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NASA NTRS1975

A mathematical examination of the press model for atmospheric turbulence

The random process used to model atmospheric turbulence in aircraft response problems is examined. The first, second, and higher order probability density and characteristic functions were developed. The concepts of the Press model lead to an approximate procedure for the analysis of the response of linear dynamic systems to a class of non-Gaussian random processes. The Press model accounts for both the Gaussian and non-Gaussian forms of measured turbulence data. The nonstationary aspects of measured data are explicitly described by the transition properties of the random process. The effects of the distribution of the intensity process upon calculated exceedances are examined. It is concluded that the press model with a Gaussian intensity distribution gives a conservative prediction of limit load values.

Sidwell, K.↗

NASA NTRS1979

System noise analysis of the dumbbell tethered satellite for gravity-gradient measurements

An analysis of the dumbbell gravity gradiometer concept for measuring short wavelength variations in the earth's gravity gradient is presented. Variations in the gradient are recorded by measuring tension variations in a vertically stabilized satellite consisting of heavy masses connected by a long wire or rod. Tension noise arises from the excitation of various mechanical oscillations of the system. The principal noise sources that were identified are fluctuations in atmospheric drag heating and drag force resulting from density variations and winds. Approximate analytical expressions are presented for the tension noise as a function of the system design parameters for various possible configurations. Computer simulations using numerical integration were performed to study the tension noise for several sample cases. Three designs consistent with Shuttle launch capabilities are discussed.

Colombo, G.↗

NASA NTRS1994

Direct Simulation of a Self-Similar Turbulent Mixing Layer

Three direct numerical simulations of incompressible turbulent plane mixing layers have been performed. All the simulations were initialized with the same two velocity fields obtained from a direct numerical simulation of a turbulent boundary layer with a momentum thickness Reynolds number of 300 computed by Spalart (J. Fluid Mech. 187, 61, 1988). In addition to a baseline case with no additional disturbances, two simulations were begun with two-dimensional disturbances of varying strength in addition to the boundary layer turbulence. After a development stage, the baseline case and the case with weaker additional two-dimensional disturbances evolve self-similarly, reaching visual thickness Reynolds numbers of up to 20 000. This self-similar period is characterized by a lack of large-scale organized pairings, a lack of streamwise vortices in the 'braid' regions, and scalar mixing that is characterized by 'marching' Probability Density Functions (PDFs). The case begun with strong additional two-dimensional disturbances only becomes approximately self-similar, but exhibits sustained organized large-scale pairings, clearly defined braid regions with streamwise vortices that span them, and scalar PDFs that are 'nonmarching.' It is also characterized by much more intense vertical velocity fluctuations than the other two cases. The statistics and structures in several experiments involving turbulent mixing layers are in better agreement with those of the simulations that do not exhibit organized pairings.

Rogers, Michael M.↗

NASA NTRS1977

Temperature, density, and composition in the disturbed thermosphere from Esro 4 gas analyzer measurements - A global model

An analysis of density measurements of Ar, N2, O, and He made at 280 km with the gas analyzer aboard the polar-orbiting satellite Esro 4 has yielded a global model of the variations in temperature, density, and composition that occur in the disturbed thermosphere. In the model the increase of temperature over quiet conditions is a nonlinear function of the planetary geomagnetic index, its latitude profile being approximated by a fourth-power sin phi law, where phi is the 'invariant' magnetic latitude. A density wave proceeding from high latitudes is approximated by a fourth power cos phi law. A strong nonlinearity in the relation between the temperature variations and the variations in the height of the homopause explains a previously found behavioral difference in the variation of atomic oxygen during magnetic storms and during periods of sustained geomagnetic activity.

Jacchia, L. G.↗

NASA NTRS1994

Comparison of dynamical approximation schemes for non-linear gravitational clustering

We have recently conducted a controlled comparison of a number of approximations for gravitational clustering against the same n-body simulations. These include ordinary linear perturbation theory (Eulerian), the adhesion approximation, the frozen-flow approximation, the Zel'dovich approximation (describable as first-order Lagrangian perturbation theory), and its second-order generalization. In the last two cases we also created new versions of approximation by truncation, i.e., smoothing the initial conditions by various smoothing window shapes and varying their sizes. The primary tool for comparing simulations to approximation schemes was crosscorrelation of the evolved mass density fields, testing the extent to which mass was moved to the right place. The Zel'dovich approximation, with initial convolution with a Gaussian e(exp -k(exp 2)/k(exp 2, sub G)) where k(sub G) is adjusted to be just into the nonlinear regime of the evolved model (details in text) worked extremely well. Its second-order generalization worked slightly better. All other schemes, including those proposed as generalizations of the Zel'dovich approximation created by adding forces, were in fact generally worse by this measure. By explicitly checking, we verified that the success of our best-choice was a result of the best treatment of the phases of nonlinear Fourier components. Of all schemes tested, the adhesion approximation produced the most accurate nonlinear power spectrum and density distribution, but its phase errors suggest mass condensations were moved to slightly the wrong location. Due to its better reproduction of the mass density distribution function and power spectrum, it might be preferred for some uses. We recommend either n-body simulations or our modified versions of the Zel'dovich approximation, depending upon the purpose. The theoretical implication is that pancaking is implicit in all cosmological gravitational clustering, at least from Gaussian initial conditions, even when subcondensations are present.

Melott, Adrian L.↗

NASA NTRS2004

Density, Electrical Conductivity and Viscosity of Hg(0.8)Cd(0.2)Te Melt

The density, viscosity, and electrical conductivity of Hg(0.8)Cd(0.2)Te melt were measured as a function of temperature. A pycnometric method was used to measure the melt density in the temperature range of 1072 to 1122 K. The viscosity and electrical conductivity were determined using a transient torque method from 1068 to 1132 K. The density result from this study is within 0.3% of the published data. However, the current viscosity result is approximately 30% lower than the existing data. The electrical conductivity of Hg(0.8)Cd(0.2)Te melt as a function of temperature, which is not available in the literature, is also determined. The analysis of the temperature dependent electrical conductivity and the relationship between the kinematic viscosity and density indicated that the structure of the melt appeared to be homogeneous when the temperature was above 1090 K. A structural transition occurred in the Hg(0.8)Cd(0.2)Te melt as the temperature was decreased to below 1090 K

Li, C.↗

NASA NTRS1977

RMS electron density fluctuation at 1 AU

Analytic expressions at 1 AU for the average RMS Electron Density Fluctuation and the ratio of RMS Electron Density Fluctuation to Electron Density, both as functions of the observational time scale, are constructed from average spacecraft in situ density measurements at approximately 1 AU and columnar phase fluctuation measurements over a wide variety of signal closet approach points. Additionally, the (one-dimensional) Electron Density Fluctuation spectrum and the Doppler phase fluctuation scale are derived, and various extrapolations to the region interior to 1 AU are made.

Berman, A. L.↗

NASA NTRS2002

A Chandra X-Ray Study of Cygnus A: The Cluster of Galaxies - 3

We present an analysis of the Chandra Advanced CCD Imaging Spectrometer (ACIS) observation of the intracluster gas associated with the cluster of galaxies surrounding Cygnus A. The dominant gaseous structure is a roughly elliptical (presumably prolate spheroidal in three dimensions) feature with semimajor axis approximately equal to 1.(prime)1 (approximately equal to 100 kpc). This structure apparently represents intracluster gas that has been swept up and compressed by a cavity inflated in this gas by relativistic material that has passed through the ends of the radio jets. The X-ray-emitting gas shows this prolate spheroidal morphology to approximately equal to 1.(prime)2 (110 kpc) from the radio galaxy but is spherical on larger scales. The X-ray emission from the intracluster gas extends to at least 8 prime (approximately equal to 720 kpc) from the radio galaxy, and a second, extended source of X-ray emission (probably associated with a second cluster of galaxies) is seen some 12 prime (approximately equal to 1 Mpc) to the northwest of Cygnus A. The X-ray spectrum of the integrated intracluster gas imaged on the S3 chip (dimensions 8 prime x 8 prime = 720 x 720 kpc), excluding the contribution from the radio galaxy and other compact sources of X-ray emission, has a gas temperature, metallicity, and unabsorbed 2-10 keV rest-frame luminosity of 7.7 keV, 0.34 times solar, and 3.5 x 10(exp 44) ergs per second, respectively. We have projected the X-ray spectra taken from 12 elliptical and circular annuli in order to derive a run of temperature, metallicity, density, and pressure as a function of radius. The temperature of the X-ray-emitting gas drops from approximately equal to 8 keV more than 100 kpc from the center to approximately equal to 5 keV some 80 kpc from the center, with the coolest gas immediately adjacent to the radio galaxy. "Belts" of slightly cooler (approximately equal to 4 keV) X-ray-emitting gas run around the minor dimension of the cavity created by the radio source, while the limb-brightened edges of the cavity are slightly hotter (approximately equal to 6 keV), perhaps as a result of heating by a bow shock driven by the probably expanding cavity into the intracluster gas. There is a metallicity gradient in the X-ray-emitting gas, with the highest metallicities (approximately solar) found close to the center, decreasing to approximately 0.3 times solar in the outer parts. We have used the assumption of hydrostatic equilibrium to derive a total cluster mass within 500 kpc of 2.0 x 10(exp 14) solar mass and 2.8 x 10(exp 14) solar mass for constant and centrally decreasing temperature profiles, respectively. The total mass of X-ray-emitting gas within the same radius is 1.1 x 10(exp 13) solar mass. Thus, the gas fraction of the cluster within 500 kpc is 0.055 and 0.039 for the constant and centrally decreasing temperature profiles, respectively.

Smith, David A.↗

NASA NTRS2004

Density, Electrical Conductivity and Viscosity of Hg(sub 0.8)Cd(sub 0.2)Te Melt

The density, viscosity, and electrical conductivity of Hg(sub 0.8)Cd(sub 0.2)Te melt were measures as a function of temperature. A pycnometric method was used to measure the melt density in the temperature range of 1072 to 1122 K. The viscosity and electrical conductivity were determined using a transient torque method from 1068 to 1132 K. The density result from this study is within 0.3% of the published data. However, the current viscosity result is approximately 30% lower than the existing data. The electrical conductivity of Hg(sub 0.8)Cd(sub 0.2)Te melt as a function of temperature, which is not available in the literature, is also determined. The analysis of the temperature dependent electrical conductivity and the relationship between the kinematic viscosity and density indicated that the structure of the melt appeared to be homogeneous when the temperature was above 1090 K. A structural transition occurred in the Hg(sub 0.8)Cd(sub 0.2)Te melt as the temperature was decreased to below 1090 K.

Li, C.↗

NASA NTRS2004

Thermophysical Properties and Structural Transition of Hg(0.8)Cd(0.2)Te Melt

Thermophysical properties, namely, density, viscosity, and electrical conductivity of Hg(sub o.8)Cd(sub 0.2)Te melt were measured as a function of temperature. A pycnometric method was used to measure the melt density in the temperature range of 1072 to 1122 K. The viscosity and electrical conductivity were simultaneously determined using a transient torque method from 1068 to 1132 K. The density result from this study is within 0.3% of the published data. However, the current viscosity result is approximately 30% lower than the existing data. The electrical conductivity of Hg(sub o.8)Cd(sub 0.2)Te melt as a function of temperature, which is not available in the literature, is also determined. The analysis of the temperature dependent electrical conductivity and the relationship between the kinematic viscosity and density indicated that the structure of the melt appeared to be homogeneous when the temperature was above 1090 K. A structural transition occurred in the Hg(sub 0.8)Cd(0.2)Te melt as the temperature was decreased from 1090 K to the liquidus temperature.

Li, C.↗

NASA NTRS1996

Use of Density Functional Method to Study Molecular Vibrations

Use of a scale factor reduces the errors in computed vibrational frequencies (errors due to anharmonicities, basis set deficiencies, and approximate treatment of electron correlation). Additional errors come from modelling solids with small molecules. Nevertheless, we hope that the present calculations add to the understanding of surface IR measurements of the heat tiles.

Chong, Delano P.↗

NASA NTRS1976

Formation of the 0.511.-MeV line in solar flares

The gamma-ray line produced at 0.51-MeV was studied and is shown to be the result of either of free annihilation of positrons with electrons or of the decay of positronium by 2-photon emission. Positron annihilation from the bound state of positronium may also proceed by 3-photon emission, resulting in a continuum with energies up to 0.51-MeV. Accurate calculations of the rates of free annihilation and positronium formation in a solar-flare plasma are presented. Estimates of the positronium-formulation rates by charge exchange and the rates of dissociation and quenching are also considered. The temperature and density dependence of the ratio of 3-photon to 2-photon emission was obtained. It is shown that when the ratio of free electrons to neutral atoms in the plasma is approximately unity or greater, the Doppler width of the 0.51-MeV line is a function of the temperature of the annihilation region. For the small ion densities characteristics of the photosphere, the width is predominantly a function of the density.

Crannell, C. J.↗

NASA NTRS1992

Prediction of thermal cycling induced matrix cracking

Thermal fatigue has been observed to cause matrix cracking in laminated composite materials. A method is presented to predict transverse matrix cracks in composite laminates subjected to cyclic thermal load. Shear lag stress approximations and a simple energy-based fracture criteria are used to predict crack densities as a function of temperature. Prediction of crack densities as a function of thermal cycling is accomplished by assuming that fatigue degrades the material's inherent resistance to cracking. The method is implemented as a computer program. A simple experiment provides data on progressive cracking of a laminate with decreasing temperature. Existing data on thermal fatigue is also used. Correlations of the analytical predictions to the data are very good. A parametric study using the analytical method is presented which provides insight into material behavior under cyclical thermal loads.

Mcmanus, Hugh L.↗

NASA NTRS1999

Cosmology with EMSS Clusters of Galaxies

We use ASCA observations of the Extended Medium Sensitivity Survey sample of clusters of galaxies to construct the first z = 0.5 - 0.8 cluster temperature function. This distant cluster temperature function, when compared to local z approximately 0 and to a similar moderate redshift (z = 0.3 - 0.4) temperature function strongly constrains the matter density of the universe. Best fits to the distributions of temperatures and redshifts of these cluster samples results in Omega(sub M) = 0.45 +/- 0.1 if Lambda = 0 and Omega = 0.27 +/- 0.1 if Lambda + Omega(sub M) = 1. The uncertainties are 1sigma statistical. We examine the systematics of our approach and find that systematics, stemming mainly from model assumptions and not measurement errors, are about the same size as the statistical uncertainty +/- 0.1. In this poster proceedings, we clarify the issue of a8 as reported in our paper Donahue & Voit (1999), since this was a matter of discussion at the meeting.

Donahue, Megan↗

NASA NTRS1983

Diffusive separation of binary mixtures of CO2-H2 in a sonic-orifice expansion

The separation of binary gas mixtures of carbon dioxide and hydrogen in sonic-orifice-generated free jets is investigated over a source Reynolds number range of 100 to 3000 using the well-known electron beam fluorescence technique. The lighter species, hydrogen, is chosen as the minor species in order to examine the extent of the validity of Sherman's first-order diffusive separation theory for large separation. The diffusive separation of mixtures containing approximately 2, 5, and 20 percent hydrogen in carbon dioxide is investigated by experimentally determining the relative number densities of the two species as a function of centerline axial distance within the free jets. Sherman's diffusive separation theory is applied to the jets using axial Mach number profiles which were a combination of experimental and analytical results for gamma = 1.40 expansions. The gamma = 1.40 expansion is shown to approximate the CO2-H2 expansion quite well, and the calculated separation agrees remarkably well with the experimentally determined values.

Mccay, T. D.↗

NASA NTRS2004

The Surface Density Distribution in the Solar Nebula

The commonly used minimum mass power law representation of the pre-solar nebula is reanalyzed using a new cumulative-mass-model. This model predicts a smoother surface density approximation compared with methods based on direct computation of surface density. The density is quantified using two independent analytical formulations. First, a best-fit transcendental function is applied directly to the basic planetary data. Next a solution to the time-dependent disk evolution equation is parametrically adapted to the solar nebula data. The latter model is shown to be a good approximation to the finite-size early Solar Nebula, and by extension to other extra solar protoplanetary disks.

Davis, Sanford S.↗

NASA NTRS1981

Radiative transfer theory for active remote sensing of a layer of small ellipsoidal scatterers

The radiative transfer theory is applied within the Rayleigh approximation to calculate the backscattering cross section of a layer of randomly positioned and oriented small ellipsoids. The orientation of the ellipsoids is characterized by a probability density function of the Eulerian angles of rotation. The radiative transfer equations are solved by an iterative approach to first order in albedo. In the half space limit the results are identical to those obtained via the approach of Foldy's and distorted Born approximation. Numerical results of the theory are illustrated using parameters encountered in active remote sensing of vegetation layers. A distinctive characteristic is the strong depolarization shown by vertically aligned leaves.

Tsang, L.↗

NASA NTRS1973

Alfven waves in spiral interplanetary field

A theoretical study is presented of the Alfven waves in the spiral interplanetary magnetic field. The Alfven waves under consideration are arbitrary, large amplitude, non-monochromatic, microscale waves of any polarization. They superpose on a mesoscale background flow of thermally anisotropic plasma. Using WKB approximation, an analytical solution for the amplitude vectors is obtained as a function of the background flow properties: density, velocity, Alfven speed, thermal anisotropy, and the spiral angel. The necessary condition for the validity of the WKB solution is discussed. The intensity of fluctuations is calculated as a function of heliocentric distance. Relative intensity of fluctuations as compared with the magnitude of the background field has its maximum in the region near l au. Thus outside of this region, the solar wind is less turbulent.

Whang, Y. C.↗