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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 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Mars: Wavelength-dependent dual polarization global scattering

During the 1988 and 1990 Mars oppositions, the first continuous-wave (CW) multi-wavelength radar observations were performed that include the entire echo in both polarizations. These observations, coordinated in subradar coverage when possible, were made with the Arecibo S-band (12.6 cm lambda) and Goldstone X-band (3.5 cm lambda) facilities. The CW spectra obtained during these oppositions have been studied using a variety of techniques to explore the spatial and wavelength dependence of both the Same-sense Circular (SC) and Opposite-sense Circular (OC) polarization returns. Earlier multi-wavelength comparisons dealt primarily with the quasispecular component of the echoes. Our work in contrast has much new information (at high signal-to-noise) for the SC 'depolarized component. The unique value of these radar observations lies in their potential for probing the subsurface scattering behavior in 'appropriate' terrain. The clearest case for wavelength dependence in the SC component is the scattering behavior over Tharsis, where the X-band features are significantly weaker than the S-band features. This hypothesis was advanced to account for the low thermal inertia of Tharsis, but also can explain the S/X differences if the layer is about 40 cm thick. In contrast to the Tharsis result, the depolarized echo from the heavily cratered terrain is actually stronger at X-band. The obvious interpretation is that more scatterers exist at the scale of the shorter wavelength, either at the surface or as a distributed subsurface scatterers. The strongest depolarized feature of the X-band spectra is associated with the south residual polar cap. The radar cross section of this feature corresponds to an equivalent full-disk albedo of unity.

Harmon, J. K.↗
NASA NTRS1989

Combined first- and second-order Fermi acceleration in cometary environments

Two-dimensional (one velocity space and one spatial dimension), time-dependent model calculations indicate that an interplay between velocity and spatial diffusion may be responsible for the acceleration of implanted heavy ions in the cometary preshock region. Velocity diffusion (second-order Fermi acceleration) accelerates the pickup ions to moderate energies, thus creating a seed population for the more efficient diffusive-compressive shock acceleration. Solar wind convection limits the time available for diffusive-compressive acceleration. Therefore, the resulting energy spectrum above the pickup energy is a combination of an exponential decrease at lower energies (up to about 100 keV) and a power law spectrum at higher energies. The calculated energy spectra constitute a surprisingly good fit to the published Vega and Giotto energy spectra above the pickup energy.

Gombosi, T. I.↗
NASA NTRSDate not supplied

Determining True Sensor Spatial Resolution of Very High Resolution Optical Imagery

Some satellite data is delivered in images with gridded pixels. This gridded pixel size is often assumed to be the spatial resolution of the satellite sensor; however, this is not always the case. An image can be grided to any arbitrary pixel size, but the sensor resolution will remain constant. For example, an image with a pixel grid size much smaller than the sensor resolution will appear blurry along what should be sharp transitions. This discrepancy between an image’s pixel size and true sensor spatial resolution can be the source of much confusion and even misinformation among data users, which may lead them to waste time and resources on using images that do not suit their spatial resolution needs. This presentation will highlight our evaluation of the true spatial resolution of various government and commercial images in the pixel size range of 0.3 m to 60 m. Images evaluated include ESA’s Sentinel-2 (60 m, 20 m, 10 m pixels), USGS’s Landsat 8/9 (30 m & 15 m pixels), Planet’s SuperDoves (3 m pixels), BlackSky’s Globals (~1 m pixels), and the optical bands of Maxar’s WorldView-2 (2.4 m – 0.41 m pixels) and WorldView-3 (1.38 m – 0.31 m pixels). Our evaluation of true sensor spatial resolution, or ‘footprint size’ is based on the sensor’s line spread function (LSF). We calculate the width at half the height of the LSF to find the full width at half maximum (FWHM). The FWHM is how we report sensor spatial resolution. Different objects are examined for constructing the LSF depending on the sensor spatial resolution. Coarser resolution sensors in this evaluation such as Sentinel-2 and Landsat 8/9 are examined at bridges over a dark water background. The bright bridge acts as a line impulse, giving a sensor’s line spread function (LSF) in one direction. Additionally, we simulate the impacts of bridge width on the apparent LSF to obtain a true LSF without the effects of bridge width for these sensors. Finer resolution sensors will image the irregularities in bridges such as trusses, sidewalks, and in some cases painted lines, interfering with the LSF construction. Instead, these sensors are evaluated at large (60 m – 140 m) black and white checkerboards known as Cal/Val sites. At these locations, the image’s transition from black to white is extracted as an edge spread function (ESF). We calculate the derivative of this ESF to obtain the sensor’s LSF. From there, we find the FWHM as we do for the coarser resolution images. With the FWHM and pixel size, we determine how over- or under-sampled the images are. When the ratio of a sensor’s spatial resolution and the gridded image’s pixel size is less than 1, the image is considered under-sampled. In this case, each pixel’s information is unique but only a portion of that pixel’s ground area has been measured. On the other side, if the ratio is greater than 1, the image is considered over-sampled. That is, each pixel’s information is sourced from within the ground extent of the pixel and some extent outside additionally. We will show the true spatial resolution and the extent of over-/under-sampling in the imagery from ESA’s Sentinel-2 (60 m, 20 m, 10 m pixels), USGS’s Landsat 8/9 (30 m & 15 m pixels), Planet’s SuperDoves (3 m pixels), BlackSky’s Globals (~1 m pixels), and the optical bands of Maxar’s WorldView-2 (2.4 m – 0.41 m pixels) and WorldView-3 (1.38 m – 0.31 m pixels).

Alana Semple↗
DOE OSTI2021

Electron Dynamics Within a MITL Containing a Load

In this paper, we derive the vacuum electric fields within specific cylindrically symmetric magnetically insulated transmission lines (MITLs) in the limit of an infinite speed of light for an arbitrary time-dependent current. We focus our attention on two types of MITLs: the radial MITL and a spherically curved MITL. We then simulate the motion of charged particles, such as electrons, present in these MITLs due to the vacuum fields. In general, the motion of charged particles due to the vacuum fields is highly nonlinear since the fields are nonlinear functions of spatial coordinates and depend on an arbitrary time-dependent current drive. Using guiding center theory, however, one can describe the gross particle kinetics using a combination of $\textbf {E} \times \textbf {B}$ and $\nabla B$ drifts. In addition, we compare our approximate inner MITL field models and particle kinetics with those from a fully electromagnetic simulation code. We find that the agreement between the approximate model and the electromagnetic simulations is excellent.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Factors Affecting Bait Site Visitation: Area of Influence of Baits

Baiting is a fundamental strategy for the global management of wild pigs (Sus scrofa); however, little information exists on how anthropogenic bait affects wild pig movements on a landscape. We investigated factors that are important in determining the spatial area of attraction for wild pigs to bait (‘area of influence’ of a bait site) using data from Global Positioning System (GPS) collars and locations of bait sites. We monitored movements of wild pigs in 2 distinct study areas in the United States from February to September 2016 and used locational data using GPS collars to analyze the influence of habitat quality (dependent on site), home range size, number of bait sites in the home range, distance to a bait site, and sex in relation to movement in time and space. We determined the average area of influence by calculating the area of a circle with the radius as the average maximum distance travelled by wild pigs to reach a bait site. The average area of influence for our bait sites was 6.7 km 2 (or a radius of approximately 1.5 km), suggesting a bait spacing of approximately 1.5 km would be adequate to capture visitation by most wild pigs and a spacing of 3 km could allow substantial visitation while minimizing redundant effort depending on the spatial structure of the populations. Eighty percent of wild pigs first visited bait sites within 8.9 days after bait deployment; and they visited earlier when their home range size was larger. As the number of bait sites in an individual's home range increased, individual pigs visited more bait sites, and the probability of a visit increased dramatically up to approximately 5 bait sites and much less thereafter. Wild pigs travelled farther distances to visit bait sites in lower quality habitat. Our results support the hypothesis that habitat quality can mediate the efficacy of baiting programs for wildlife by influencing their movement patterns and motivation to use anthropogenic resources. Our results suggest wild pigs will travel extensively within their home range to visit bait sites, and that in lower quality habitat, most animals will find bait sites more quickly. Determining the area of influence of bait sites can increase the efficacy of planning and monitoring management programs. Overall, our study provides new information to help managers plan baiting designs to attract the greatest number of pigs.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Thermal relaxation of strain and twist in ferroelectric hexagonal boron nitride moiré interfaces

New properties can arise at van der Waals (vdW) interfaces hosting a moiré pattern generated by interlayer twist and strain. However, achieving precise control of interlayer twist/strain remains an ongoing challenge in vdW heterostructure assembly, and even subtle variation in these structural parameters can create significant changes in the moiré period and emergent properties. Characterizing the rate of interlayer twist/strain relaxation during thermal annealing is critical to establish a thermal budget for vdW heterostructure construction and may provide a route to improve the homogeneity of the interface or to control its final state. Here, we characterize the spatial and temporal dependence of interfacial twist and strain relaxation in marginally-twisted hBN/hBN interfaces heated under conditions relevant to vdW heterostructure assembly and typical sample annealing. We find that the ferroelectric hBN/hBN moiré at very small twist angles (θ ≤ 0.1°) relaxes minimally during annealing in air at typical assembly temperatures of 170°C. However, at 400°C, twist angle relaxes significantly, accompanied by a decrease in spatial uniformity. Uniaxial heterostrain initially increases and then decreases over time, becoming increasingly non-uniform in direction. Structural irregularities such as step edges, contamination bubbles, or contact with the underlying substrate result in local inhomogeneity in the rate of relaxation.

2D materials↗
NASA NTRS1993

Evapotranspiration and runoff from large land areas: Land surface hydrology for atmospheric general circulation models

A land surface hydrology parameterization for use in atmospheric GCM's is presented. The parameterization incorporates subgrid scale variability in topography, soils, soil moisture and precipitation. The framework of the model is the statistical distribution of a topography-soils index, which controls the local water balance fluxes, and is therefore taken to represent the large land area. Spatially variable water balance fluxes are integrated with respect to the topography-soils index to yield our large topography-soils distribution, and interval responses are weighted by the probability of occurrence of the interval. Grid square averaged land surface fluxes result. The model functions independently as a macroscale water balance model. Runoff ratio and evapotranspiration efficiency parameterizations are derived and are shown to depend on the spatial variability of the above mentioned properties and processes, as well as the dynamics of land surface-atmosphere interactions.

Famiglietti, J. S.↗
DOE OSTI2023

Sensitivity of the pseudo-global warming method under flood conditions: a case study from the northeastern US

Abstract. Intensified extreme precipitation and corresponding floods are the most relevant consequences of climate change over the northeastern US (NEUS). To evaluate the impacts of climate change or certain climate perturbations on future extreme weather events which are dynamically similar to historic analogs, the pseudo-global warming (PGW) method has been frequently employed; however, this method lacks precise definition and guidelines, thus limiting its application. More specifically, three key questions related to the application of the PGW method remain unanswered: at what spatial scale should climate perturbations be applied? Among the different meteorological variables available, which ones should be perturbed? And will PGW projections vary significantly when different perturbations are applied? To address these questions, we examine the sensitivity and robustness of conclusions drawn from the PGW method over the NEUS by conducting multiple PGW experiments with varied perturbation spatial scales and choice of perturbed meteorological variables. The results show that the projections of precipitation and other essential variables at the regional mean scale are consistent across the PGW simulations, with a relative difference of much less than 10 %; however, different perturbation modifications can cause significant displacements of the storm events being simulated. Several previously assumed advantages of modifying only the temperature at regional mean scale, such as the preservation of geostrophic balance, do not appear to hold. Also, for these experiments, we find the regional mean perturbation produces a positive precipitation bias because it ignores the land–ocean warming contrast, which is a robust regional response to global warming. Overall, PGW experiments with perturbations from temperature or the combination of temperature and wind at the grid point scale are both recommended, depending on the research questions. The first approach can isolate the spatially dependent thermodynamic impact, and the latter incorporates both the thermodynamic and dynamic impacts.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

The phononic and charge density wave behavior of entire rare-earth tritelluride series with chemical pressure and temperature

Here, we present comprehensive phononic and charge density wave properties (CDW) of rare-earth van der Waals tritellurides through temperature dependent angle-resolved Raman spectroscopy measurements. All the possible rare-earth tritellurides (RTe3) ranging from R = La–Nd, Sm, Gd–Tm were synthesized through a chemical vapor transport technique to achieve high quality crystals with excellent CDW characteristics. Raman spectroscopy studies successfully identify the emergence of the CDW state and transition temperature (TCDW), which offers a non-destructive method to identify their CDW response with micron spatial resolution. Temperature dependent Raman measurements further correlate how the atomic mass of metal cations and the resulting chemical pressure influence its CDW properties and offer detailed insight into the strength of CDW amplitude mode-phonon coupling during the CDW transition. Angle-resolved Raman measurements offer the first insights into the CDW-phonon symmetry interplay by monitoring the change in the symmetry of phonon mode across the CDW transition. Overall results introduce the library of RTe3 CDW materials and establish their characteristics through the non-destructive angle-resolved Raman spectroscopy technique.

36 MATERIALS SCIENCE↗
NASA NTRS2005

Precision Requirements for Space-based XCO2 Data

Precision requirements have been determined for the column-averaged CO2 dry air mole fraction (X(sub CO2)) data products to be delivered by the Orbiting Carbon Observatory (OCO). These requirements result from an assessment of the amplitude and spatial gradients in X(sub CO2), the relationship between X(sub CO2) precision and surface CO2 flux uncertainties calculated from inversions of the X(sub CO2) data, and the effects of X,,Z biases on CO2 flux inversions. Observing system simulation experiments and synthesis inversion modeling demonstrate that the OCO mission design and sampling strategy provide the means to achieve the X(sub CO2) precision requirements. The impact of X(sub CO2) biases on CO2 flux uncertainties depend on their spatial and temporal extent since CO2 sources and sinks are inferred from regional-scale X(sub CO2) gradients. Simulated OCO sampling of the TRACE-P CO2 fields shows the ability of X(sub CO2) data to constrain CO2 flux inversions over Asia and distinguish regional fluxes from India and China.

Miller, C. E.↗
NASA NTRS1992

Relative timing of substorm features in MHD simulations

An investigation of the temporal sequence of substorm phenomena based on three dimensional MHD (magnetohydrodynamic) simulations of magnetic reconnection and plasmoid formation is presented. The investigation utilizes a spatially localized resistivity model which leads to a significantly faster evolution than found in previous investigations. The analysis of the results concentrates on substorm features that have received considerable attention in the past. The formation of magnetic neutral lines, the occurrence of fast flows directed both earthward and tailward, and the magnetic field changes leading to the formation of the substorm current wedge, and to the depolarization of the magnetic field earthward of the reconnection region and its dependence on the spatial distribution of resistivity, are discussed. These phenomena are seen as an integral part of the nonlinear evolution of the three dimensional tearing instability.

Hesse, Michael↗
DOE OSTI2021

Spatial coherence of room-temperature monolayer WSe 2 exciton-polaritons in a trap

The emergence of spatial and temporal coherence of light emitted from solid-state systems is a fundamental phenomenon intrinsically aligned with the control of light-matter coupling. It is canonical for laser oscillation, emerges in the superradiance of collective emitters, and has been investigated in bosonic condensates of thermalized light, as well as exciton-polaritons. Our room temperature experiments show the strong light-matter coupling between microcavity photons and excitons in atomically thin WSe 2 . We evidence the density-dependent expansion of spatial and temporal coherence of the emitted light from the spatially confined system ground-state, which is accompanied by a threshold-like response of the emitted light intensity. Additionally, valley-physics is manifested in the presence of an external magnetic field, which allows us to manipulate K and K’ polaritons via the valley-Zeeman-effect. Our findings validate the potential of atomically thin crystals as versatile components of coherent light-sources, and in valleytronic applications at room temperature.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2017

Estimating Evaporative Fraction From Readily Obtainable Variables in Mangrove Forests of the Everglades, U.S.A.

A remote-sensing-based model to estimate evaporative fraction (EF) the ratio of latent heat (LE; energy equivalent of evapotranspiration -ET-) to total available energy from easily obtainable remotely-sensed and meteorological parameters is presented. This research specifically addresses the shortcomings of existing ET retrieval methods such as calibration requirements of extensive accurate in situ micro-meteorological and flux tower observations, or of a large set of coarse-resolution or model-derived input datasets. The trapezoid model is capable of generating spatially varying EF maps from standard products such as land surface temperature [T(sub s)] normalized difference vegetation index (NDVI)and daily maximum air temperature [T(sub a)]. The 2009 model results were validated at an eddy-covariance tower (Fluxnet ID: US-Skr) in the Everglades using T(sub s) and NDVI products from Landsat as well as the Moderate Resolution Imaging Spectroradiometer (MODIS) sensors. Results indicate that the model accuracy is within the range of instrument uncertainty, and is dependent on the spatial resolution and selection of end-members (i.e. wet/dry edge). The most accurate results were achieved with the T(sub s) from Landsat relative to the T(sub s) from the MODIS flown on the Terra and Aqua platforms due to the fine spatial resolution of Landsat (30 m). The bias, mean absolute percentage error and root mean square percentage error were as low as 2.9% (3.0%), 9.8% (13.3%), and 12.1% (16.1%) for Landsat-based (MODIS-based) EF estimates, respectively. Overall, this methodology shows promise for bridging the gap between temporally limited ET estimates at Landsat scales and more complex and difficult to constrain global ET remote-sensing models.

trapezoid↗
NASA NTRS2004

Global Autocorrelation Scales of the Partial Pressure of Oceanic CO2

A global database of approximately 1.7 million observations of the partial pressure of carbon dioxide in surface ocean waters (pCO2) collected between 1970 and 2003 is used to estimate its spatial autocorrelation structure. The patterns of the lag distance where the autocorrelation exceeds 0.8 is similar to patterns in the spatial distribution of the first baroclinic Rossby radius of deformation indicating that ocean circulation processes play a significant role in determining the spatial variability of pCO2. For example, the global maximum of the distance at which autocorrelations exceed 0.8 averages about 140 km in the equatorial Pacific. Also, the lag distance at which the autocorrelation exceed 0.8 is greater in the vicinity of the Gulf Stream than it is near the Kuroshio, approximately 50 km near the Gulf Stream as opposed to 20 km near the Kuroshio. Separate calculations for times when the sun is north and south of the equator revealed no obvious seasonal dependence of the spatial autocorrelation scales. The pCO2 measurements at Ocean Weather Station (OWS) 'P', in the eastern subarctic Pacific (50 N, 145 W) is the only fixed location where an uninterrupted time series of sufficient length exists to calculate a meaningful temporal autocorrelation function for lags greater than a few days. The estimated temporal autocorrelation function at OWS 'P', is highly variable. A spectral analysis of the longest four pCO2 time series indicates a high level of variability occurring over periods from the atmospheric synoptic to the maximum length of the time series, in this case 42 days. It is likely that a relative peak in variability with a period of 3-6 days is related to atmospheric synoptic period variability and ocean mixing events due to wind stirring. However, the short length of available time series makes identifying temporal relationships between pCO2 and atmospheric or ocean processes problematic.

Li, Zhen↗
NASA NTRS2001

Remote Sensing of Wind Fields and Aerosol Distribution with Airborne Scanning Doppler Lidar

The coherent Doppler laser radar (lidar), when operated from an airborne platform, is a unique tool for the study of atmospheric and surface processes and features. This is especially true for scientific objectives requiring measurements in optically-clear air, where other remote sensing technologies such as Doppler radar are typically at a disadvantage. The atmospheric lidar remote sensing groups of several US institutions, led by Marshall Space Flight Center, have developed an airborne coherent Doppler lidar capable of mapping the wind field and aerosol structure in three dimensions. The instrument consists of an eye-safe approx. 1 Joule/pulse lidar transceiver, telescope, scanner, inertial measurement unit, and flight computer system to orchestrate all subsystem functions and tasks. The scanner is capable of directing the expanded lidar beam in a variety of ways, in order to extract vertically-resolved wind fields. Horizontal resolution is approx. 1 km; vertical resolution is even finer. Winds are obtained by measuring backscattered, Doppler-shifted laser radiation from naturally-occurring aerosol particles (of order 1 micron diameter). Measurement coverage depends on aerosol spatial distribution and composition. Velocity accuracy has been verified to be approx. 1 meter per second. A variety of applications have been demonstrated during the three flight campaigns conducted during 1995-1998. Examples will be shown during the presentation. In 1995, boundary layer winds over the ocean were mapped with unprecedented resolution. In 1996, unique measurements were made of. flow over the complex terrain of the Aleutian Islands; interaction of the marine boundary layer jet with the California coastal mountain range; a weak dry line in Texas - New Mexico; the angular dependence of sea surface scattering; and in-flight radiometric calibration using the surface of White Sands National Monument. In 1998, the first measurements of eyewall and boundary layer winds within a hurricane were made with the airborne Doppler lidar. Potential applications and plans for improvement will also be described.

Rothermel, Jeffry↗
NASA NTRS2004

Small-Scale Variability of Large Cloud Drops

Cloud droplet size distribution is one of the most fundamental subjects in cloud physics. Understanding of spatial distribution and small-scale fluctuations of cloud droplets is essential for both cloud physics and atmospheric radiation. For cloud physics, it relates to the coalescence growth of raindrops while for radiation, it has a strong impact on a cloud's radiative properties. Most of the existing cloud radiation and precipitation formation models assume that the mean number of drops with a given radius varies proportionally to volume. The analysis of microphysical data on liquid water drop sizes shows that, for sufficiently small volumes, the number is proportional to the drop size dependent power of the volume. For abundant small drops present, the exponent is 1 as assumed in the conventional approach. However, for rarer large drops, the exponents fall below unity. At small scales, therefore, the mean number of large drops decreases with volume at a slower rate than the conventional approach assumes, suggesting more large drops at these scales than conventional models account for; their impact is consequently underestimated. Size dependent models of spatial distribution of cloud drops that simulate the observed power laws show strong drop clustering, the more so the larger the drops. The degree of clustering is determined by the observed exponents. The strong clustering of large drops arises naturally from the observed power-law statistics. Current theories of photon-cloud interaction and warm rain formation will need radical revision in order to produce these statistics; their underlying equations are unable to yield the observed power law.

Marshak, Alexander↗
NASA NTRS2000

Remote Sensing of Wind Fields and Aerosol Distributions with Airborne Scanning Doppler Lidar

The coherent Doppler lidar, when operated from an airborne platform, offers a unique measurement capability for study of atmospheric and surface processes and feature. This is especially true for scientific objectives requiring measurements in optically-clear air, where other remote sensing technologies such as Doppler radar are at a disadvantage in terms of spatial resolution and coverage. The atmospheric lidar remote sensing groups of several US institutions, led by Marshall Space Flight Center, have developed an airborne coherent Doppler lidar capable of mapping the wind field and aerosol structure in three dimensions. The instrument consists of about a 1 Joule/pulse (eyesafe) lidar transceiver, telescope, scanner, inertial measurement unit, and operations control system to orchestrate all subsystem functions and tasks. The scanner is capable of directing the expanded lidar beam in a variety of ways, in order to extract vertically resolved wind fields. Horizontal resolution is about 1 km; vertical resolution is even finer. Winds are obtained by measuring backscattered, Doppler-shifted laser radiation from naturally-occurring aerosol particles (on an order of 1 micron in diameter). Measurement coverage depends on aerosol spatial distribution and concentration. Velocity accuracy has been verified to be about 1 m/s. A variety of applications has been demonstrated during the three flight campaigns conducted during 1995-1998. Examples will be shown during the presentation. In 1995, boundary layer winds over the ocean were mapped with unprecedented resolution. In 1996, unique measurements were made of flow over the complex terrain of the Aleutian Islands; interaction of the marine boundary layer jet with the California coastal mountain range; a weak dry line in Texas - New Mexico; an upper tropospheric jet stream; the angular dependence of sea surface scattering; and in-flight radiometric calibration using the surface of White Sands National Monument. In 1998, the first measurements of eyewall and boundary layer winds within a hurricane were made with the airborne Doppler lidar. Potential future applications, and plans for improvements, will also be identified.

Rothermel, Jeffry↗
NASA NTRS1981

Computing aerodynamic sound using advanced statistical turbulence theories

It is noted that the calculation of turbulence-generated aerodynamic sound requires knowledge of the spatial and temporal variation of Q sub ij (xi sub k, tau), the two-point, two-time turbulent velocity correlations. A technique is presented to obtain an approximate form of these correlations based on closure of the Reynolds stress equations by modeling of higher order terms. The governing equations for Q sub ij are first developed for a general flow. The case of homogeneous, stationary turbulence in a unidirectional constant shear mean flow is then assumed. The required closure form for Q sub ij is selected which is capable of qualitatively reproducing experimentally observed behavior. This form contains separation time dependent scale factors as parameters and depends explicitly on spatial separation. The approximate forms of Q sub ij are used in the differential equations and integral moments are taken over the spatial domain. The velocity correlations are used in the Lighthill theory of aerodynamic sound by assuming normal joint probability.

Hecht, A. M.↗