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

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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

Studying Room Acoustics using a Monopole-Dipole Microphone Array

The use of a soundfield microphone for examining the directional nature of a room impulse response was reported recently. By cross-correlating monopole and co-located dipole microphone signals aligned with left-right, up-down, and front-back axes, a sense of signal direction of arrival is revealed. The current study is concerned with the array's ability to detect individual reflections and directions of arrival, as a function of the cross-correlation window duration. If is window is too long, weak reflections are overlooked; if too short, spurious detections result. Guidelines are presented for setting the window width according to perceptual criteria. Formulas are presented describing the accuracy with which direction of arrival can be estimated as a function of room specifics and measurement noise. The direction of arrival of early reflections is more accurately determined than that of later reflections which are quieter and more numerous. The transition from a fairly directional sound field at the beginning of the room impulse response to a uni-directional diffuse field is examined. Finally, it is shown that measurements from additional dipole orientations can significantly improve the ability to detect reflections and estimate their directions of arrival.

Begault, Durand R.↗
DOE OSTI2024

Temporal contrast degradation from mid-spatial-frequency surface error on stretcher mirrors

Temporal contrast degradation due to mid-spatial-frequency error in chirped-pulse amplification stretcher optics is studied. Third-order cross-correlation measurements reveal a temporal peak that appears when using two different mirrors processed by magnetorheological finishing, despite an improvement in rms roughness compared to a third unprocessed mirror. Simulations based on measured power spectral density show how the actual impact on contrast is different from measurements using a typical bandwidth-limited third-order cross correlator. Furthermore, strategies are proposed to avoid this type of contrast degradation while exploiting computer numerically controlled polishing techniques for enhancement of surface figure and roughness.

47 OTHER INSTRUMENTATION↗
NASA NTRS1987

Mass flow meter using the triboelectric effect for measurement in cryogenics

The use of triboelectric charge to measure the mass flow rate of cryogens for the Space Shuttle Main Engine was investigated. Cross correlation of the triboelectric charge signals was used to determine the transit time of the cryogen between two sensor locations in a .75-in tube. The ring electrode sensors were mounted in a removable spool piece. Three spool pieces were constructed for delivery, each with a different design. One set of electronics for implementation of the cross correlation and flow calculation was constructed for delivery. Tests were made using a laboratory flow loop using liquid freon and transformer oil. The measured flow precision was 1 percent and the response was linear. The natural frequency distribution of the triboelectric signal was approximately 1/f. The sensor electrodes should have an axial length less than approximately one/tenth pipe diameter. The electrode spacing should be less than approximately one pipe diameter. Tests using liquid nitrogen demonstrated poor tribo-signal to noise ratio. Most of the noise was microphonic and common to both electrode systems. The common noise rejection facility of the correlator was successful in compensating for this noise but the signal was too small to enable reliable demonstration of the technique in liquid nitrogen.

Bernatowicz, Henry↗
NASA NTRS1981

Raman scattering as a probe of planetary atmospheres

The observable effects of Raman scattering on the spectra of the giant planets may provide new information on the composition and structure of these atmospheres. Satellite observations have already shown the influence of Raman scattering on the UV continuum albedo. A cross correlation technique is presented for detecting rotational and vibrational transitions of the Raman active gases in the atmosphere. This technique has been applied to ground-based visible spectra of Venus, Jupiter, Saturn and Uranus. Extension of this method into the UV would improve the detectability of the Raman lines because the ratio of Raman to Rayleigh cross section increases with decreasing wavelength. The technology currently exists to efficiently obtain high-signal-to-noise ratio UV spectra through the use of silicon diode array detectors. Application of the cross-correlation technique to UV spectra obtained from space vehicles would give a new important probe of the structure and composition of planetary atmospheres by enabling the use of the UV spectra of a planet to observe what would normally be an infrared molecular transition.

Cochran, W. D.↗
NASA NTRS1986

Hard X-ray delays

High time resolution hard X-ray rates with good counting statistics over 5 energy intervals were obtained using a large area balloon-borne scintillation detector during the 27 June 1980 solar flare. The impulsive phase of the flare was comprised of a series of major bursts of several to several tens of seconds long. Superimposed on these longer bursts are numerous smaller approximately 0.5 to 1.0 second spikes. The time profiles for different energies were cross-correlated for the major bursts. The rapid burst decay rates and the simultaneous peaks below 120 keV both indicate a rapid electron energy loss process. Thus, the flux profiles reflect the electron acceleration/injection process. The fast rate data was obtained by a burst memory in 8 and 32 msec resolution over the entire main impulsive phase. These rates will be cross-correlated to look for short time delays and to find rapid fluctuations. However, a cursory examination shows that almost all fluctuations, down to the 5% level, were resolved with 256 msec bins.

Schwartz, Richard A.↗
DOE OSTI2025

Measurement of Parity-Violating Modes of the Dark Energy Spectroscopic Instrument (DESI) Year 1 Luminous Red Galaxies' 4-Point Correlation Function

Here we report the first measurement of the parity-violating (PV) 4-Point Correlation Function (4PCF) of the Dark Energy Spectroscopic Instrument's Year 1 Luminous Red Galaxy (DESI Y1 LRG) sample, motivated by the potential detection of the PV 4PCF in the Sloan Digital Sky Survey Baryon Oscillation Spectroscopic Survey (SDSS BOSS) galaxies. In our auto-correlation ("auto") analysis, we find a statistically significant excess of the PV signal compared to mocks without any PV, at 4-10$σ$ depending on details of the analysis. This could arise either from genuine PV or from an underestimation of the variance in the mocks; it is unlikely to arise, at the signal level, from a systematic. We then cross-correlate ("cross") the putative PV signal between different, independent patches of sky, and there find no detection of parity violation. The two measurements are in significant tension: while the cross has somewhat larger error bars than the auto, this is not sufficient to explain the discrepancy. We thus present the current work as an intriguing addition to the PV work on BOSS and as motivation for exploring further the relationship between the auto and cross PV 4PCF analyses.

Slepian, Zachary [Florida U.]↗
NASA NTRSDate not supplied

Effect of Electronic Shot Noise on Dynamic Measurements using Optical Techniques: Examples from Rayleigh Scattering and Unsteady PSP

Electronic shot noise is an unavoidable reality in all optical techniques that depend on measuring light intensity. For steady-state, time-averaged measurements the impact of shot noise can be easily reduced by increasing the exposure time, or by averaging over multiple-exposures. That is not the case for unsteady measurements, where time histories of light intensity variations need to be created either by high-speed photography (unsteady PSP) or via photoelectron counting (spectrally resolved Rayleigh scattering) over short time durations using a photo-multiplier tube (PMT) and photon counting electronics. Electronic shot noise introduces a fixed amount of random error, which can overwhelm the light intensity variation caused by turbulent fluctuations. Spectrum computed from such time series shows a fixed noise floor that is independent of the number of data points in the time series. For a fixed optical system, where the collected power of the luminescent light (uPSP), or the scattered light (Rayleigh) is fixed, one needs to resort to special techniques to obtain enough signal-to noise ratio (SNR). For the uPSP application it is shown that averaging of the adjacent pixels improves SNR; although this may lead to a sacrifice of spatial resolution. A second means is to increase the exposure time, which leads to a lowering of the frequency range. For the Rayleigh application, improvements of SNR can be achieved via two different cross-correlation based approaches. The first involves measuring the light intensity using two PMTs using short, contiguous gates; thereby, creating two time-series of data. The second one involves collecting one long time-series of data using one set of measurement device, followed by an odd-even splitting into two time series. When the two time-series are cross-correlated, and a power spectrum is calculated, a significant reduction in the shot noise floor can be achieved. Examples from measurements of density and velocity fluctuations spectra from two different Rayleigh setup are presented to demonstrate the process.

uPSP↗
NASA NTRS1992

Atmospheric disturbance model for aircraft and space capable vehicles

An atmospheric disturbance model (ADM) is developed that considers the requirements of advanced aerospace vehicles and balances algorithmic assumptions with computational constraints. The requirements for an ADM include a realistic power spectrum, inhomogeneity, and the cross-correlation of atmospheric effects. The baseline models examined include the Global Reference Atmospheric Model Perturbation-Modeling Technique, the Dryden Small-Scale Turbulence Description, and the Patchiness Model. The Program to Enhance Random Turbulence (PERT) is developed based on the previous models but includes a revised formulation of large-scale atmospheric disturbance, an inhomogeneous Dryden filter, turbulence statistics, and the cross-correlation between Dryden Turbulence Filters and small-scale thermodynamics. Verification with the Monte Carlo approach demonstrates that the PERT software provides effective simulations of inhomogeneous atmospheric parameters.

Chimene, Beau C.↗
NASA NTRS1999

The Spectral Evolution of Gamma-Ray Bursts

The proposed project was a continuation of our work on the spectral evolution of gamma-ray bursts begun when the Co-I on this proposal. Lyle Ford, was my graduate student. In the proposal we discussed two projects. The first was finishing and publishing the last chapter of Professor Ford's thesis. In this research effort we looked for correlations in the energies of pairs of counts recorded by the BATSE Spectroscopy Detectors within a short time of each other. A greater correlation within a short time would indicate that the observed broadband spectrum is really composed of narrowband spectral components which last for a short time and which rapidly sum to the observed spectrum. We did not find any evidence for such narrowband emission, and are setting limits on its presence. Professor Ford is revising the last chapter of his thesis for publication with my participation. The second project was a continuation of my study of the cross-correlations between the gamma-ray burst lightcurves in different energy bands. I published a first study with this technique (1997. Ap.J., 486, 928) which showed that "hard-to-soft" spectral evolution is prevalent both within and between the bursts' intensity spikes. I proposed to continue developing this technique. However, I have been somewhat disillusioned about using this methodology quantitatively since it averages the spectral evolution on a given timescale over the entire burst. Nonetheless, I have been applying the technique to new bursts which are scientifically interesting for other reasons. Attached I include the cross-correlations for the burst GRB 990123, the burst during which ROTSE discovered an optical transient. The solid curve is the autocorrelatl'on of BATSE's channel 3 (100-300 keV), while the dashed, dot-dashed and 3 dots-dashed curves are the crosscorrelations of channel 3 with channels 1 (25-50 keV), 2 (50-100 keV), and 4 (300-2000 keV). The order of, and separation between, the curves on the positive lag side indicate "hard-to-soft" evolution on all timescales, while the FWHM of the crosscorrelations shows that the intensity spikes are narrower at high energy than at low energy. I have also been participating with my colleague on the BATSE team on other spectral evolution studies. Note that while I continue as a member of the BATSE team, I no longer receive funding from the team. For example, Preece et al. (1998, Ap.J., 496, 849) showed that the high energy spectral index varies during a burst, usually following a "hard-to-soft" trend. In addition, we have just submitted a catalog (Preece et al. 1999, Ap. J., submitted) of time-resolved spectral fits.

Band, David L.↗
NASA NTRS1981

Automatic cloud tracking applied to GOES and Meteosat observations

An improved automatic processing method for the tracking of cloud motions as revealed by satellite imagery is presented and applications of the method to GOES observations of Hurricane Eloise and Meteosat water vapor and infrared data are presented. The method is shown to involve steps of picture smoothing, target selection and the calculation of cloud motion vectors by the matching of a group at a given time with its best likeness at a later time, or by a cross-correlation computation. Cloud motion computations can be made in as many as four separate layers simultaneously. For data of 4 and 8 km resolution in the eye of Hurricane Eloise, the automatic system is found to provide results comparable in accuracy and coverage to those obtained by NASA analysts using the Atmospheric and Oceanographic Information Processing System, with results obtained by the pattern recognition and cross correlation computations differing by only fractions of a pixel. For Meteosat water vapor data from the tropics and midlatitudes, the automatic motion computations are found to be reliable only in areas where the water vapor fields contained small-scale structure, although excellent results are obtained using Meteosat IR data in the same regions. The automatic method thus appears to be competitive in accuracy and coverage with motion determination by human analysts.

Endlich, R. M.↗
NASA NTRS1992

Dayside ionospheric convection changes in response to long-period interplanetary magnetic field oscillations - Determination of the ionospheric phase velocity

Ground magnetic field perturbations recorded by the CANOPUS magnetometer network in the 7 to 13 MLT sector are used to examine how reconfigurations of the dayside polar ionospheric flow take place in response to north-south changes of the IMF. During the 6-h interval in question, IMF Bz oscillates between +/- 7 nT with about a 1-h period. Corresponding variations in the ground magnetic disturbance are observed which we infer are due to changes in ionospheric flow. Cross correlation of the data obtained from two ground stations at 73.5 deg magnetic latitude, but separated by about 2 hours in MLT, shows that changes in the flow are initiated in the prenoon sector (about 10 MLT) and then spread outward toward dawn and dusk with a phase speed of about 5 km/s over the longitude range about 8 to 12 MLT, slowing to about 2 km/s outside this range. Cross correlating the data from these ground stations with IMP 8 IMF Bz records produces a MLT variation in the ground response delay relative to the IMF which is compatible with these deduced phase speeds.

Saunders, M. A.↗
DOE OSTI2025

Cosmology from Planck CMB lensing and DESI DR1 quasar tomography

We present a measurement of the amplitude of matter fluctuations over the redshift range 0.8 ≤ z ≤ 3.5 from the cross correlation of over 1.2 million spectroscopic quasars selected by the Dark Energy Spectroscopic Instrument (DESI) across 7,200 deg 2 (∼ 170 quasars/deg 2 ) and Planck PR4 (NPIPE) cosmic microwave background (CMB) lensing maps. We perform a tomographic measurement in three bins centered at effective redshiftsz=1.44, 2.27 and 2.75, which have ample overlap with the CMB lensing kernel. From a joint fit using the angular clustering of all three redshift bins (auto and cross-spectra), and including an Q m prior from DESI DR1 baryon acoustic oscillations to break the $Ω_{m}-σ_{8}$ degeneracy, we constrain the amplitude of matter fluctuations in the matter-dominated regime to be $σ_{8}=0.929^{+0.059}_{-0.074}$ and $S_{8}≡σ_{8}(Ω_m/0.3)^{0.5} = 0.922^{+0.059}_{-0.073}$. We provide a growth of structure measurement with the largest spectroscopic quasar sample to date at high redshift, which is ∼ 1.5σ higher than predictions from ΛCDM fits to measurements of the primary CMB from Planck PR4. The cross-correlation between PR4 lensing maps and DESI DR1 quasars is detected with a signal-to-noise ratio of 21.7 and the quasar auto-correlation at 27.2 for the joint analysis of all redshift bins. We combine our measurement with the CMB lensing auto-spectrum from the ground-based Atacama Cosmology Telescope (ACT DR6) and Planck PR4 to perform a sound-horizon-free measurement of the Hubble constant, yielding $H_{0}=69.1^{+2.2}_{-2.6} {\rm \ km\ s}^{-1}{\rm Mpc}^{-1}$ through its sensitivity to the matter-radiation equality scale.

baryon acoustic oscillations↗
NASA NTRS1990

Precise measurement method for ionospheric total electron content using signals from GPS satellites

A GPS codeless receiver called GTR-2 was for measuring total electron content (TEC) along the line of sight to the GPS satellite by using the cross correlation amplitude of the received P-code signals carried by L1(1575.42 MHz) and L2(1227.6 MHz). This equipment has the performance of uncertainty in the measurement of TEC of about 2 X 10(exp 16) electrons/sq m when a 10 dBi gain antenna was used. To increase the measurement performance, an upper version of GTR-2 called GTR-3 is planned which uses the phase information of the continuous signals obtained by making a cross correlation or multiplication of the received L1 and L2 P-code signals. By using the difference of these measured phases values, the ionospheric delay with the ambiguities of the periods of L1+L2 and L1-L2 signals can be estimated.

Imae, Michito↗
NASA NTRSDate not supplied

Performance Assessment of LunaNet’s Augmented Forward Signal

LunaNet provides a common set of interoperable specifications for communication and position, navigation and time (PNT) services and interfaces soon to be implemented in lunar vicinity. The LunaNet Interoperability Specification (LNIS) provides the design for the GNSS-like Augmented Forward Signal (AFS), which enables orbiting and surface users in lunar space, such as Artemis, to estimate their position, velocity, and time. The specification of AFS defines two orthogonal signal components on a single carrier: the in-phase component (AFS-I), a lower-chip-rate data channel tailored for applications where low SWaP (Size, Weight, and Power) is critical (e.g., IoT devices or search and rescue), and the quadrature component (AFS-Q), a high-chip-rate data-less pilot signal for high-precision, robust lunar navigation and positioning applications. An initial description of AFS was provided in [1], with initial analysis results shown in [2] and [3] and the current signal in space description provided in [4]. As part of NASA's Lunar Communication Relay and Navigation Systems (LCRNS) project, this work expands upon the initial analysis results and proposes a new expanded set of AFS-Q spreading codes that exceed the cross-correlation and autocorrelation sidelobe performance of L1C and other GNSS signals, while providing additional expansion capabilities for future provider satellites. A set of 420 codes was selected from a Weil-based code derived from the prime number 10247, which is larger than the 10243 prime number used to derive Beidou’s B1C Weil sequences. Both the initial set of 210 codes and the expanded set of 420 codes are shown to provide the best cross-correlation of any 10230-chip satellite navigation codes. The performance is demonstrated for hierarchical sets of spreading codes optimized and organized in sets of 30 codes. The new codes were developed using an optimization approach and correlation methodology described in [5]. The work also compares LunaNet’s AFS to terrestrial GNSS signals in terms of acquisition, tracking, and data demodulation performance. Performance is evaluated for receivers that only track the 1.023 MCPS data channel spreading code for low SWaP IoT use cases, as well as for receivers that track both the 1.023 MCPS data channel and the 5.115 MCPS pilot channel spreading code for high-performance use cases. Performance is assessed in the presence of interference and thermal noise. The analysis is performed in terms of expected operating conditions on the lunar surface. Several unique flexibility aspects of the augmented forward signal are described, including the use of the Q channel’s secondary and tertiary codes to enable variable coherent integrations during acquisition. This is compared to GNSS signals such as L5/E5 and MBOC in terms of achievable processing gain for interference mitigation versus acquisition complexity. The work details acquisition and tracking techniques used to optimally acquire and track the primary, secondary, and tertiary codes on the Q channel, as well as acquisition of the I channel spreading code. Acquisition of the 8 ms Q channel spreading code is also compared to joint acquisition of the I and Q channel primary codes in noise and interference environments.

LCRNS↗
NASA NTRSDate not supplied

Performance Assessment of LunaNet’s Augmented Forward Signal

LunaNet provides a common set of interoperable specifications for communication and position, navigation and time (PNT) services and interfaces soon to be implemented in lunar vicinity. The LunaNet Interoperability Specification (LNIS) provides the design for the GNSS-like Augmented Forward Signal (AFS), which enables orbiting and surface users in lunar space, such as Artemis, to estimate their position, velocity, and time. The specification of AFS defines two orthogonal signal components on a single carrier: the in-phase component (AFS-I), a lower-chip-rate data channel tailored for applications where low SWaP (Size, Weight, and Power) is critical (e.g., IoT devices or search and rescue), and the quadrature component (AFS-Q), a high-chip-rate data-less pilot signal for high-precision, robust lunar navigation and positioning applications. An initial description of AFS was provided in LNIS 2023, with initial analysis results shown in Dafesh 2024 and Dafesh 2025, and the current signal in space description provided in LNIS 2025. As part of NASA's Lunar Communication Relay and Navigation Systems (LCRNS) project, this work expands upon the initial analysis results and proposes a new expanded set of AFS-Q spreading codes that exceed the cross-correlation and autocorrelation sidelobe performance of L1C and other GNSS signals, while providing additional expansion capabilities for future service satellites. A set of 420 codes was selected from a Weil-based code derived from the prime number 10247, which is larger than the 10243 prime number used to derive BeiDou’s B1C Weil sequences. Both the initial set of 210 codes and the expanded set of 420 codes are shown to provide the best cross-correlation of any 10230-chip satellite navigation codes. The performance is demonstrated for hierarchical sets of spreading codes optimized and organized in sets of 30 codes. The work also compares LunaNet’s AFS to terrestrial GNSS signals in terms of acquisition, tracking, and data demodulation performance. Performance is evaluated for receivers that only track the 1.023 MCPS data channel spreading code for low SWaP IoT use cases, as well as for receivers that track both the 1.023 MCPS data channel and the 5.115 MCPS pilot channel spreading code for high-performance use cases. Performance is assessed in the presence of interference and thermal noise. The analysis is performed in terms of expected operating conditions on the lunar surface. Several unique flexibility aspects of the augmented forward signal are described, including the use of the Q channel’s secondary and tertiary codes to enable variable coherent integrations during acquisition. This is compared to GNSS signals such as L5/E5 and MBOC in terms of achievable processing gain for interference mitigation versus acquisition complexity. The work details acquisition and tracking techniques used to optimally acquire and track the primary, secondary, and tertiary codes on the Q channel, as well as acquisition of the I channel spreading code. Acquisition of the 8 ms, Q channel spreading code is also compared to joint acquisition of the I and Q channel primary codes in noise and interference environments

LCRNS↗
DOE OSTI2024

A three-point velocity estimation method for two-dimensional coarse-grained imaging data

Time delay and velocity estimation methods have been widely studied subjects in the context of signal processing, with applications in many different fields of physics. The velocity of waves or coherent fluctuation structures is commonly estimated as the distance between two measurement points divided by the time lag that maximizes the cross correlation function between the measured signals, but this is demonstrated to result in erroneous estimates for two spatial dimensions. We present an improved method to accurately estimate both components of the velocity vector, relying on three non-aligned measurement points. We introduce a stochastic process describing the fluctuations as a superposition of uncorrelated pulses moving in two dimensions. Using this model, we show that the three-point velocity estimation method, using time delays calculated through cross correlations, yields the exact velocity components when all pulses have the same velocity. The two- and three-point methods are tested on synthetic data generated from realizations of such processes for which the underlying velocity components are known. The results reveal the superiority of the three-point technique. Finally, we demonstrate the applicability of the velocity estimation on gas puff imaging data of strongly intermittent plasma fluctuations due to the radial motion of coherent, blob-like structures at the boundary of the Alcator C-Mod tokamak.

Materials Science↗
DOE OSTI2024

The gravitational lensing imprints of DES Y3 superstructures on the CMB: a matched filtering approach

Low-density cosmic voids gravitationally lens the cosmic microwave background (CMB), leaving a negative imprint on the CMB convergence |$\kappa$|⁠. This effect provides insight into the distribution of matter within voids, and can also be used to study the growth of structure. We measure this lensing imprint by cross-correlating the Planck CMB lensing convergence map with voids identified in the Dark Energy Survey Year 3 (DES Y3) data set, covering approximately 4200 deg|$^2$| of the sky. We use two distinct void-finding algorithms: a 2D void-finder that operates on the projected galaxy density field in thin redshift shells, and a new code, Voxel, which operates on the full 3D map of galaxy positions. We employ an optimal matched filtering method for cross-correlation, using the Marenostrum Institut de Ciències de l’Espai N-body simulation both to establish the template for the matched filter and to calibrate detection significances. Using the DES Y3 photometric luminous red galaxy sample, we measure |$A_\kappa$|⁠, the amplitude of the observed lensing signal relative to the simulation template, obtaining |$A_\kappa = 1.03 \pm 0.22$| (⁠|$4.6\sigma$| significance) for Voxel and |$A_\kappa = 1.02 \pm 0.17$| (⁠|$5.9\sigma$| significance) for 2D voids, both consistent with Lambda cold dark matter expectations. We additionally invert the 2D void-finding process to identify superclusters in the projected density field, for which we measure |$A_\kappa = 0.87 \pm 0.15$| (⁠|$5.9\sigma$| significance). The leading source of noise in our measurements is Planck noise, implying that data from the Atacama Cosmology Telescope, South Pole Telescope and CMB-S4 will increase sensitivity and allow for more precise measurements.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1990

Experiments on a separation bubble over an Eppler 387 airfoil at low Reynolds numbers using thin-film arrays

Experiments carried out at the NASA Langley Low-Turbulence Pressure Tunnel on an Eppler 387 airfoil at several angles of attack for Reynolds numbers of 100,000 to 300,000 are discussed. Cross-correlations and phase diagrams are used in calculating velocities, while spectra are used in checking for amplified frequencies, and coherence plots for causality. Hot-film measurements, oil-flow visualization, pressure measurements, and Drela code are compared for finding the leading and trailing edges of the bubble. It is observed that all methods agree in showing the beginning and end of the separation bubble, the velocity measurements agree in magnitude for the lower velocities, and wave packets appear in the cross-correlation.

Mousseux, Marc C.↗