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At least 1,531 records · Page 85
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Observation and Numerical Simulation of Cold Ions Energized by EMIC Waves

This is the first report of significant energization (up to 7,000 eV) of low-energy He + ions, which occurred simultaneously with H-band electromagnetic ion cyclotron (EMIC) wave activity, in a direction mostly perpendicular to the ambient magnetic field. The event was detected by the Arase satellite in the dayside plasmatrough region off the magnetic equator on 15 May 2019. The peak energy of the He + flux enhancements is mostly above 1,000 eV. At some interval, the He + ions are energized up to ~7,000 eV. The H-band waves are excited in a frequency band between the local crossover and helium gyrofrequencies and are close to a linear polarization state with weakly left-handed or right-handed polarization. The normal angle of the waves exhibits significant variation between 0° and 80°, indicating a non-parallel propagation. Here, we run a hybrid code with parameters estimated from the Arase observations to examine the He + energization. The simulations show that cold He + ions are energized up to more than 1,000 eV, similar to the spacecraft observations. From the analysis of the simulated wave fields and cold plasma motions, we found that the ratio of the wave frequency to He + gyrofrequency is a primary factor for transverse energization of cold He + ions. As a consequence of the numerical analysis, we suggest that the significant transverse energization of He + ions observed by Arase is attributed to H-band EMIC waves excited near the local helium gyrofrequency.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

A data-driven approach to construct a quantitative relationship between microstructural features of fatigue cracks and contact acoustic nonlinearity

This study demonstrates the feasibility of a data-driven approach to construct a quantitative relationship between nonlinear acoustic parameters and microstructural features of contact interfaces. The near-surface nonlinearity is measured using dynamic acousto-elastic testing (DAET) with a surface wave probe, while the microstructural features are extracted from scanning electron microscopy (SEM) images of fatigue cracks. Four aluminum alloy samples, each having a fatigue crack are prepared. Six local nonlinearity parameters are measured at different locations along the crack propagation direction. A total of 40 local measurements are acquired. A principal component analysis (PCA) reveals that all six nonlinearity parameters are correlated and hence can be replaced by one principal component (PC). Fifteen crack micro-geometrical features at each measurement point were extracted from the SEM images. Regression analysis is used to relate the PC of the nonlinearity parameters to the microstructural features at the crack interface. We compare three regression models that take variable selection into account: stepwise multiple linear regression (MLR), stepwise principal component regression (PCR), and least absolute shrinkage and selection operator (LASSO). Despite having different principles, the three predictive models identify two features as the most significant in predicting the interface nonlinearity: the crack aperture (opening) distribution and the distance to the crack tip. The differences between the three models and the physical interpretation of the data-driven predictions are discussed.

36 MATERIALS SCIENCE↗
NASA NTRS1993

The effect of dissipative inhomogeneous medium on the statistics of the wave intensity

One of the main theoretical points in the theory of wave propagation in random medium is the derivation of closed form equations to describe the statistics of the propagating waves. In particular, in one dimensional problems, the closed form representation of the multiple scattering effects is important since it contributes in understanding such problems like wave localization, backscattering enhancement, and intensity fluctuations. In this the propagation of plane waves in a layer of one-dimensional dissipative random medium is considered. The medium is modeled by a complex permittivity whose real part is a constant representing the absorption. The one dimensional problem is mathematically equivalent to the analysis of a transmission line with randomly perturbed distributed parameters and a single mode lossy waveguide and the results can be used to study the propagation of radio waves through atmosphere and the remote sensing of geophysical media. It is assumed the scattering medium consists of an ensemble of one-dimensional point scatterers randomly positioned in a layer of thickness L with diffuse boundaries. A Poisson impulse process with density lambda is used to model the position of scatterers in the medium. By employing the Markov properties of this process an exact closed form equation of Kolmogorov-Feller type was obtained for the probability density of the reflection coefficient. This equation was solved by combining two limiting cases: (1) when the density of scatterers is small; and (2) when the medium is weakly dissipative. A two variable perturbation method for small lambda was used to obtain solutions valid for thick layers. These solutions are then asymptotically evaluated for small dissipation. To show the effect of dissipation, the mean and fluctuations of the reflected power are obtained. The results were compared with a lossy homogeneous medium and with a lossless inhomogeneous medium and the regions where the effect of absorption is not essential were discussed.

Saatchi, Sasan S.↗
DOE OSTI2022

The radial phase variation of reversed-shear and toroidicity-induced Alfvén eigenmodes in DIII-D

The eigenfunction of an instability contains information about energy flow in the wave. Here, the amplitude and phase of electron cyclotron emission radiometer data from hundreds of DIII-D reversed shear Alfvén eigenmodes (RSAE) and toroidicity-induced Alfvén eigenmodes (TAE) are analyzed along the outboard horizontal midplane. The radial phase profile can be flat, linearly rising or falling, convex or concave; in other words, a wide variety of shapes is observed. For a particular mode, often the radial phase profile remains approximately constant as the mode evolves in time but sometimes it changes rapidly. Many TAEs and some RSAEs have phase profiles that are rather flat where the mode amplitude is largest but rise steadily by ~2π at large major radius. Rapid phase changes are observed when the frequencies of an RSAE and TAE overlap and the modes couple. The phase profile depends weakly on the fast-ion gradient that would appear in the absence of wave-induced transport. Linear and quadratic fits to the phase profiles, together with many plasma parameters, are assembled into RSAE and TAE databases. In both cases, large variability is observed. For RSAEs, the strongest phase dependencies are on electron temperature T e , RSAE mode frequency, and the density of carbon impurities. For TAEs, the strongest dependencies are on beam power and major radius of the mode. In general, the average RSAE radial phase profile is essentially flat but the TAE profile has non-zero slope and curvature.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1999

Semiempirical Two-Dimensional Magnetohydrodynamic Model of the Solar Corona and Interplanetary Medium

We have developed a two-dimensional semiempirical MHD model of the solar corona and solar wind. The model uses empirically derived electron density profiles from white-light coronagraph data measured during the Skylub period and an empirically derived model of the magnetic field which is fitted to observed streamer topologies, which also come from the white-light coronagraph data The electron density model comes from that developed by Guhathakurta and coworkers. The electron density model is extended into interplanetary space by using electron densities derived from the Ulysses plasma instrument. The model also requires an estimate of the solar wind velocity as a function of heliographic latitude and radial component of the magnetic field at 1 AU, both of which can be provided by the Ulysses spacecraft. The model makes estimates as a function of radial distance and latitude of various fluid parameters of the plasma such as flow velocity V, effective temperature T(sub eff), and effective heat flux q(sub eff), which are derived from the equations of conservation of mass, momentum, and energy, respectively. The term effective indicates that wave contributions could be present. The model naturally provides the spiral pattern of the magnetic field far from the Sun and an estimate of the large-scale surface magnetic field at the Sun, which we estimate to be approx. 12 - 15 G. The magnetic field model shows that the large-scale surface magnetic field is dominated by an octupole term. The model is a steady state calculation which makes the assumption of azimuthal symmetry and solves the various conservation equations in the rotating frame of the Sun. The conservation equations are integrated along the magnetic field direction in the rotating frame of the Sun, thus providing a nearly self-consistent calculation of the fluid parameters. The model makes a minimum number of assumptions about the physics of the solar corona and solar wind and should provide a very accurate empirical description of the solar corona and solar wind Once estimates of mass density rho, flow velocity V, effective temperature T(sub eff), effective heat flux q(sub eff), and magnetic field B are computed from the model and waves are assumed unimportant, all other plasma parameters such as Mach number, Alfven speed, gyrofrequency, etc. can be derived as a function of radial distance and latitude from the Sun. The model can be used as a planning tool for such missions as Slar Probe and provide an empirical framework for theoretical models of the solar corona and solar wind The model will be used to construct a semiempirical MHD description of the steady state solar corona and solar wind using the SOHO Large Angle Spectrometric Coronagraph (LASCO) polarized brightness white-light coronagraph data, SOHO Extreme Ultraviolet Imaging Telescope data, and Ulysses plasma data.

Sittler, Edward C., Jr.↗
DOE OSTI2016

Predicting electromagnetic ion cyclotron wave amplitude from unstable ring current plasma conditions

Electromagnetic ion cyclotron (EMIC) waves in the Earth's inner magnetosphere are enhanced fluctuations driven unstable by ring current ion temperature anisotropy. EMIC waves can resonate with relativistic electrons and play an important role in precipitation of MeV radiation belt electrons. In this study, we investigate the excitation and saturation of EMIC instability in a homogeneous plasma using both linear theory and nonlinear hybrid simulations. We have explored a four-dimensional parameter space, carried out a large number of simulations, and derived a scaling formula that relates the saturation EMIC wave amplitude to initial plasma conditions. Finally, such scaling can be used in conjunction with ring current models like ring current-atmosphere interactions model with self-consistent magnetic field to provide global dynamic EMIC wave maps that will be more accurate inputs for radiation belt modeling than statistical models.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2007

Nonstandard Analysis and Shock Wave Jump Conditions in a One-Dimensional Compressible Gas

Nonstandard analysis is a relatively new area of mathematics in which infinitesimal numbers can be defined and manipulated rigorously like real numbers. This report presents a fairly comprehensive tutorial on nonstandard analysis for physicists and engineers with many examples applicable to generalized functions. To demonstrate the power of the subject, the problem of shock wave jump conditions is studied for a one-dimensional compressible gas. It is assumed that the shock thickness occurs on an infinitesimal interval and the jump functions in the thermodynamic and fluid dynamic parameters occur smoothly across this interval. To use conservations laws, smooth pre-distributions of the Dirac delta measure are applied whose supports are contained within the shock thickness. Furthermore, smooth pre-distributions of the Heaviside function are applied which vary from zero to one across the shock wave. It is shown that if the equations of motion are expressed in nonconservative form then the relationships between the jump functions for the flow parameters may be found unambiguously. The analysis yields the classical Rankine-Hugoniot jump conditions for an inviscid shock wave. Moreover, non-monotonic entropy jump conditions are obtained for both inviscid and viscous flows. The report shows that products of generalized functions may be defined consistently using nonstandard analysis; however, physically meaningful products of generalized functions must be determined from the physics of the problem and not the mathematical form of the governing equations.

Baty, Roy S.↗
DOE OSTI2017

Optimization of sensors based on surface waves in flat-layered structures

A method for increasing the sensitivity of surface-wave sensors in multifilm structures is proposed based on the results of a theoretical study of the reflection of a plane electromagnetic wave from a flat-layered structure containing homogeneous films. A method for optimizing the parameters of the films forming the surface structure is developed and tested. The devices proposed are characterized by high field amplification in a surface layer of multifilm structure and a higher sensitivity to variations in the optical properties of the thin near-surface layer. Application of the proposed multifilm structures is expected to increase significantly the sensitivity of the existing sensors based on surface-plasmon polaritons, which are applied in modern optical multichannel biological, chemical, and physical sensor systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Design, dynamic modeling and wave basin verification of a Hybrid Wave–Current Energy Converter

Massive and high-density Marine and Hydrokinetic (MHK) energy is contained in the ocean, including waves, tidal streams, and ocean currents. Traditional MHK energy converters harvest energy from only a single MHK energy source, which does not fully exploit the energy potential that co-exists in multiple forms of MHK energy in the ocean. This paper presents the design and dynamics of a Hybrid Wave–Current Energy Converter (HWCEC) that can simultaneously convert both wave and current energy to electricity with a single Power Take-off (PTO) through the engagement and disengagement of the three one-way clutches. The critical design parameters are analyzed through modeling and simulation, including the transmission ratios, the electrical impedance, and the turbine-heave plate distance. Water basin tests in a wave–current tank were conducted, which shows the prototyped HWCEC can improve the electric power output by 38%–71% for regular waves and 79% for irregular waves, while providing a 70% reduction of the Peak to Average Ratio (PAR) of power compared to the baseline Wave Energy Converter (WEC). Here we further analyze the occurring percentages of the instant power of both WEC and HWCEC in irregular wave tests, shedding new insight on how HWCEC reduces the PAR.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2018

Analysis of steady compaction waves in polyurea aerogel

In this work, steady compaction waves in an inert porous material are investigated using a p - α model. In a steady traveling wave reference frame, the one-dimensional Euler equations are reduced to a set of ordinary differential equations. A Mie-Grüneisen equation of state (EOS) is used with parameters calibrated for polyurea aerogel (PUA). Analytic solutions for non-equilibrium compaction are developed which compliment numerical simulations and are able to predict the complete wave structure, including the compaction wave speed, zone length, and final compacted solid volume fraction. The dynamic compaction of PUA is studied for a range of piston velocities. Three regions of behavior are identified: supersonic, subsonic-complete, and subsonic-partial compaction. Below a critical piston velocity, a subsonic compaction wave is produced without a leading shock. Finally, at even lower piston velocities, there is partial compaction and a greater dependence on the dynamic compaction relation. Some features and limitations of the current model are discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2017

On Excited Frequencies for Alfvén Waves in a Coronal Arcade

The normal modes of oscillation for a magnetic arcade are used to analytically solve an initial value problem and estimate the power spectra of wave frequencies generated by a reconnection event in the solar corona. Over a realistic range of parameters, I find that such a disturbance generates a peak power at ∼10 s mHz frequency and substantial power up to ∼4 Hz. The cadence and sensitivity of current instrumentation does not allow observations of oscillations at these frequencies, but in the near future, new instrumentation will be able to probe this regime and observationally determine its energetic importance.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Variational Monte Carlo calculations of n + H 3 scattering

A paramount goal in nuclear physics is to unify ab initio treatments of bound and unbound states. The position-space quantum Monte Carlo (QMC) methods have a long history of successful bound-state calculations in light systems but have seen minimal implementation in unbound systems. Here, we introduce a numerical method to improve the efficiency and accuracy of unbound-state calculations in QMC. As an initial application, we compute scattering observables for the smallest system available to probe three-body forces, the neutron-triton system, using variational Monte Carlo (VMC) wave functions. The method involves inferring long-range amplitudes in the wave function from integrals over the short-range region where all the particles interact. This approach using integral relations is well established in the literature; here, we develop it for the QMC framework. We validate our approach with a consistency check between short-range spectroscopic overlap functions computed from direct evaluation and from the integral relations; scattering amplitudes are long-range asymptotics of those overlaps. Comparison against published benchmark calculations using the same potential demonstrates that when applied to the current VMC wave functions, the integral method produces more accurate scattering observables than direct evaluation from the same variational wave function. However, it still differs noticeably from the exact results. Using additional interactions, we then present phase shifts and mixing parameters for the n + 3 H system. In particular, we present one of the first applications of the Norfolk family of local coordinate-space chiral potentials in unbound systems of A > 2. The Norfolk results accurately describe s-wave scattering but predict p-wave cross sections too large. Compared with previous QMC scattering calculations, the integral method avoids difficulties associated with the precise computation of energy differences and with convergence outside the interaction region, which is particularly severe in the variational calculation. Application of the integral method here paves the way for its use in Green's function Monte Carlo (GFMC) calculations. In GFMC, the wave functions are more accurate, but the high-precision convergence of their tails is slow, and there are additional difficulties in reading out amplitudes. Here, the integral methods will address both of those remaining problems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS2010

High Resolution ECG for Evaluation of Heart Function During Exposure to Subacute Hypobaric Hypoxia

High altitude climbing presents a wide spectrum of health risks, including exposure to hypobaric hypoxia. Risks are also typically exacerbated by the difficulty in appropriately monitoring for early signs of organ dysfunction in remote areas. We investigated whether high resolution advanced ECG analysis might be helpful as a non-invasive and easy-to-use tool (e.g., instead of Doppler echocardiography) for evaluating early signs of heart overload in hypobaric hypoxia. Nine non-acclimatized healthy trained alpine rescuers (age 43.7 plus or minus 7.3 years) climbed in four days to the altitude of 4,200 m on Mount Ararat. Five-minute high-resolution 12-lead electrocardiograms (ECGs) were recorded (Cardiosoft) in each subject at rest in the supine position on different days but at the same time of day at four different altitudes: 400 m (reference altitude), 1,700 m, 3,200 m and 4,200 m. Changes in conventional and advanced resting ECG parameters, including in beat-to-beat QT and RR variability, waveform complexity, signal-averaged, high-frequency and spatial/spatiotemporal ECG was estimated by calculation of the regression coefficients in independent linear regression models. A p-value of less than 0.05 was adopted as statistically significant. As expected, the RR interval and its variability both decreased with increasing altitude, with trends k = -96 ms/1000 m with p = 0.000 and k = -9 ms/1000 m with p = 0.001, respectively. Significant changes were found in P-wave amplitude, which nearly doubled from the lowest to the highest altitude (k = 41.6 microvolt/1000 m with p = 0.000), and nearly significant changes in P-wave duration (k = 2.9 ms/1000 m with p = 0.059). Changes were less significant or non-significant in other studied parameters including those of waveform complexity, signal-averaged, high-frequency and spatial/spatiotemporal ECG. High resolution ECG analysis, particularly of the P wave, shows promise as a tool for monitoring early changes in heart function due to exposure to high altitude.

Zupet, Petra↗
NASA NTRS1995

Coronal heating by the resonant absorption of Alfven waves: Wavenumber scaling laws.

The importance of global modes in coronal loop heating is well established. In the present work the scaling of the global-mode resonant heating rate with the perturbation wavenumbers is studied with the numerical solution of the linearized time-dependent MHD equations for a full compressible, low-beta, resistive plasma using an implicit integration scheme. The numerical simulations demonstrate that the dissipation on inhomogeneties in the background Alfven speed occurs in narrow resonant layer with the highest heating rate at the global-mode frequency. The global-mode heating rate H (sub r) was found to scale as H (Sub r) approximately k (sub y) (exp 1.03) when k (sub z) = 0.1, and as H (sub r) approximately k (sub y) (exp -1.93) when k (sub z) = 0.75, where k (sub y) and k (sub z) are the wavenumbers in the perpendicular and parallel to the magnetic field directions, respectively, while the dependence of H (sub r) on k (sub z) is more complex. The quality factor Q of the MHD resonance cavity scales as Q approximately k (sub y) (exp -1.8) for k (sub z) = 0.75 and as Q approximately k (sub y) (exp -1.46) for k (sub z) = 0.1. The numerically determined heating rate scaling, the global-mode fequency, and the quality factor are in good agreement with the analytical linear theory. The magnitude of the perturbed velocities was found to decrease with k (sub y). Assuming typical coronal loop parameters (B (sub 0) = 100-200 G, upsilon (sub A) = 2000-4000 km/s), the Alfven waves can supply the required heating to a low-Q loops.

Ofman, L.↗
NASA NTRS1993

Orientation of Planar Deformation Features (PDFs) in quartz

Differently oriented single crystal quartz was shocked experimentally at pressures of 20 to 32 GPa and pre-shock temperatures up to 630 C. Based on this systematic investigation, we can demonstrate that the orientation of planar deformation features in quartz is not only dependent on shock pressure but also on pre-shock temperature and shock direction. Moreover, the orientation of Planar Deformation Features (PDF's) is strongly influenced by the set-up in recovery experiments. PDF's in quartz are defined as optically recognizable, planar microstructures diagnostically produced by shock compression. PDF's differ from all kinds of microstructures found in volcanic environment and therefore, their presence is a primary criterion for recognizing impact craters and ejecta layers such as the K/T boundary. Because experiments have shown a pressure dependence of the orientation of PDF's, this property is used extensively for shock wave barometry in natural impact sites. However, the unreflected application of experimental results neglects that parameters such as pre-shock temperature, shock direction, or the experimental arrangement may influence the spatial distribution of PDF's. In order to test this assumption, shock experiments on single crystal quartz at pre-shock temperatures of 20, 275, 540, and 630 C, and with shock directions (1010) and (0001) were performed. Most of the recovery experiments were carried out by using a reverberation technique, whereas in only one experiment a single shock was produced (impedance method). In the former case 0.5 mm thin discs of single crystal quartz were used, in the latter a 15 mm thick cylinder. The orientation of PDF's was measured by means of a conventional universal stage and the results are given. Effects of the experimentation technique can be derived showing the orientation of PDF's in quartz shocked at 27.5 GPa. In comparison to the well defined peaks at (1012) found in samples from reverberation experiments, the impedance matching technique causes PDF's with a broad distribution pattern and indistinct maxima. Our results have serious implications for shock-wave barometry in nature: the existing classification scheme which relates PDF orientation exclusively to shock pressure is no longer applicable. In consequence more experimental data is needed.

Langenhorst, F.↗
DOE OSTI2025

Real-Time Bayesian Inference at Extreme Scale: A Digital Twin for Tsunami Early Warning Applied to the Cascadia Subduction Zone

We present a Bayesian inversion-based digital twin that employs acoustic pressure data from seafloor sensors, along with 3D coupled acoustic–gravity wave equations, to infer earthquake-induced spatiotemporal seafloor motion in real time and forecast tsunami propagation toward coastlines for early warning with quantified uncertainties. Our target is the Cascadia subduction zone, with one billion parameters. Computing the posterior mean alone would require 50 years on a 512 GPU machine. Instead, exploiting the shift invariance of the parameter-to-observable map and devising novel parallel algorithms, we induce a fast offline–online decomposition. The offline component requires just one adjoint wave propagation per sensor; using MFEM, we scale this part of the computation to the full El Capitan system (43,520 GPUs) with 92% weak parallel efficiency. Moreover, given real-time data, the online component exactly solves the Bayesian inverse and forecasting problems in 0.2 seconds on a modest GPU system, a ten-billion-fold speedup.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1996

Electromagnetic radiation generated by arcing in low density plasma

An unavoidable step in the process of space exploration is to use high-power, very large spacecraft launched into Earth orbit. Obviously, the spacecraft will need powerful energy sources. Previous experience has shown that electrical discharges occur on the surfaces of a high-voltage array, and these discharges (arcs) are undesirable in many respects. Moreover, any high voltage conductor will interact with the surrounding plasma, and that interaction may result in electrical discharges between the conductor and plasma (or between two conductors with different potentials, for example, during docking and extravehicular activity). One very important aspect is the generation of electromagnetic radiation by arcing. To prevent the negative influence of electromagnetic noise on the operation of spacecraft systems, it seems necessary to determine the spectra and absolute levels of the radiation, and to determine limitations on the solar array bias voltage that depend on the parameters of LEO plasma and the technical requirements of the spacecraft equipment. This report describes the results of an experimental study and computer simulation of the electromagnetic radiation generated by arcing on spacecraft surfaces. A large set of high quality data was obtained during the Solar Array Module Plasma Interaction Experiment (SAMPIE, flight STS-62) and ground test. These data include the amplitudes of current, pulse forms, duration of each arc, and spectra of plasma waves. A theoretical explanation of the observed features is presented in this report too. The elaborated model allows us to determine the parameters of the electromagnetic noise for different frequency ranges, distances from the arcing site, and distinct kinds of plasma waves.

Vayner, Boris V.↗
NASA NTRS1998

Effects of Nose Radius and Aerodynamic Loading on Leading Edge Receptivity

An analysis is presented of the effects of airfoil thickness and mean aerodynamic loading on boundary-layer receptivity in the leading-edge region. The case of acoustic free-stream disturbances, incident on a thin cambered airfoil with a parabolic leading edge in a low Mach number flow, is considered. An asymptotic analysis based on large Reynolds number is developed, supplemented by numerical results. The airfoil thickness distribution enters the theory through a Strouhal number based on the nose radius of the airfoil, S = (omega)tau(sub n)/U, where omega is the frequency of the acoustic wave and U is the mean flow speed. The influence of mean aerodynamic loading enters through an effective angle-of-attack parameter ti, related to flow around the leading edge from the lower surface to the upper. The variation of the receptivity level is analyzed as a function of S, mu, and characteristics of the free-stream acoustic wave. For an unloaded leading edge, a finite nose radius dramatically reduces the receptivity level compared to that for a flat plate, the amplitude of the instability waves in the boundary layer being decreased by an order of magnitude when S = 0.3. Modest levels of aerodynamic loading are found to further decrease the receptivity level for the upper surface of the airfoil, while an increase in receptivity level occurs for the lower surface. For larger angles of attack close to the critical angle for boundary layer separation, a local rise in the receptivity level occurs for the upper surface, while for the lower surface the receptivity decreases. The effects of aerodynamic loading are more pronounced at larger values of S. Oblique acoustic waves produce much higher receptivity levels than acoustic waves propagating downstream parallel to the airfoil chord.

Hammerton, P. W.↗