applying a long-term correction based on the site wind rose, the reduction in wake losses increases to 9.3%. As a function of wind speed, we find large energy improvements near cut-in wind speed, where wake steering can prevent the downstream wind turbine from shutting down. Yet for wind speeds between 6–8 m/s, we observe little change in performance with wake steering. However, wake steering was found to improve energy production significantly for below-rated wind speeds from 8–12 m/s. By measuring the relationship between yaw misalignment and power production using a nacelle lidar, we attribute much of the improvement in wake-steering performance at higher wind speeds to a significant reduction in the power loss of the upstream turbine as wind speed increases. Additionally, we find higher wind direction variability at lower wind speeds, which contributes to poor performance in the 6–8 m/s wind speed bin because of slow yaw controller dynamics. Further, we compare the measured performance of wake steering to predictions using the FLORIS (FLOw Redirection and Induction in Steady State) wind farm control tool coupled with a wind direction variability model. Although the achieved yaw offsets at the upstream wind turbine fall short of the intended yaw offsets, we find that they are predicted well by the wind direction variability model. When incorporating the expected yaw offsets, estimates of the energy improvement from wake steering using FLORIS closely match the experimental results.

17 WIND ENERGY↗