SEARCH · Engineering Papers

Results for “WAVE REFLECTION”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records

All sources NASA NTRS DOE OSTI

DOE OSTI2026

Topographic effects on reflected acoustic waves from the OSIRIS-REx reentry observed from stratospheric balloons

During long-distance sound propagation in planetary atmospheres, acoustic waves may reflect off the air/surface interface one or more times. For low sound frequencies and flat interfaces, the incident and reflected wave tend to be nearly identical. However, this may not be the case when the downgoing acoustic wave encounters topography. Here, we describe a set of direct and reflected acoustic signals recorded on free-flying balloons during the hypersonic entry of the OSIRIS-REx sample return capsule (SRC). In two of the three cases presented here, an impulsive reflected arrival similar in form to the direct sonic boom of the SRC is observed, followed by a diffuse coda. In contrast, one of the floating stations lacked an impulsive reflection entirely, with only the coda present. We use full waveform modeling to show how reflection in the presence of complex topography can explain coda seen in all three examples as well as the lack of impulsive arrival on the third. Our results indicate that the complex signals often observed in long range acoustic propagation could be due, in part, to interactions with topography during transmission.

Lees, Jonathan M. [University of North Carolina, C↗

DOE OSTI2025

Meteorological Conditions in Urban Sites in Knoxville, USA. 2023

This 2023 dataset, which contains four csv files, reports hourly air temperature, wind speed, solar radiation, incident short wave, reflected short wave, incident long wave, emitted long wave, net radiation, and photosynthetically active radiation (PAR) data measured in urban parks in Knoxville, Tennessee, USA. The sites include Cumberland Estates Park (CEP), Socially Equal Energy Efficient Development (SEEED), West Hills (WHP), and Victor Ashe Park (VAP). Air temperature, wind speed and direction, and solar radiation data were obtained from a METER ATMOS 41 All-in-One Weather Station (Pullman, Washington, USA). Incident and emitted radiation (shortwave and longwave) measurements were made using an Apogee (Logan, Utah, USA) net radiometer (Model SN-500-SS). The SQ-521 Full-Spectrum Quantum sensor (Apogee Instruments, Inc) recorded the PAR. The measurement data for CEP, SEEED, and VAP started on July 1, 2023, while WHP started on August 26, 2023. All measurement ended on December 31, 2023. This work is a part of a larger study which investigates the impact of soil moisture and plant evapotranspiration on ambient temperature and relative humidity in several city parks in Knoxville, Tennessee.

Salvador, Christian [ORNL] (ORCID:0000000283287777↗

DOE OSTI2026

Meteorological Conditions in Urban Sites in Knoxville, USA. 2025

This 2025 dataset, which contains five csv files, reports hourly air temperature, wind speed, solar radiation, incident short wave, reflected short wave, incident long wave, emitted long wave, net radiation, and photosynthetically active radiation (PAR) data measured in urban parks in Knoxville, Tennessee, USA. The sites include Cumberland Estates Park (CEP), Socially Equal Energy Efficient Development (SEEED), West Hills Park (WHP), West View Park (WVP), and Victor Ashe Park (VAP). Air temperature, wind speed, and solar radiation data were obtained from a METER ATMOS 41 All-in-One Weather Station (Pullman, Washington, USA). Incident and emitted radiation (shortwave and longwave) measurements were made using an Apogee (Logan, Utah, USA) net radiometer (Model SN-500-SS). The SQ-521 Full-Spectrum Quantum sensor (Apogee Instruments, Inc) recorded the PAR. The measurement data for all the sites started on January 1, 2025. and all measurement ended on December 31, 2025. This work is a part of a larger study which investigates the impact of soil moisture and plant evapotranspiration on ambient temperature and relative humidity in several city parks in Knoxville, Tennessee.

Salvador, Christian [ORNL] (ORCID:0000000283287777↗

DOE OSTI2025

Outflow Boundary Conditions for Turbine-Integrated Rotating Detonation Combustors

This study examines outflow boundary conditions (BCs) in computational fluid dynamics (CFD) simulations of a transition duct with and without guide vanes that converts supersonic flow exiting a rotating detonation combustor (RDC) to subsonic flow to drive a turbine. Since the flow exiting the transition duct has swirling shock waves with significant spatial and temporal variations in pressure, temperature, and Mach number, imposing proper BCs poses a challenge. To ensure all swirling shock waves exit the transition duct without creating non-physical reflected waves at its outlet, this study examined three outflow BCs: (1) the average pressure imposed at the duct’s outlet, (2) a nonreflecting BC (NRBC) with a specified average pressure imposed at the duct’s outlet, (3) the average pressure imposed at the outlet of an extension duct made up of a buffer layer and a sponge layer. This study is based on the three-dimensional, unsteady density-weighted-ensemble-averaged continuity, Navier–Stokes, and energy equations for a thermally perfect gas closed by the realizable k–ε model and “enhanced” wall functions. The results obtained show that imposing an average pressure at the transition duct’s outlet produces spurious waves that degrade the physical meaningfulness of the solution. When the NRBC was applied, swirling shock waves exited the duct’s outlet without creating spurious waves. However, its usage requires the gas to be thermally, as well as calorically, perfect, which this study shows could be a concern. By imposing the average pressure at the outlet of an extension duct, the gas does not need to be calorically perfect. The results obtained show the effects of the sponge layer’s length and coarsening ratio on damping nonuniformities in non-physical reflected waves to ensure the flow exiting the transition duct’s outlet can do so as if there are no boundaries present and has the desired average pressure—even though the BC is applied at the extension duct’s outlet.

gas turbines↗

DOE OSTI2025

Prediction of the Wave Normal Angle of Proton‐Band EMIC Waves Near Geosynchronous Orbit

We investigate how the wave normal angle (WNA) and polarization of proton-band electromagnetic ion cyclotron (EMIC) waves change as they travel from their source to Earth. This paper marks a significant milestone as the first full-wave simulation of proton-band EMIC waves reflecting from the ionosphere. Our findings show that the WNA can change rapidly during propagation, primarily due to plasma inhomogeneities, such as variations in the Alfvén speed. The wave polarization is strongly related to the WNA, consistent with theory. Newly generated EMIC waves near the equator propagate with a WNA of 0° , then the WNA gradually shifts to 90° as they move toward Earth. In contrast, reflecting waves having 90° of WNA at Earth maintain a relatively larger WNA even near the magnetic equator. As a result, only the newly generated waves close to the source, where the magnetic latitude is less than approximately 20° , show left-handed polarization, while linear polarization remains dominant throughout the rest of the propagation.

EMIC wave↗

DOE OSTI2026

FAIR Data and Interpretable AI Framework for Architectured Metamaterials (Final Report)

This research program established a transformative framework for the discovery and design of mechanical metamaterials, which are architected structures engineered to control physical phenomena like sound and vibration in ways natural materials cannot. To overcome the traditional reliance on trial-and-error, the project developed an interpretable Artificial Intelligence (AI) framework that moves beyond "black box" models to reveal the specific geometric patterns—such as "unit-cell templates"—that govern a material’s performance. A major breakthrough was the development of a hierarchical design method, which allows a single material to block vibrations across multiple frequency ranges simultaneously by layering patterns at different scales without them interfering with one another. This was further expanded to include irregular, graph-based designs that use spanning tree algorithms to ensure structural connectivity while allowing for customized, direction-dependent properties like stiffness and acoustic impedance. Beyond design, the project addressed the practicalities of real-world production by developing uncertainty quantification techniques that account for manufacturing defects and material variability, reducing the need for expensive physical testing by orders of magnitude. To speed up the discovery process, the team implemented Gaussian Process Regression and other surrogate models that provide accurate performance predictions at a fraction of the traditional computational cost. The AI-generated designs were successfully validated through fabrication of physical samples and wave propagation experiments, confirming their ability to accurately guide or reflect waves as predicted. By contributing these tools and high-quality FAIR benchmark datasets to the wider scientific community, this work provides a scalable foundation for advancing technologies in aerospace vibration control, medical imaging, and noise reduction.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Perfectly Matched Layers and Characteristic Boundaries in Lattice Boltzmann: Accuracy vs Cost

Artificial boundary conditions (BCs) play a ubiquitous role in numerical simulations of transport phenomena in several diverse fields, such as fluid dynamics, electromagnetism, acoustics, geophysics, and many more. They are essential for accurately capturing the behavior of physical systems whenever the simulation domain is truncated for computational efficiency purposes. Ideally, an artificial BC would allow relevant information to enter or leave the computational domain without introducing artifacts or unphysical effects. Boundary conditions designed to control spurious wave reflections are referred to as nonreflective boundary conditions (NRBCs). Another approach is given by the perfectly matched layers (PMLs), in which the computational domain is extended with multiple dampening layers, where outgoing waves are absorbed exponentially in time. Here, in this work, the definition of PML is revised in the context of the lattice Boltzmann method. The impact of adopting different types of BCs at the edge of the dampening zone is evaluated and compared, in terms of both accuracy and computational costs. It is shown that for sufficiently large buffer zones, PMLs allow stable and accurate simulations even when using a simple zeroth-order extrapolation BC. Moreover, employing PMLs in combination with NRBCs potentially offers significant gains in accuracy at a modest computational overhead, provided the parameters of the BC are properly tuned to match the properties of the underlying fluid flow.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Towards the Ultimate Strength of Medium‐Entropy Alloys Through Pulsed Lasers

The tensile strength of metals at extreme strain rates is a key predictor of their performance in ballistic and structural impact applications. An important experimental method to reach these extreme strain rates is the use of high-amplitude, short-duration pulsed lasers. The Jupiter Laser Facility at the Lawrence Livermore National Laboratory enabled probing for the first time the mechanical response of several promising High Entropy Alloys at times on the order of nanoseconds (strain rates of ∼10 7 and ∼10 9 s −1 ). The measured strength is in the range of 6 to 10 GPa, ten times the quasistatic value. The mechanisms of plastic deformation and failure were identified and quantified through analysis and molecular dynamics simulation. The reflected wave amplitudes, obtained by VISAR, were used to determine the tensile (spall) stress. The high tensile strength obtained is due to two factors: the strain-rate dependence of plastic flow and the kinetics of void nucleation, growth, and coalescence. The experimental results are compared with an analytical prediction considering both grain-interior and grain-boundary void initiation. Molecular dynamics simulations, conducted at strain rates of 10 8 and 10 9 s −1 , rationalize the experimental results. In conclusion, they provide valuable information about the process of failure evolution, and reveal that grain boundary separation plays a pivotal role in spalling.

Materials science↗

DOE OSTI2025

Hydraulic performance and wave transmission through nature-inspired perforated hollow-base piles breakwater

Nature-based Solutions (NbS) are critical to achieving long-term sustainable coastlines in deltaic coastlines, particularly susceptible to severe impacts under climate change. In recent years, coastal erosion has accelerated in the Vietnam Mekong Delta (VMD), particularly in the West Sea (from Ca Mau to Kien Giang). Due to the characteristics of muddy coastlines and eroded mangrove forests in this region, only a few engineering solutions have effectively reduced waves and promoted sediment accumulation to facilitate beach accretion. However, these solutions require significant investment and cannot be relocated or reused. Therefore, this study introduces a coastal mangrove-inspired perforated hollow-base piles breakwater (PHBPB), which uses the principle of biomimicry by studying the ability of mangrove groups to protect the coastline, stimulate sediment deposition, and over time, restore mangrove forests in the VMD. The hydraulic parameters of PHBPB were tested in 260 scenarios using a physical model, which included varying parameters such as crest width (B), pile row numbers (n c ), crest freeboard (R c ), and wave parameters (H s , T p ) in determining the capabilities of wave transmission, reflection, and wave dissipation. The results showed that the process of wave energy dissipation through perforated hollow-base breakwaters without piles (PHBBWP) is governed by three main parameters, including the relative water depth of the crest (R c /H m0,i ), the relative width of the crest (B/H m0,i ), and the wave slope at the structure location (s m = H m0,i /L m ). In contrast, for PHBPB, the primary influencing factors are the relative submergence depth or the length of the submerged pile portion (R c /H m0,i ) and the relative width of the pile system (X b /L m ). Finally, the hollow structure is suitable for the soft, weak mud geology in this region with poor load-bearing capacity, allows for rapid installation, is reasonably cost-effective, and can be relocated and reused once regeneration has been completed in each stretch of coastline.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Shock-induced twinning/detwinning and spall failure in Cu–Ta nanolaminates at atomic scales

Here, this study provides new insights into the role of interfaces on the deformation and failure mechanisms in shock-loaded Cu–Ta–Cu trilayer system. The thickness of the Ta layer, piston velocities, and shock pulse durations were varied to explore the impact of impedance mismatch and loading conditions on spallation behavior and twin formation. It was found that the interfaces play a crucial role in the dynamic response of these multilayered systems since secondary reflection waves generated at the interfaces significantly affected the peak stress and pressure profiles, influencing void nucleation and failure modes. In the trilayer systems, failure predominantly occurred at interfaces and within the Ta layer, with void nucleation sites and twinning behavior being markedly different compared to single-crystal Cu and Ta. Increasing the Ta layer thickness modified the wave interactions, leading to different failure locations. Higher piston velocities were associated with increased spall strength by enhancing wave interactions and void formation, particularly at the interfaces and within the Ta layer, under specific configurations. Additionally, shorter shock pulse durations facilitated earlier initiation of the release fan, reducing twin formation and altering the failure dynamics by accelerating twin annihilation and pressure release.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Cold-air outbreaks in the continental US: Connections with stratospheric variations

Mid-latitude Northern Hemisphere extreme cold events continue to occur despite overall winter warming trends. These events have been linked to weakened stratospheric polar vortex (SPV) states. In this study, we analyze both the upper and lower polar stratosphere for links to extreme winter cold and snow in the continental US, finding two SPV variations of interest. The first features an upper-level vortex displaced toward western Canada and linked to northwestern US severe winter weather. The second features a weakened upper-level vortex displaced toward the North Atlantic and linked to central-eastern US severe winter weather. Both variations feature lower-level stretched vortices and stratospheric wave reflection. Since 2015, a northwestward shift in severe winter weather across the US is concurrent with an increase in the frequency of the westward-focused variation relative to the eastward-focused variation and a shift to more negative phases of the El Niño–Southern Oscillation.

Science & Technology - Other Topics↗

DOE OSTI2025

Measurement of Energy Reduction of Inertial Alfvén Waves Propagating through Parallel Gradients in the Alfvén Speed

We have studied the propagation of inertial Alfvén waves through parallel gradients in the Alfvén speed using the Large Plasma Device at the University of California, Los Angeles. The reflection and transmission of Alfvén waves through inhomogeneities in the background plasma are important for understanding wave propagation, turbulence, and heating in space, laboratory, and astrophysical plasmas. Here we present inertial Alfvén waves under conditions relevant to solar flares and the solar corona. We find that the transmission of the inertial Alfvén waves is reduced as the sharpness of the gradient is increased. Any reflected waves were below the detection limit of our experiment, and reflection cannot account for all of the energy not transmitted through the gradient. Our findings indicate that, for both kinetic and inertial Alfvén waves, the controlling parameter for the transmission of the waves through an Alfvén speed gradient is the ratio of the Alfvén wavelength along the gradient divided by the scale length of the gradient. Furthermore, our results suggest that an as-yet-unidentified damping process occurs in the gradient.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Absorbing boundary conditions in material point method adopting perfectly matched layer theory

This study focuses on solving the numerical challenges of imposing absorbing boundary conditions for dynamic simulations in the material point method (MPM). To attenuate elastic waves leaving the computational domain, the current work integrates the Perfectly Matched Layer (PML) theory into the implicit MPM framework. The proposed approach introduces absorbing particles surrounding the computational domain that efficiently absorb outgoing waves and reduce reflections, allowing for accurate modeling of wave propagation and its further impact on geotechnical slope stability analysis. The study also includes several benchmark tests to validate the effectiveness of the proposed method, such as several types of impulse loading and symmetric and asymmetric base shaking. The conducted numerical tests also demonstrate the ability to handle large deformation problems, including the failure of elasto-plastic soils under gravity and dynamic excitations. The findings extend the capability of MPM in simulating continuous analysis of earthquake-induced landslides, from shaking to failure.

58 GEOSCIENCES↗

DOE OSTI2025

Investigating the relationship between simulation parameters and flow variables in simulating atmospheric gravity waves for wind energy applications

Wind farms, particularly offshore clusters, are becoming larger than ever before. Besides influencing the surface wind flow and the inflow for downstream wind farms, large wind farms can trigger atmospheric gravity waves in the inversion layer and the free atmosphere aloft. Wind-farm-induced gravity waves can cause adverse pressure gradients upstream of the wind farm, which contribute to the global blockage effect, and can induce favorable pressure gradients above and downstream of the wind farm that enhance wake recovery. Numerical modeling is a powerful means of studying these wind-farm-induced atmospheric gravity waves, but it comes with the challenge of handling spurious reflections of these waves from domain boundaries. Typically, approaches which employ radiation boundary conditions and forcing zones are used to avoid these reflections. However, the simulation setup of these approaches relies heavily on ad hoc processes. For instance, the widely used Rayleigh damping method requires ad hoc tuning to produce a setup that may only produce satisfactory results for a particular case. To provide more systematic guidance on setting up realistic simulations of atmospheric gravity waves, we conduct a large-eddy simulation (LES) study of flow over a 2D hill and through a wind farm canopy that explores the optimum domain size and damping layer setup depending on the fundamental parameters which determine the flow characteristics. In this work, we only consider linearly stratified conditions (i.e., no inversion layer), thereby focusing on internal gravity waves in the free atmosphere and their reflections from the domain boundaries. This type of flow is governed by a single Froude number, which dictates most of the internal wave properties, such as wavelength, amplitude, and direction. This, in turn, will dictate the optimum domain size and Rayleigh damping layer setup. We find the effective horizontal and vertical wavelengths (the representative wavelengths of the entire wave spectrum) to be the appropriate length scales to size the domain and damping layer thickness, and the optimal Rayleigh damping coefficient scales with the Brunt–Väisälä frequency. Considering Froude numbers seen in wind farm applications, we propose recommendations to limit the reflections to less than 10 % of the total upward-propagating wave energy. Typically, damping is done at the top boundary, but given the non-periodic lateral boundary conditions of practical wind farm simulation domains, we find that damping the inflow–outflow boundaries is of equal importance to damping the top boundary. The Brunt–Väisälä frequency-normalized damping coefficient should be between 1 and 10. The damping layer thickness should be at least one effective vertical wavelength; damping layers exceeding 1.5 times the vertical wavelength are found to be unnecessary. The domain length and height should accommodate at least one effective horizontal and vertical wavelength, respectively. Moreover, Rayleigh damping does not damp the waves completely, and the non-damped energy might accumulate over the simulation time.

17 WIND ENERGY↗

DOE OSTI2025

Analyzing LF/VLF Lightning Waveforms to Estimate D-region Electron Density Profiles

Lightning waveforms in the low frequency (LF; 30-300 kHz) and the very low frequency (VLF; 3-30 kHz) bands can be exploited to produce data-driven ionospheric D-region electron density profile (EDP) estimates with significantly higher spatial and temporal coverage than previously available. The lightning waveforms used in this paper are signals detected in the LF/VLF of negative cloud-to-ground lightning by the Earth Networks Total Lightning Detection Network. Each waveform contains a ground wave and a time-delayed ionospheric reflection. The time delay between the ground wave and ionospheric reflection has previously been used to estimate a single specular reflection altitude, where LF/VLF emissions are reflected by the ionosphere. Here, we expand upon previous methods to include filtering and spectral analysis, and account for oblique propagation to produce higher-order estimates for reflection altitudes and corresponding electron densities. Once estimated, reflection altitudes and corresponding electron densities can be used to derive parameters β and h’, which define an EDP for the D-region. In this study, the lightning waveform (LW) analysis is demonstrated using a single representative 24-hour dataset over the Southeast United States, and then extended to a total of 10 separate datasets with varying locations and ionospheric conditions. The LW-derived D-region EDPs are in agreement with predictions made by the Faraday International Reference Ionosphere model, and the LW EDPs β and h’ values are consistent with previous LF/VLF-derived estimates.

D-region ionosphere↗

DOE OSTI2025

Infrasonic directivity of monopole, dipole and bipole ground-surface reflected sources

Infrasound (acoustic waves below 20 Hz) can be used to detect, locate and quantify activity in the atmosphere such as volcanic eruptions and anthropogenic explosions. Attempts to quantify volcanic eruption parameters such as exit velocity, plume height and mass flow rate using infrasound data depend strongly on assumptions of the acoustic source type. Infrasonic sources may produce omnidirectional or directional wavefields, while propagation effects, such as interaction with topography, can induce further wavefield directivity that is measured by field instrumentation. Limited sampling of these wavefields can hinder our ability to infer the underlying source, and thus our understanding of the eruption characteristics. Equivalent sources are often used to represent acoustic source mechanisms and resultant wavefields. In this study, we review equivalent acoustic sources as they pertain to infrasonic scale and wavelengths commonly encountered in very local (⁠<5 km range) geophysical field deployments. We highlight the equivalent infrasonic bipole source that can be induced by ground-reflection of an elevated monopole; we are not aware of any prior infrasound studies that use the bipole source concept. We use analytical and numerical methods to explore source directivity of monopole, dipole and bipole ground-reflected sources at infrasonic frequencies as well as the additional directivity complications introduced by interactions with topography. We illustrate that for typical volcano-infrasound wavelengths, increasing height above the ground as well as increasing source frequency leads to increased wavefield directivity. Numerical modelling using a simple omnidirectional monopole source embedded in topography further illustrates that both horizontal and vertical infrasound directionality can be induced by topography at the distance scales appropriate for local volcano infrasound monitoring. Information summarized in this analytical and numerical exploration of infrasound directivity may be used to help guide future volcano-infrasound field deployments intended to estimate source parameters or quantify wavefield directivity. Analytic solutions for simple whole-space or half-space atmospheres provide useful formulations for planning or initially analysing geophysical field-scale experimental data; however, especially at very local distances from the source (⁠<5 km), 3-D simulations are necessary to account for complex topography commonly encountered in volcano-infrasound applications.

Infrasound↗

DOE OSTI2025

Observations of Coastal Wind Momentum Flux: Dependence on Fetch and Waves with Comparisons to COARE

Here, using observations from the Martha’s Vineyard Coastal Observatory, this paper investigates how momentum flux in the marine atmospheric surface layer over the coastal ocean varies with fetch, wave age, and wave slope and assesses the performance of the COARE 3.5 bulk parameterization. Long-fetch (at least 300 km) and short-fetch (3–6 km away from land) conditions have very similar momentum flux, with the latter being just 15% higher. The COARE 3.5 wind speed–dependent formulation closely matches the observations. The sea state dependence of wave age and wave slope is analyzed by considering both peak frequency and mean frequency in a wave spectrum. The slope of regression lines between normalized roughness and wave age is sensitive to wind speed ranges and the scatter of momentum flux, potentially explaining why earlier studies did not find a universal formula to characterize the wave dependence. Although the observed momentum flux exhibits an obvious dependence on wave age, a robust quadratic fit between momentum flux and the 10-m neutral wind speed exists only for young waves. For the short-fetch conditions, the momentum flux does not increase as wave slope increases. This may be because waves generated by local wind are still weak and swell that propagates from other areas dominates the wave spectra. In other words, the wave slope computed by considering the spectra does not properly reflect the local wind–wave interaction.

Air-sea interaction↗

DOE OSTI2026

Dependence of wind-farm-induced gravity waves and wind farm performance on non-dimensional atmospheric parameters and simulation configuration

This large-eddy simulation (LES) study examines how wind-farm-induced atmospheric gravity waves (AGWs) and wind farm performance depend on non-dimensional atmospheric parameters and simulation configuration. A hypothetical aligned wind farm of actuator disks is simulated under neutral surface conditions, with a stable capping inversion and a mildly stable free atmosphere, to assess the effects of stratification beyond the atmospheric boundary layer (ABL) on ABL flow. Simulation set-ups fully resolving AGWs are validated to minimize spurious wave generation and reflection from the domain boundaries. The validated set-up is then used to analyze AGW types and characteristics, as well as stratification impacts under conventionally neutral boundary layer (CNBL) conditions. These conditions are governed by four non-dimensional parameters: the Froude numbers of the free atmosphere and capping inversion (Fr, Fr i ), and the aspect ratios of the ABL and wind farm (H̃ i , S h ). Simulation configurations that fully resolve AGWs – capturing at least one wavelength both horizontally and vertically – yield the most realistic stratification effects on ABL flow, whereas partial or unresolved configurations produce non-physical, channel-like behavior. A coherent description of the AGW phenomena is provided, highlighting the central role of capping inversion displacement in linking ABL fluctuations with AGWs. Trapped waves are confined within the capping inversion, while interfacial and internal waves aloft are identified as the AGW types most relevant to wind farm performance. The wavy inversion, analogous to an interfacial wave, forms converging and diverging zones that drive power fluctuations across the farm. The interfacial wavelength, measured over the wind farm, corresponds to one diverging, one converging, and one mildly diverging zone. As the interfacial wavelength decreases with Fr i , multiple convergence–divergence zones develop under sub-critical conditions (Fr i <1.0), while for super-critical conditions (Fr i > 1.0), the wavelength approaches the farm length. Wave amplitude increases with decreasing H̃ i (i.e., shallower capping inversions). Wind farm performance is most sensitive to H̃ i : shallow boundary layers increase blockage and reduce efficiency, while deeper layers enhance efficiency. Increasing Fr and Fr i mitigates blockage, and increasing S h mainly improves wake recovery. Although local power fluctuations arise from AGWs, overall wind farm efficiency remains nearly constant with Fr and Fr i , improving primarily with larger H̃ i and S h .

17 WIND ENERGY↗