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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Galaxy cluster profiles: a Gaussian mixture model approach to halo miscentering

Measurements of the galaxy density and weak-lensing profiles of galaxy clusters typically rely on an assumed cluster center, which is taken to be the brightest cluster galaxy or other proxies for the true halo center defined as the minimum in the potential well. Departure of the assumed cluster center from the true halo center bias the resultant profile measurements, an effect known as miscentering bias. Currently, miscentering is typically modeled in stacked profiles of clusters with a two parameter model. We use an alternate approach in which the profiles of individual clusters are used with the corresponding likelihood computed using a Gaussian mixture model. We test the approach using halos and the corresponding subhalo profiles from the IllustrisTNG hydrodynamic simulations. We obtain significantly improved estimates of the miscentering parameters for both 3D and projected 2D profiles relevant for imaging surveys. We discuss applications to upcoming cosmological surveys. Our Python package for the Gaussian mixture model is publicly available at https://github.com/KyleMiller1/Halo-Miscentering-Mixture-Model.

Bayesian reasoning↗
NASA NTRS2006

Technology Assessment in Support of the Presidential Vision for Space Exploration

This paper discusses the process and results of technology assessment in support of the United States Vision for Space Exploration of the Moon, Mars and Beyond. The paper begins by reviewing the Presidential Vision: a major endeavor in building systems of systems. It discusses why we wish to return to the Moon, and the exploration architecture for getting there safely, sustaining a presence, and safely returning. Next, a methodology for optimal technology investment is proposed with discussion of inputs including a capability hierarchy, mission importance weightings, available resource profiles as a function of time, likelihoods of development success, and an objective function. A temporal optimization formulation is offered, and the investment recommendations presented along with sensitivity analyses. Key questions addressed are sensitivity of budget allocations to cost uncertainties, reduction in available budget levels, and shifting funding within constraints imposed by mission timeline.

technology↗
NASA NTRS2012

Sensitivity Analysis for Atmospheric Infrared Sounder (AIRS) CO2 Retrieval

The Atmospheric Infrared Sounder (AIRS) is a thermal infrared sensor able to retrieve the daily atmospheric state globally for clear as well as partially cloudy field-of-views. The AIRS spectrometer has 2378 channels sensing from 15.4 micrometers to 3.7 micrometers, of which a small subset in the 15 micrometers region has been selected, to date, for CO2 retrieval. To improve upon the current retrieval method, we extended the retrieval calculations to include a prior estimate component and developed a channel ranking system to optimize the channels and number of channels used. The channel ranking system uses a mathematical formalism to rapidly process and assess the retrieval potential of large numbers of channels. Implementing this system, we identifed a larger optimized subset of AIRS channels that can decrease retrieval errors and minimize the overall sensitivity to other iridescent contributors, such as water vapor, ozone, and atmospheric temperature. This methodology selects channels globally by accounting for the latitudinal, longitudinal, and seasonal dependencies of the subset. The new methodology increases accuracy in AIRS CO2 as well as other retrievals and enables the extension of retrieved CO2 vertical profiles to altitudes ranging from the lower troposphere to upper stratosphere. The extended retrieval method for CO2 vertical profile estimation using a maximum-likelihood estimation method. We use model data to demonstrate the beneficial impact of the extended retrieval method using the new channel ranking system on CO2 retrieval.

sensitivity analysis↗
NASA NTRSDate not supplied

Predicting Maximum Temperatures of a Li-ion Battery on a Simulated Flight Profile using a Model-based Prognostics

One of the challenges in using Li-ion packs in aeronautics is their safety, and thermal runaway (TR) is a major concern. The current engineering solutions to prevent a Li-ion pack from a catastrophic TR require additional mass and volume to isolate cells. The excess mass could be reduced by improving detection and, thus, preventing a TR event. One of the possible early warning indicators of a TR is crossing a threshold temperature. We have developed an approach, based on the Unscented Kalman Filter (UKF), to predict the likelihood of reaching the threshold temperature for simulated flight profiles. The current battery prognostics algorithms for aerospace predict state-of-charge (SOC) and end-of-life (EOL) [1]. We extended this two-level algorithm to predict the maximum temperature during discharge. The amount of heat generated in a cell depends on factors such as cell chemistry, cell packaging, total cycles, operating temperature, and abuse history [2]. Our semi-empirical thermal model depends on three phenomenological parameters which account for those factors. In addition, a two-parameter reduced-order model is developed to predict the temperature rise for short bursts of “random-walk” (RW) discharge current sequence, which simulates a flight's current-loading profile. The performance of these models on different datasets and types of current loading will be presented. To predict the maximal temperatures for future cycles we must estimate the evolution of thermal parameters as the batteries age. It is found that the parameters of the 3-parametric thermal model cannot be estimated only from the RW data. To address the issue, we will present two alternative approaches: i) expanding the datasets to include discharge profiles beyond RWs; ii) model reduction to a two-parametric model. The two approaches will be illustrated by an application to the cycling data from a commercial LG 18650 cell. References: 1. M. Daigle, C.S. Kulkarni, End-of-discharge and End-of-life Prediction in Lithium-ion Batteries with Electrochemistry-based Aging Models, in: AIAA Infotech @ Aerospace, American Institute of Aeronautics and Astronautics, San Diego, California, USA, 2016. 2. M. Börner, et. al, Correlation of aging and thermal stability of commercial 18650-type lithium ion batteries, Journal of Power Sources. 342 (2017) 382–392.

Thermal runaway↗
NASA NTRS1998

A Conceptual Approach to Assimilating Remote Sensing Data to Improve Soil Moisture Profile Estimates in a Surface Flux/Hydrology Model: Overview - Part 1

Knowledge of the amount of water in the soil is of great importance to many earth science disciplines. Soil moisture is a key variable in controlling the exchange of water and energy between the land surface and the atmosphere. Thus, soil moisture information is valuable in a wide range of applications including weather and climate, runoff potential and flood control, early warning of droughts, irrigation, crop yield forecasting, soil erosion, reservoir management, geotechnical engineering, and water quality. Despite the importance of soil moisture information, widespread and continuous measurements of soil moisture are not possible today. Although many earth surface conditions can be measured from satellites, we still cannot adequately measure soil moisture from space. Research in soil moisture remote sensing began in the mid 1970s shortly after the surge in satellite development. Recent advances in remote sensing have shown that soil moisture can be measured, at least qualitatively, by several methods. Quantitative measurements of moisture in the soil surface layer have been most successful using both passive and active microwave remote sensing, although complications arise from surface roughness and vegetation type and density. Early attempts to measure soil moisture from space-borne microwave instruments were hindered by what is now considered sub-optimal wavelengths (shorter than 5 cm) and the coarse spatial resolution of the measurements. L-band frequencies between 1 and 3 GHz (10-30 cm) have been deemed optimal for detection of soil moisture in the upper few centimeters of soil. The Electronically Steered Thinned Array Radiometer (ESTAR), an aircraft-based instrument operating a 1,4 GHz, has shown great promise for soil moisture determination. Initiatives are underway to develop a similar instrument for space. Existing space-borne synthetic aperture radars (SARS) operating at C- and L-band have also shown some potential to detect surface wetness. The advantage of radar is its much higher resolution than passive microwave systems, but it is currently hampered by surface roughness effects and the lack of a good algorithm based on a single frequency and single polarization. In addition, its repeat frequency is generally low (about 40 days). In the meantime, two new radiometers offer some hope for remote sensing of soil moisture from space. The Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI), launched in November 1997, possesses a 10.65 GHz channel and the Advanced Microwave Scanning Radiometer (AMSR) on both the ADEOS-11 and Earth Observing System AM-1 platforms to be launched in 1999 possesses a 6.9 GHz channel. Aside from issues about interference from vegetation, the coarse resolution of these data will provide considerable challenges pertaining to their application. The resolution of TMI is about 45 km and that of AMSR is about 70 km. These resolutions are grossly inconsistent with the scale of soil moisture processes and the spatial variability of factors that control soil moisture. Scale disparities such as these are forcing us to rethink how we assimilate data of various scales in hydrologic models. Of particular interest is how to assimilate soil moisture data by reconciling the scale disparity between what we can expect from present and future remote sensing measurements of soil moisture and modeling soil moisture processes. It is because of this disparity between the resolution of space-based sensors and the scale of data needed for capturing the spatial variability of soil moisture and related properties that remote sensing of soil moisture has not met with more widespread success. Within a single footprint of current sensors at the wavelengths optimal for this application, in most cases there is enormous heterogeneity in soil moisture created by differences in landcover, soils and topography, as well as variability in antecedent precipitation. It is difficult to interpret the meaning of 'mean' soil moisture under such conditions and even more difficult to apply such a value. Because of the non-linear relationships between near-surface soil moisture and other variables of interest, such as surface energy fluxes and runoff, mean soil moisture has little applicability at such large scales. It is for these reasons that the use of remote sensing in conjunction with a hydrologic model appears to be of benefit in capturing the complete spatial and temporal structure of soil moisture. This paper is Part I of a four-part series describing a method for intermittently assimilating remotely-sensed soil moisture information to improve performance of a distributed land surface hydrology model. The method, summarized in section II, involves the following components, each of which is detailed in the indicated section of the paper or subsequent papers in this series: Forward radiative transfer model methods (section II and Part IV); Use of a Kalman filter to assimilate remotely-sensed soil moisture estimates with the model profile (section II and Part IV); Application of a soil hydrology model to capture the continuous evolution of the soil moisture profile within and below the root zone (section III); Statistical aggregation techniques (section IV and Part II); Disaggregation techniques using a neural network approach (section IV and Part III); and Maximum likelihood and Bayesian algorithms for inversely solving for the soil moisture profile in the upper few cm (Part IV).

Crosson, William L.↗
NASA NTRS2013

Impact of Gender on Pharmocokinetics of Intranasal Scopolamine

Introduction: An intranasal gel dosage formulation of scopolamine (INSCOP) was developed for the treatment of Space Motion Sickness (SMS), which is commonly experienced by astronauts during space missions. The bioavailability and pharmacokinetics (PK) were evaluated under IND guidelines. Since information is lacking on the effect of gender on the PK of Scopolamine, we examined gender differences in PK parameters of INSCOP at three dose levels of 0.1, 0.2 and 0.4 mg. Methods: Plasma scopolamine concentrations as a function of time data were collected from twelve normal healthy human subjects (6 male/6 female) who participated in a fully randomized double blind crossover study. The PK parameters were derived using WinNonlin. Covariate analysis of PK profiles was performed using NONMEN and statistically compared using a likelihood ratio test on the difference of objective function value (OFV). Statistical significance for covariate analysis was set at P<0.05(ΔOFV=3.84). Results: No significant difference in PK parameters between male and female subjects was observed with 0.1 and 0.2 mg doses. However, CL and Vd were significantly different between male and female subjects at the 0.4 mg dose. Results from population covariate modeling analysis indicate that a onecompartment PK model with first-order elimination rate offers best fit for describing INSCOP concentration-time profiles. The inclusion of sex as a covariate enhanced the model fitting (ΔOFV=-4.1) owing to the genderdependent CL and Vd differences after the 0.4 mg dose. Conclusion: Statistical modeling of scopolamine concentration-time data suggests gender-dependent pharmacokinetics of scopolamine at the high dose level of 0.4 mg. Clearance of the parent compound was significantly faster and the volume of distribution was significantly higher in males than in females, As a result, including gender as a covariate to the pharmacokinetic model of scopolamine offers the best fit for PK modeling of the drug at dose of 0.4 mg or higher.

Putcha, L.↗
NASA NTRS2000

The Extended-Image Tracking Technique Based on the Maximum Likelihood Estimation

This paper describes an extended-image tracking technique based on the maximum likelihood estimation. The target image is assume to have a known profile covering more than one element of a focal plane detector array. It is assumed that the relative position between the imager and the target is changing with time and the received target image has each of its pixels disturbed by an independent additive white Gaussian noise. When a rotation-invariant movement between imager and target is considered, the maximum likelihood based image tracking technique described in this paper is a closed-loop structure capable of providing iterative update of the movement estimate by calculating the loop feedback signals from a weighted correlation between the currently received target image and the previously estimated reference image in the transform domain. The movement estimate is then used to direct the imager to closely follow the moving target. This image tracking technique has many potential applications, including free-space optical communications and astronomy where accurate and stabilized optical pointing is essential.

Tsou, Haiping↗
NASA NTRS2019

A NICER view of PSR J0030+0451: Implications for the Dense Matter Equation of State

Both the mass and radius of the millisecond pulsar PSRJ0030+0451 have been inferred via pulse-profile modeling of X-ray data obtained by NASA’s Neutron Star Interior Composition Explorer (NICER) mission. In this Letter we study the implications of the mass–radius inference reported for this source by Riley et al. for the dense matter equation of state (EoS), in the context of prior information from nuclear physics at low densities. Using a Bayesian framework we infer central densities and EoS properties for two choices of high-density extensions: a piecewise-polytropic model and a model based on assumptions of the speed of sound in dense matter. Around nuclear saturation density these extensions are matched to an EoS uncertainty band obtained from calculations based on chiral effective field theory interactions, which provide a realistic description of atomic nuclei as well as empirical nuclear matter properties within uncertainties. We further constrain EoS expectations with input from the current highest measured pulsar mass; together, these constraints offer a narrow Bayesian prior informed by theory as well as laboratory and astrophysical measurements. The NICER mass–radius likelihood function derived by Riley et al. using pulse-profile modeling is consistent with the highest-density region of this prior. The present relatively large uncertainties on mass and radius for PSR J0030+0451 offer, however, only a weak posterior information gain over the prior. We explore the sensitivity to the inferred geometry of the heated regions that give rise to the pulsed emission, and find a small increase in posterior gain for an alternative (but less preferred) model. Lastly, we investigate the hypothetical scenario of increasing the NICER exposure time for PSRJ0030+0451.

G Raaijmakers↗
DOE OSTI2026

Measurements of three-flavor neutrino oscillations from a PISCES two-detector fit to the NOvA Experiment data

NOvA is a long-baseline neutrino oscillation experiment with two functionally identical detectors: a Near Detector (ND) at Fermilab, placed 1 km from the neutrino source, and a Far Detector (FD) located 810 km away from the ND in Minnesota. NOvA s primary physics goals are to measure the neutrino oscillation parameters $\theta_{23}$ and $\Delta m^2_{32}$ with high precision, determine the neutrino mass hierarchy, and constrain the value of $\delta_{CP}$, primarily via the study of muon neutrino to electron neutrino oscillation. Extracting values for oscillation parameters from fits to data usually relies on treating systematic uncertainties as nuisance parameters, a strategy that suffers from poor scalability as the number of uncertainties becomes larger. This work introduces PISCES (Parameter Inference with Systematic Covariance and Exact Statistics), a novel method that circumvents this scalability problem by encoding systematic uncertainties into a covariance matrix. PISCES utilizes a nested minimization in which optimal systematic pulls are first computed using the covariance matrix in an inner minimization step, then the oscillation parameters are profiled over in the outer minimization. PISCES also uses a Poisson Likelihood term, making it ideal for the inclusion of low-statistic samples in the fits. PISCES is a flexible framework that also supports complex fits, such as a joint Near and Far detector fit. In the standard NOvA analysis, oscillation parameters are extracted using an extrapolation technique in which the ND data indirectly constrain the FD prediction via a ratio method. PISCES, on the other hand, enables a simultaneous ND+FD fit, allowing the high-statistics ND data to directly constrain systematic uncertainties across all samples. This thesis presents the full PISCES joint ND+FD fit for the NOvA three-flavor analysis, details its implementation, and evaluates its performance through extensive robustness tests and fake data studies. It also provides a comparison between the PISCES joint ND+FD results and the standard NOvA extrapolation method using the full NOvA 10-year data set. The results demonstrate that PISCES can successfully fit NOvA data while incorporating the constraints from the ND detectors consistently, using physically motivated systematic uncertainties to account for data/MC discrepancies.

Rajaoalisoa, Miriama [Cincinnati U.]↗
NASA NTRS1998

Solar Flare Physics

We have continued our previous efforts in studies of fourier imaging methods applied to hard X-ray flares. We have performed physical and theoretical analysis of rotating collimator grids submitted to GSFC(Goddard Space Flight Center) for the High Energy Solar Spectroscopic Imager (HESSI). We have produced simulation algorithms which are currently being used to test imaging software and hardware for HESSI. We have developed Maximum-Entropy, Maximum-Likelihood, and "CLEAN" methods for reconstructing HESSI images from count-rate profiles. This work is expected to continue through the launch of HESSI in July, 2000. Section 1 shows a poster presentation "Image Reconstruction from HESSI Photon Lists" at the Solar Physics Division Meeting, June 1998; Section 2 shows the text and viewgraphs prepared for "Imaging Simulations" at HESSI's Preliminary Design Review on July 30, 1998.

Schmahl, Edward J.↗
DOE OSTI2025

Large deviations of ionic currents in dilute electrolytes

Here, we evaluate the exponentially rare fluctuations of the ionic current for a dilute electrolyte by means of macroscopic fluctuation theory. We consider the fluctuating hydrodynamics of a fluid electrolyte described by a stochastic Poisson–Nernst–Planck equation. We derive the Euler–Lagrange equations that dictate the optimal concentration profiles of ions conditioned on exhibiting a given current, whose form determines the likelihood of that current in the long-time limit. For a symmetric electrolyte under small applied voltages, number density fluctuations are small, and ionic current fluctuations are Gaussian with a variance determined by the Nernst–Einstein conductivity. Under large applied potentials, the ionic current distribution is generically non-Gaussian. Its structure is constrained thermodynamically by Gallavotti–Cohen symmetry and the thermodynamic uncertainty principle.

Farhadi, Jafar [University of California, Berkeley↗
DOE OSTI2025

Exploring the transition from continuous turbulence fluctuations to bursting ELMs in high SOL density regimes

BOUT++ turbulence simulations of the DIII-D reveal that the density profile between the separatrix and pedestal plays a crucial role in the dynamics of edge localized modes (ELMs) and edge plasma turbulent transport. Nonlinear simulations demonstrate that small ELMs in the DIII-D hybrid scenario under high SOL density conditions are predominantly driven by local ballooning modes near the separatrix, stabilizing global instabilities while enhancing localized pressure fluctuations. A key control parameters for ELM dynamics is the separatrix-to-pedestal density ratio, n e,sep /n e,ped . A high ratio indicates a shallow gradient, favoring small ELMs, while a lower ratio signals a steep gradient, which increases the likelihood of large ELMs. Comprehensive parameter scans, including n e,sep /n e,ped , density gradient profiles near the separatrix, and resistivity, reveal the critical role of these parameters in shaping transitions between turbulence-driven transport and ELM bursting. The scans demonstrate that in high SOL density regimes, small ELMs can result from either global resistive MHD instabilities or local ballooning modes near the separatrix, depending on the steepness of the separatrix density gradient. These findings also highlight the transition from continuous turbulence to small ELMs. The post-crash peak in pressure fluctuations, δP rms serves as a critical metric for identifying transition from continuous turbulence fluctuations to ELM bursting. Larger δP rms values correlate with ELM bursts driven by local or global instabilities, whereas smaller values indicate turbulence-dominated transport. Drift-Alfvén and resistive ballooning turbulence enhance the entrainment of fluctuations from the pedestal to the SOL, contributing to the complex interplay of dynamics in this regime. These findings emphasize the importance of separatrix density shaping and pedestal gradient control for optimizing ELM behavior in ITER and future fusion devices.

Li, Nami [Lawrence Livermore National Laboratory (↗
NASA NTRS1980

Radial velocity study of four southern RS CVn candidates and related field stars

Radial velocity variations are demonstrated for four southern RS CVn candidates: HD 39937, 101379, 155555, and 174429. The period of HD 155555 appears to have decreased by about one part in 100,000 over the past 18 yr. In addition, high-resolution observations of the Ca II H and K profiles and the Mg II 2800-A emission doublet are presented. These enhance the likelihood of these being RS CVn objects. Radial velocity data for 15 other late-type bright field stars are presented. Some of these were observed by Copernicus and may exhibit unusual chromospheres, while the rest lack radial velocity information as tabulated in the Bright Star Catalog. All velocity measures have been corrected to the IAU heliocentric system.

Stacy, J. G.↗
NASA NTRS2014

OMPS Limb Profiler Instrument Performance Assessment

Following the successful launch of the Ozone Mapping and Profiler Suite (OMPS) aboard the Suomi National Polar-orbiting Partnership (SNPP) spacecraft, the NASA OMPS Limb team began an evaluation of instrument and data product performance. The focus of this paper is the instrument performance in relation to the original design criteria. Performance that is closer to expectations increases the likelihood that limb scatter measurements by SNPP OMPS and successor instruments can form the basis for accurate long-term monitoring of ozone vertical profiles. The team finds that the Limb instrument operates mostly as designed and basic performance meets or exceeds the original design criteria. Internally scattered stray light and sensor pointing knowledge are two design challenges with the potential to seriously degrade performance. A thorough prelaunch characterization of stray light supports software corrections that are accurate to within 1% in radiances up to 60 km for the wavelengths used in deriving ozone. Residual stray light errors at 1000nm, which is useful in retrievals of stratospheric aerosols, currently exceed 10%. Height registration errors in the range of 1 km to 2 km have been observed that cannot be fully explained by known error sources. An unexpected thermal sensitivity of the sensor also causes wavelengths and pointing to shift each orbit in the northern hemisphere. Spectral shifts of as much as 0.5nm in the ultraviolet and 5 nm in the visible, and up to 0.3 km shifts in registered height, must be corrected in ground processing.

ozone↗
NASA NTRS1983

Establishment of a center of excellence for applied mathematical and statistical research

The state of the art was assessed with regards to efforts in support of the crop production estimation problem and alternative generic proportion estimation techniques were investigated. Topics covered include modeling the greeness profile (Badhwarmos model), parameter estimation using mixture models such as CLASSY, and minimum distance estimation as an alternative to maximum likelihood estimation. Approaches to the problem of obtaining proportion estimates when the underlying distributions are asymmetric are examined including the properties of Weibull distribution.

Woodward, W. A.↗
NASA NTRS1982

Modeling methodology for MLS range navigation system errors using flight test data

Flight test data was used to develop a methodology for modeling MLS range navigation system errors. The data used corresponded to the constant velocity and glideslope approach segment of a helicopter landing trajectory. The MLS range measurement was assumed to consist of low frequency and random high frequency components. The random high frequency component was extracted from the MLS range measurements. This was done by appropriate filtering of the range residual generated from a linearization of the range profile for the final approach segment. This range navigation system error was then modeled as an autoregressive moving average (ARMA) process. Maximum likelihood techniques were used to identify the parameters of the ARMA process.

Karmali, M. S.↗
NASA NTRS1998

Spacecraft Charging and the Microwave Anisotropy Probe Spacecraft

The Microwave Anisotropy Probe (MAP), a MIDEX mission built in partnership between Princeton University and the NASA Goddard Space Flight Center (GSFC), will study the cosmic microwave background. It will be inserted into a highly elliptical earth orbit for several weeks and then use a lunar gravity assist to orbit around the second Lagrangian point (L2), 1.5 million kilometers, anti-sunward from the earth. The charging environment for the phasing loops and at L2 was evaluated. There is a limited set of data for L2; the GEOTAIL spacecraft measured relatively low spacecraft potentials (approx. 50 V maximum) near L2. The main area of concern for charging on the MAP spacecraft is the well-established threat posed by the "geosynchronous region" between 6-10 Re. The launch in the autumn of 2000 will coincide with the falling of the solar maximum, a period when the likelihood of a substorm is higher than usual. The likelihood of a substorm at that time has been roughly estimated to be on the order of 20% for a typical MAP mission profile. Because of the possibility of spacecraft charging, a requirement for conductive spacecraft surfaces was established early in the program. Subsequent NASCAP/GEO analyses for the MAP spacecraft demonstrated that a significant portion of the sunlit surface (solar cell cover glass and sunshade) could have nonconductive surfaces without significantly raising differential charging. The need for conductive materials on surfaces continually in eclipse has also been reinforced by NASCAP analyses.

Timothy, VanSant J.↗
NASA NTRS1985

Transition in a disturbed environment

The title of this presentation is the title of our research grant. While transition study is the objective of the work, the results to date are principally on the properties of turbulent boundary layers at low Reynolds numbers are discussed. Testing was done in a small return wind tunnel. Mean boundary layer development is given. The skin friction behavior of the turbulent points are considered. No standard laminar flow was observed. Furthermore, the turbulent mean flow data seem reasonable for the elevated disturbance levels of the tests in the sense that there is no discernible wake component to any of the profiles and that the variation of skin friction with R sub theta is consistent with zero wake strength. The no-grid data are in all likelihood transitional.

Reshotko, E.↗