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At least 973 records · Page 54

Ultrasonic Characterization of Interfaces in Composite Bonds

The inverse determination of imperfect interfaces from reflection spectra of normal and oblique incident ultrasonic waves in adhesive bonds of multidirectional composites is investigated. The oblique measurements are complicated by the highly dispersed nature of oblique wave spectra at frequencies above 3MHz. Different strategies for bond property reconstruction, including a modulation method, are discussed. The relation of measured interfacial spring density to the physico-chemical model of a composite interface described by polymer molecular bonds to emulate loss of molecular strength on an adhesive composite interface is discussed. This potentially relates the interfacial (adhesion) strength (number of bonds at the adhesive substrate interface) to the spring constant (stiffness) area density (flux), which is an ultrasonically measurable parameter.

Wang, N.↗

Telescope Spacer Design Investigations

Space-based interferometric gravitational wave observatories will measure changes in the distance between free falling proof masses inside widely separated spacecraft with pm sensitivity. These observatories will use fast telescopes to exchange laser beams. These telescopes are part of the probed optical distances and any length change in the gravitational wave band between secondary and primary can limit the sensitivity of the observatories. Furthermore, the large distance between and space constrains on the spacecraft require to use very fast telescopes with f-numbers approaching unity. These telescopes are very sensitive against any absolute length change which would reduce interferometer visibility and, ultimately, sensitivity. Our group has assembled a Silicon Carbide test structure and investigated its dimensional in the 1 OA-4 to 1 Hz frequency band at different operating temperatures. We also measured the overall length change and started investigating asymmetric length changes during cool down which would lead to misalignments in the telescope.

Livas, Jeffrey↗

Space-Time Localization of Plasma Turbulence Using Multiple Spacecraft Radio Links

Space weather is described as the variability of solar wind plasma that can disturb satellites and systems and affect human space exploration. Accurate prediction requires information of the heliosphere inside the orbit of the Earth. However, for predictions using remote sensing, one needs not only plane-of-sky position but also range information the third spatial dimension to show the distance to the plasma disturbances and thus when they might propagate or co-rotate to create disturbances at the orbit of the Earth. Appropriately processed radio signals from spacecraft having communications lines-of-sight passing through the inner heliosphere can be used for this spacetime localization of plasma disturbances. The solar plasma has an electron density- and radio-wavelength-dependent index of refraction. An approximately monochromatic wave propagating through a thin layer of plasma turbulence causes a geometrical-optics phase shift proportional to the electron density at the point of passage, the radio wavelength, and the thickness of the layer. This phase shift is the same for a wave propagating either up or down through the layer at the point of passage. This attribute can be used for space-time localization of plasma irregularities. The transfer function of plasma irregularities to the observed time series depends on the Doppler tracking mode. When spacecraft observations are in the two-way mode (downlink radio signal phase-locked to an uplink radio transmission), plasma fluctuations have a two-pulse response in the Doppler. In the two-way mode, the Doppler time series y2(t) is the difference between the frequency of the downlink signal received and the frequency of a ground reference oscillator. A plasma blob localized at a distance x along the line of sight perturbs the phase on both the up and down link, giving rise to two events in the two-way tracking time series separated by a time lag depending the blob s distance from the Earth: T2-2x/c, where T2 is the two-way time-of-flight of radio waves to/from the spacecraft and c is the speed of light. In some tracking situations, more information is available. For example, with the 5-link Cassini radio system, the plasma contribution to the up and down links, y(sub up)(t) and y(sub dn)(t), can be computed separately. The times series y(sub up)(t) and y(sub dn)(t) respond to a localized plasma blob with one event in each time series. These events are also separated in time by T2-2x/c. By cross-correlating the up and down link Doppler time series, the time separation of the plasma events can be measured and hence the plasma blob s distance from the Earth determined. Since the plane-of-sky position is known, this technique allows localization of plasma events in time and three space dimensions.

Armstrong, John W.↗

Evaluation of Precipitation Simulated by Seven SCMs against the ARM Observations at the SGP Site

This study evaluates the performances of seven single-column models (SCMs) by comparing simulated surface precipitation with observations at the Atmospheric Radiation Measurement Program Southern Great Plains (SGP) site from January 1999 to December 2001. Results show that although most SCMs can reproduce the observed precipitation reasonably well, there are significant and interesting differences in their details. In the cold season, the model-observation differences in the frequency and mean intensity of rain events tend to compensate each other for most SCMs. In the warm season, most SCMs produce more rain events in daytime than in nighttime, whereas the observations have more rain events in nighttime. The mean intensities of rain events in these SCMs are much stronger in daytime, but weaker in nighttime, than the observations. The higher frequency of rain events during warm-season daytime in most SCMs is related to the fact that most SCMs produce a spurious precipitation peak around the regime of weak vertical motions but rich in moisture content. The models also show distinct biases between nighttime and daytime in simulating significant rain events. In nighttime, all the SCMs have a lower frequency of moderate-to-strong rain events than the observations for both seasons. In daytime, most SCMs have a higher frequency of moderate-to-strong rain events than the observations, especially in the warm season. Further analysis reveals distinct meteorological backgrounds for large underestimation and overestimation events. The former occur in the strong ascending regimes with negative low-level horizontal heat and moisture advection, whereas the latter occur in the weak or moderate ascending regimes with positive low-level horizontal heat and moisture advection.

Model comparison↗

California Reservoir Inflow Projections Using a Hybrid EMD-Matalas Method

Inflow projections provide scenarios for future water availability and are integral to operational reservoir management. They can aid water practitioners in decision-making for conservation efforts, multiyear storage retention, managing flood risk, downstream water releases, and regional growth planning. However, conventional methods are often limited in terms of their ability to incorporate non-stationarity, long run persistence, and the cross-correlation of multiple series in a region. This research aims to address these issues with a hybrid approach that integrates Empirical Mode Decomposition (EMD) with the Matalas multisite generation method. Multiple long-run inflows were examined for the Shasta/Trinity Reservoirs and Oroville Reservoir of California. EMD is used to decompose each inflow series into a set of independent intrinsic mode functions (IMFs) that have different timescales and frequencies. These IMFs were grouped into intradecadal (less-than- 10-year average periodicity) and interdecadal (greater-than-10-year average periodicity) series for each site. The IMF projections at each site were then combined to produce replicates of the historical data. This preserves the correlation structure of the intra- and interdecadal components of the series. The hybrid EMD-Matalas method was compared to a traditional autoregressive lag-one model. Both methods were found to retain the statistical characteristics of the historical data. However, the EMD-Matalas method retained the multiyear wet and dry periods to a greater degree. This was examined by comparing the 5-year and 10-year sums from the traditional model with the hybrid EMD-Matalas model. An advantage of the EMD-Matalas method is the ability to explicitly incorporate modes of non-stationary long-run persistence often associated with large-scale climate drivers such as the El Nino Southern Oscillation (ENSO) or the Pacific Decadal Oscillation (PDO). This contributes to scenario planning that may be particularly important for managing multiyear low flow periods.

inflow projections↗

The Salience of Nonlinearities in the Boreal Winter Response to ENSO: Arctic Stratosphere and Europe

The salience of nonlinearities in the Arctic stratospheric response to El Niño - Southern Oscillation (ENSO) is evaluated in a 41 member ensemble of the period 1980 to 2009 in the NASA Goddard Earth Observing System Chemistry-Climate Model. Central Pacific El Niño (CP EN) events preferentially increase zonal wavenumber 2, while Eastern Pacific El Niño (EP EN) events preferentially increase zonal wavenumber 1, though these nonlinearities become statistically robust only after more than 45 events are considered. This leads to a difference in the morphology of SSW events preferentially forced by each ENSO flavor. While the zonal-mean Arctic stratospheric response is little different between EP and CP EN once one accounts for the relative weakness of CP events, the tropospheric subpolar negative North Atlantic Oscillation response is stronger for CP events. Other nonlinearities are even less salient: there is no indication of any nonlinearities in the wave driving between moderate EP EN and extreme EP EN, nor between EN and La Niña (LN). However in approximately 15% of the integrations within our ensemble, there is no difference in SSW frequency between EN and LN, suggesting that a similar SSW frequency for both EN and LN, as has occurred over the past 60 years, can occur by chance. The intra-ensemble variability in LN SSW frequency can be related back to intra-ensemble variability in the tropospheric response to LN.

Arctic↗

Toward Relating Open- and Closed-Test Section Microphone Phased Array Aeroacoustic Measurements

Aeroacoustic measurements utilizing microphone phased arrays are becoming more commonplace in large-scale wind tunnels. However, for such costly tests it is difficult to assess the influence of a given facility's configuration on the acquired data. One such opportunity has recently arisen in the NASA Langley Research Center 14- by 22-Foot Subsonic Tunnel, where the High-Lift configuration of the Common Research Model was tested in both open-jet and closed wall configurations. Acoustic data were acquired on the same model with the same specific hardware at the same Mach number; and for similar model angles of attack, array apertures, and array angles relative to the model location. Initial deconvolution comparisons using DAMAS appear poor. The closed test section results show contamination likely due to background noise and reflections. The open-jet results show severe blurring due to the decorrelation of acoustic waves passing through a turbulent free shear layer. However, accounting for image sources in the DAMAS grid reduces visual artifacts in the closed test section results, and a preliminary coherence correction technique mitigates the blurring in the open-jet results. Qualitatively, both tests identify similar source behavior. Quantitatively, summed spectra of the slat noise agree in some frequency bands but differ in others. Proposals that may mitigate the difference are given for each configuration, such as correcting for the array protective cover and applying background subtraction in the closed wall configuration, and further developing the coherence loss correction for deconvolution methods in the open-jet setup.

microphone array↗

Chile Wildfires: Utilizing NASA and NOAA Earth Observations to Determine Lightning-ignited Wildfire Risks in Central Chile

In recent years, Central Chile has experienced wildfires of increasing frequency and intensity which threaten natural resources and communities. The Corporación Nacional Forestal (CONAF) responds to wildfires caused by a variety of ignitions, including lightning, but it is difficult to determine the prevalence of lightning-ignited wildfires based solely on ground observations. In collaboration with CONAF and the Embassy of Chile, Agricultural Office, the team used Earth observations to map coincidence of lightning strikes and wildfire ignitions. The Active Fire Product of Suomi NPP Visible Infrared Imaging Radiometer Suite (VIIRS) identified wildfires as thermal anomalies, which the team compared to the lightning events detected by NOAA’s GOES-16 Geostationary Lightning Mapper (GLM). Next, the team mapped lightning strike frequency and lightning related wildfires across the study area. Finally, the team calculated and mapped a relative estimate of lightning-ignited wildfire vulnerability across the year, fire season (December – March), and off-season (April – November) by summing the following factors: lightning frequency, the Normalized Difference Moisture Index (NDMI) and land surface temperature (LST). These risks were then weighted by fuel availability. Preliminary analysis of the lightning fire relationship showed a spatiotemporal coincidence, primarily in the South-central region of study, near Temuco, and isolated areas on the Andean front. The team identified areas at risk of lightning-induced wildfires, predominantly in the northern third of the study area and along the Andean front. Adjusting the relative weight of risk factors and improving the lightning and fire coincidence map by clustering VIIRS thermal anomalies into fire events could reduce discrepancies and improve risk assessments for future work.

Christopher Matechik↗

New Report Highlights LAMP's Role as a Robust and Reliable System for Wave Energy Converter Testing

Harnessing the power of waves requires more than just putting devices in the ocean - it takes tools that can refine and accelerate innovation before the first deployment. That's where NLR's largeamplitude motion platform, or LAMP, comes in. LAMP is a six-degree-of-freedom motion system designed to replicate the response of a wave energy converter (WEC) device in realistic ocean conditions. By letting researchers evaluate WEC performance in a safe, controlled lab environment before moving offshore, LAMP helps accelerate innovation while reducing risk. An NLR report, titled Initial Characterization of the NLR LargeAmplitude Motion Platform (https://www.nrel.gov/docs/fy26osti/93733.pdf), provides a deeper understanding of LAMP's capabilities and also lays the groundwork for future advancements in WEC testing methodologies. Researchers studied LAMP's amplitude and frequency limits across different payloads and collected data from 16 test profiles. Testing demonstrated that platform accuracy remained consistent across all payloads evaluated; researchers expect similar accuracy up to LAMP's 10,000-kilogram capacity limit. The measured position limits for single degrees of freedom experienced by WECs, including surge, sway, heave, roll, pitch, and yaw, also exceeded the original manufacturer specifications, providing new insight into the true boundaries of the system.

16 TIDAL AND WAVE POWER↗

Multifrequency observations

Analyses of synthetic aperture radar (SAR) image data were performed at DLR to classify various kinds of vegetation and different terrain types. The data were collected both with the DLR experimental synthetic aperture radar (E-SAR) in X-band, C-band, and L-band and with the NASA/JPL DC-8 SAR in C-band, L-band, and P-band. E-SAR is a single frequency and single polarization system (both parameters can be selected) but several flights were used to collect multifrequency/multipolarization data which were geometrically matched after processing. Classification of different crop types was based on comparison of the backscatter coefficients of calibrated SAR data in different frequency bands and polarizations. The DC-8 STAR collects polarimetric data in different bands simultaneously. Data acquired with the NASA/JPL DC-8 STAR are qualified for scientific investigations by reducing the cross-talk and channel imbalance to a tolerable extent. The data are absolutely calibrated by using reference targets with known backscattering cross-sections. The signatures and polarimetric features of terrain types, such as grassland, concrete, sea, forest (coniferous; deciduous) and urban areas, are extracted and discussed with respect to frequency and incidence angle dependence. A multifrequency polarimetric feature vector was applied for classification. The results of this new approach for separating and classifying different object classes are presented.

Glitz, R.↗

Three-dimensional organization of otolith-ocular reflexes in rhesus monkeys. II. Inertial detection of angular velocity

1. The dynamic contribution of otolith signals to three-dimensional angular vestibuloocular reflex (VOR) was studied during off-vertical axis rotations in rhesus monkeys. In an attempt to separate response components to head velocity from those to head position relative to gravity during low-frequency sinusoidal oscillations, large oscillation amplitudes were chosen such that peak-to-peak head displacements exceeded 360 degrees. Because the waveforms of head position and velocity differed in shape and frequency content, the particular head position and angular velocity sensitivity of otolith-ocular responses could be independently assessed. 2. During both constant velocity rotation and low-frequency sinusoidal oscillations, the otolith system generated two different types of oculomotor responses: 1) modulation of three-dimensional eye position and/or eye velocity as a function of head position relative to gravity, as presented in the preceding paper, and 2) slow-phase eye velocity as a function of head angular velocity. These two types of otolith-ocular responses have been analyzed separately. In this paper we focus on the angular velocity responses of the otolith system. 3. During constant velocity off-vertical axis rotations, a steady-state nystagmus was elicited that was maintained throughout rotation. During low-frequency sinusoidal off-vertical axis oscillations, dynamic otolith stimulation resulted primarily in a reduction of phase leads that characterize low-frequency VOR during earth-vertical axis rotations. Both of these effects are the result of an internally generated head angular velocity signal of otolithic origin that is coupled through a low-pass filter to the VOR. No change in either VOR gain or phase was observed at stimulus frequencies larger than 0.1 Hz. 4. The dynamic otolith contribution to low-frequency angular VOR exhibited three-dimensional response characteristics with some quantitative differences in the different response components. For horizontal VOR, the amplitude of the steady-state slow-phase velocity during constant velocity rotation and the reduction of phase leads during sinusoidal oscillation were relatively independent of tilt angle (for angles larger than approximately 10 degrees). For vertical and torsional VOR, the amplitude of steady-state slow-phase eye velocity during constant velocity rotation increased, and the phase leads during sinusoidal oscillation decreased with increasing tilt angle. The largest steady-state response amplitudes and smallest phase leads were observed during vertical/torsional VOR about an earth-horizontal axis. 5. The dynamic range of otolith-borne head angular velocity information in the VOR was limited to velocities up to approximately 110 degrees/s. Higher head velocities resulted in saturation and a decrease in the amplitude of the steady-state response components during constant velocity rotation and in increased phase leads during sinusoidal oscillations. 6. The response characteristics of otolith-borne angular VORs were also studied in animals after selective semicircular canal inactivation. Otolith angular VORs exhibited clear low-pass filtered properties with a corner frequency of approximately 0.05-0.1 Hz. Vectorial summation of canal VOR alone (elicited during earth-vertical axis rotations) and otolith VOR alone (elicited during off-vertical axis oscillations after semicircular canal inactivation) could not predict VOR gain and phase during off-vertical axis rotations in intact animals. This suggests a more complex interaction of semicircular canal and otolith signals. 7. The results of this study show that the primate low-frequency enhancement of VOR dynamics during off-vertical axis rotation is independent of a simultaneous activation of the vertical and torsional "tilt" otolith-ocular reflexes that have been characterized in the preceding paper. (ABSTRACT TRUNCATED).

NASA Discipline Neuroscience↗

The Anharmonic Force Field of Ethylene, C2H4, by Means of Accurate Ab Initio Calculations

The quartic force field of ethylene, C2H4, has been calculated ab initio using augmented coupled cluster, CCSD(T), methods and correlation consistent basis sets of spdf quality. For the C-12 isotopomers C2H4, C2H3D, H2CCD2, cis-C2H2D2, trans-C2H2D2, C2HD3, and C2D4, all fundamentals could be reproduced to better than 10 per centimeter, except for three cases of severe Fermi type 1 resonance. The problem with these three bands is identified as a systematic overestimate of the Kiij Fermi resonance constants by a factor of two or more; if this is corrected for, the predicted fundamentals come into excellent agreement with experiment. No such systematic overestimate is seen for Fermi type 2 resonances. Our computed harmonic frequencies suggest a thorough revision of the accepted experimentally derived values. Our computed and empirically corrected re geometry differs substantially from experimentally derived values: both the predicted rz geometry and the ground-state rotational constants are, however, in excellent agreement with experiment, suggesting revision of the older values. Anharmonicity constants agree well with experiment for stretches, but differ substantially for stretch-bend interaction constants, due to equality constraints in the experimental analysis that do not hold. Improved criteria for detecting Fermi and Coriolis resonances are proposed and found to work well, contrary to the established method based on harmonic frequency differences that fails to detect several important resonances for C2H4 and its isotopomers. Surprisingly good results are obtained with a small spd basis at the CCSD(T) level. The well-documented strong basis set effect on the v8 out-of-plane motion is present to a much lesser extent when correlation-optimized polarization functions are used. Complete sets of anharmonic, rovibrational coupling, and centrifugal distortion constants for the isotopomers are available as supplementary material to the paper.

Martin, Jan M. L.↗

Microwave-optical quantum frequency conversion

Photons at microwave and optical frequencies are principal carriers for quantum information. While microwave photons can be effectively controlled at the local circuit level, optical photons can propagate over long distances. High-fidelity conversion between microwave and optical photons will allow the distribution of quantum states across different quantum technology nodes and enhance the scalability of hybrid quantum systems toward a future “Quantum Internet.” Despite a frequency difference of five orders of magnitude, there has been significant progress recently toward the transfer between microwave and optical photons with steadily improved efficiency in a coherent and bidirectional manner. In this review, we summarize this progress, emphasizing integrated device approaches, and provide a perspective for device implementation that enables quantum state transfer and entanglement distribution across microwave and optical domains.

74 ATOMIC AND MOLECULAR PHYSICS↗

Spatially resolved x-ray detection with photonic crystal scintillators

We study the self-collimation phenomenon in photonic crystals (PhC) of wide bandgap materials for ultra-fast and high spatial resolution x-ray detection. We work on various heavy inorganic scintillators: BaF 2 , GaN, ZnO, CsI:Tl, NaI:Tl, LYSO, WO 4 compounds, and plastic scintillators. Conventional scintillator detectors do not rely on a direct detection mechanism; hence, they require intricate design and fabrication processes. We offer a PhC design to observe self-collimation phenomena and overcome the ongoing spatial resolution challenges with these types of materials. We investigate the photonic band diagrams and iso-frequency contours. Fourier transforms based on finite-difference time-domain and frequency domain simulations are done for verifying and analyzing the self-collimation with the selected material. Light extraction efficiency at the PhC–air interface, depending on the truncation distance from the excitation point, is measured. Beam divergence values are calculated at 1 mm propagation distance. The vertical field profiles are obtained to observe the confinement. For the spatial resolution analysis, cross-sectional beam profiles have been examined. Furthermore, Gaussian envelopes are fitted to beam profiles for a consistent data analysis, and full-width-at-half-maximum values are considered. As a result, we theoretically prove and demonstrate the spatially resolved x-ray detection at the sub-micrometer level for a wide range of scintillator materials.

36 MATERIALS SCIENCE↗

Low-temperature microwave characteristics of pseudomorphic In(x)Ga(1-x) As/In(0.52)Al(0.48)As modulation-doped field-effect transistors

Low-temperature microwave measurements of both lattice-matched and pseudomorphic In(x)Ga(1-x)As/In(0.48)As (x = 0.53, 0.60, and 0.70) channel MODFETs on InP substrates were carried out in a cryogenic measurement system. The measurements were done in the temperature range of 77 to 300 K and in the frequency range of 0.5 to 11.0 GHz at different bias conditions. The cutoff frequency (fT) for the In(x)Ga(1-x)As/In(0.52)Al(0.48)As MODFETs improved from 22 to 29 GHz, 29 to 38 GHz, and 39 to 51 GHz, for x = 0.53, 0.60, and 0.70, respectively, as the temperature was lowered from 300 to 77 K, which is approximately a 31 percent increase at each composition. No degradations were observed in device performance. These results indicate an excellent potential of the pseudomorphic devices at low temperatures.

Lai, R.↗

Multifrequency polarimetric synthetic aperture radar observations of sea ice

The present study introduces a fully polarimetric airborne SAR data set of sea ice. Images were acquired in the Beaufort, Bering, and Chukchi seas in March 1988. Statistics of the magnitude, phase, and polarization of complex backscattered signals recorded by three-frequency SAR are examined for various scenes with different ice characteristics. Results indicate that combinations of frequency and polarization enhance current capability to distinguish ice of different properties using single-frequency fixed-polarization-microwave radar. A specific example is the polarimetric identification of new ice formation which may not be easily distinguished in ERS-1 5.3-GHz VV polarization of SAR data. Such findings are consistent with theoretical model simulations of scattering characteristics of sea ice.

Drinkwater, Mark R.↗

Enhanced Frequency Support Scheme of Generic Inverter-Based Resource Models for Renewable-Dominated Power Grids

The frequency response of SG-dominated power grids is predictable ahead of an occurrence of a frequency event because the frequency response of SGs is consistent, and it can be inferred from the swing equation [1]. However, increasing the portion of IBRs in an SG-dominated power grid might make the characteristics of the conventional power grids no longer valid because this changing resource mix affects grid dynamics and controls [2]. Thus, maintaining these characteristics greatly benefits the control and operation of the power grids with high penetration of IBRs. To maintain these characteristics in IBR-dominated power grids, IBRs should have frequency response capability similar to that of an SG. The WECC modeling validation subcommittee has developed generic IBR models for large system planning [3]-[5]. These models can represent various vendors' dynamic behavior for WTG, PV, and ESS [5]. The current generic IBR models approved by WECC can provide frequency response only from droop control loops in REPC models [6], [7]. The contribution of the loops is proportional to the frequency deviation from the nominal frequency. Thus, it presents an insufficient contribution to arrest frequency variation compared to the frequency response of SGs because it allows a high ROCOF in the early stage of frequency events. This shortfall will become greater as the PL of IBRs increases in power grids. Controller enhancement for the generic IBR models is required to secure the frequency stability under high PL of IBRs as in the SG-dominated power grids. This paper proposes a control extension for the generic IBR models to enhance the frequency support capabilities and discusses the classification of frequency support for the different types of IBR considering their operating constraints. An inertial control scheme is implemented in the REPC and REEC models of the generic IBR models to achieve these objectives. The inertial control scheme includes the following stages: Control area data acquisition, inertia time constant estimation, IBR-related constraint check, IBR contribution determination, and inertial response provision. In the scheme, a REPC acquires control area data from a system operator and estimates a total inertia time constant for the control area the applicable IBR power plant belongs. Then, the estimated inertial time constant is transferred to each IBR controller—REEC—within the power plant. Each REEC checks the availability of applicable IBR for inertial response participation. If the IBR is available, the REEC amplifies the estimated inertial time constant to utilize it for inertial response provision. In this way, the proposed inertial response scheme extends the functionality of the generic IBR models to provide SG-like frequency response within their constraints. Various scenarios considering different IBR types, IBR penetration levels, and frequency control schemes were simulated and compared in an IEEE 39-bus system using PSCAD simulator to verify the effectiveness of the proposed scheme.

Kim, Jinho↗

Nonlinear Interaction of Detuned Instability Waves in Boundary-Layer Transition: Resonant-Triad Interaction

The non-equilibrium critical-layer analysis of a system of frequency-detuned resonant-triads is presented using the generalized scaling of Lee. It is shown that resonant-triads can interact nonlinearly within the common critical layer when their (fundamental) Strouhal numbers are different by a factor whose magnitude is of the order of the growth rate multiplied by the wavenumber of the instability wave. Since the growth rates of the instability modes become larger and the critical layers become thicker as the instability waves propagate downstream, the frequency-detuned resonant-triads that grow independently of each other in the upstream region can interact nonlinearly in the later downstream stage. In the final stage of the non-equilibrium critical-layer evolution, a wide range of instability waves with the scaled frequencies differing by almost an Order of (l) can nonlinearly interact. Low-frequency modes are also generated by the nonlinear interaction between oblique waves in the critical layer. The system of partial differential critical-layer equations along with the jump equations are presented here. The amplitude equations with their numerical solutions are given in Part 2. The nonlinearly generated low-frequency components are also investigated in Part 2.

Lee, Sang Soo↗