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NASA NTRS1990

Sun's inertial motion and luminosity

Fast Fourier analysis of the detrended record of solar irradiance obtained by the Nimbus-7 cavity pyrheliometer shows a rich spectrum of significant frequencies between about 30 and 850 nHz (periods between 13 and 400 days). Wolff and Hickey (1987), elaborating on a model developed by Wolff (1974, 1976, 1983, and 1984), suggest that many of these peaks arise due to interference of rigidly rotating global solar oscillations (r- and g-modes). Their model fit is quite good in the region above about 135 nHz, but less satisfactory below this threshold. It is noted that the FFT spectrum of d-sq L/d-sq t, the second derivative of angular momentum of the solar inertial motion, contains peaks matching the large peaks in the irradiance spectrum below 400 nHz with periods near 0.08, 0.24, 0.65, and about 1 yr. The origins of the peaks in the d-sq L/d-sq t spectra are discussed, and some previous studies are reviewed bearing on the question of a possible relationship of solar motion and solar activity.

Sperber, Kenneth R.↗

NASA NTRS1991

Determination of shuttle orbiter center of gravity from flight measurements

Flight measurements of pitch, yaw, and roll rates and the resultant rotationally induced linear accelerations during three orbital maneuvers on Shuttle mission space transportation system (STS) 61-C were used to calculate the actual orbiter center-of-gravity location. The calculation technique reduces error due to lack of absolute calibration of the accelerometer measurements and compensates for accelerometer temperature bias and for the effects of gravity gradient. Accuracy of the technique was found to be limited by the nonrandom and asymmetrical distribution of orbiter structural vibration at the accelerometer mounting location. Fourier analysis of the vibration was performed to obtain the power spectral density profiles which show magnitudes in excess of 10(exp 4) ug (sup 2)/Hz for the actual vibration and over 500 ug (sup 2)/Hz for the filtered accelerometer measurements. The data from this analysis provide a characterization of the Shuttle acceleration environment which may be useful in future studies related to accelerometer system application and zero-g investigations or processes.

Hinson, E. W.↗

NASA NTRS1990

Effects of large-scale wind driven turbulence on sound propagation

Acoustic measurements made in the atmosphere have shown significant fluctuations in amplitude and phase resulting from the interaction with time varying meteorological conditions. The observed variations appear to have short term and long term (1 to 5 minutes) variations at least in the phase of the acoustic signal. One possible way to account for this long term variation is the use of a large scale wind driven turbulence model. From a Fourier analysis of the phase variations, the outer scales for the large scale turbulence is 200 meters and greater, which corresponds to turbulence in the energy-containing subrange. The large scale turbulence is assumed to be elongated longitudinal vortex pairs roughly aligned with the mean wind. Due to the size of the vortex pair compared to the scale of the present experiment, the effect of the vortex pair on the acoustic field can be modeled as the sound speed of the atmosphere varying with time. The model provides results with the same trends and variations in phase observed experimentally.

Noble, John M.↗

NASA NTRS1990

The use and misuse of statistics in space physics

This paper presents several statistical techniques most commonly used in space physics, including Fourier analysis, linear correlation, auto- and cross-correlation, power spectral density and superimposed epoch analysis, and presents tests to assess the significance of the results. New techniques such as bootstrapping and jackknifing are presented. When no test of significance is in common usage, a plausible test is suggested.

Reiff, Patricia H.↗

NASA NTRS1990

Trace element and isotopic effects arising from magma migration beneath mid-ocean ridges

The trace element concentrations and isotopic ratios in the magma erupted on mid-ocean ridges may differ from those in the source material due to physical effects such as porous flow dispersion, exchange of trace elements between the fluid and solid phases during magma migration, and convective mixing in magma chambers. These differences are in addition to those produced by better known processes such as fractional crystallization and partial melting. The effects of the three former processes are described. It is predicted that magma typically reaches the subridge magma chambers with a spatial heterogeneity only slightly reduced from that of the source material, but with a subdued variation in time. Convective mixing then further reduces the spatial heterogeneity. Application of the results for convective mixing to a recent Fourier analysis of Sr-87/Sr-86 variations along the Mid-Atlantic Ridge suggests that the falloff in amplitude of variation observed with decreasing wavelength in the Mid-Atlantic Ridge data cannot be explained by convective mixing in magma chambers. Instead, it is postulated that this falloff is due to the mechanics of the production and/or the solid-state convective mixing of chemical and isotopic heterogeneities in the solid mantle.

Kenyon, Patricia M.↗

NASA NTRS1991

A solar infrared photometer for space flight application

A photometer concept which is capable of nearly simultaneous measurements of solar radiation from 1.6 to 200 microns in seven wavelength bands is described. This range of wavelengths can probe the solar photosphere from below the level of unit optical depth in the visible to the temperature minimum, about 500 km above it. An instrument package including a 20-cm Gregorian telescope and a filter wheel photometer utilizing noncryogenic pyroelectric infrared detectors is described. Approaches to the rejection of the visible solar spectrum in the instrument, the availability of optical and mechanical components, and the expected instrumental sensitivity are discussed. For wavelengths below 35 microns, the projected instrumental sensitivity is found to be adequate to detect the intensity signature of solar p-mode oscillations during 5 min of integration. For longer wavelengths, clear detection is expected through Fourier analysis of modest data sets.

Kostiuk, Theodor↗

NASA NTRS1991

Progress with multigrid schemes for hypersonic flow problems

Several multigrid schemes are considered for the numerical computation of viscous hypersonic flows. For each scheme, the basic solution algorithm uses upwind spatial discretization with explicit multistage time stepping. Two level versions of the various multigrid algorithms are applied to the two dimensional advection equation, and Fourier analysis is used to determine their damping properties. The capabilities of the multigrid methods are assessed by solving three different hypersonic flow problems. Some new multigrid schemes based on semicoarsening strategies are shown to be quite effective in relieving the stiffness caused by the high aspect ratio cells required to resolve high Reynolds number flows. These schemes exhibit good convergence rates for Reynolds numbers up to 200 x 10(exp 6) and Mach numbers up to 25.

Radespiel, R.↗

NASA NTRS1992

Identification of aerodynamic models for maneuvering aircraft

A Fourier analysis method was developed to analyze harmonic forced-oscillation data at high angles of attack as functions of the angle of attack and its time rate of change. The resulting aerodynamic responses at different frequencies are used to build up the aerodynamic models involving time integrals of the indicial type. An efficient numerical method was also developed to evaluate these time integrals for arbitrary motions based on a concept of equivalent harmonic motion. The method was verified by first using results from two-dimensional and three-dimensional linear theories. The developed models for C sub L, C sub D, and C sub M based on high-alpha data for a 70 deg delta wing in harmonic motions showed accurate results in reproducing hysteresis. The aerodynamic models are further verified by comparing with test data using ramp-type motions.

Lan, C. Edward↗

NASA NTRS1991

Search for TeV gamma-ray emission from Hercules X-1

Six years of observations of Hercules X-1 with the Whipple Observatory gamma-ray telescope have been subjected to a Fourier analysis to search for emission at the 0.8079 Hz neutron star frequency. Evidence for a signal is found at the 99.5 percent confidence level for data taken with the medium-resolution imaging camera with some indications of emission at frequencies blueshifted from the fundamental frequency. However, analysis of the high-resolution camera data base have failed to substantiate this effect. Selection of events on the basis of gamma-ray-like image parameters did not enhance the signal from the medium-resolution data nor produce any indication of a signal from the high-resolution data. The overall conclusion is that no statistically significant evidence for TeV gamma-ray emission was found in the Whipple Observatory data base when the 6 years of data are taken as a whole.

Reynolds, P. T.↗

NASA NTRS1992

Antarctic marine gravity field from high-density satellite altimetry

High-density (about 2-km profile spacing) Geosat/GM altimetry profiles were obtained for Antarctic waters (6-deg S to 72 deg S) and converted to vertical gravity gradient, using Laplace's equation to directly calculate gravity gradient from vertical deflection grids and Fourier analysis to construct gravity anomalies from two vertical deflection grids. The resultant gravity grids have resolution and accuracy comparable to shipboard gravity profiles. The obtained gravity maps display many interesting and previously uncharted features, such as a propagating rift wake and a large 'leaky transform' along the Pacific-Antarctic Rise.

Sandwell, David T.↗

NASA NTRS1992

A VLSI architecture for simplified arithmetic Fourier transform algorithm

The arithmetic Fourier transform (AFT) is a number-theoretic approach to Fourier analysis which has been shown to perform competitively with the classical FFT in terms of accuracy, complexity, and speed. Theorems developed in a previous paper for the AFT algorithm are used here to derive the original AFT algorithm which Bruns found in 1903. This is shown to yield an algorithm of less complexity and of improved performance over certain recent AFT algorithms. A VLSI architecture is suggested for this simplified AFT algorithm. This architecture uses a butterfly structure which reduces the number of additions by 25 percent of that used in the direct method.

Reed, Irving S.↗

NASA NTRS1991

Solution to the indexing problem of frequency domain simulation experiments

A frequency domain simulation experiment is one in which selected system parameters are oscillated sinusoidally to induce oscillations in one or more system statistics of interest. A spectral (Fourier) analysis of these induced oscillations is then performed. To perform this spectral analysis, all oscillation frequencies must be referenced to a common, independent variable - an oscillation index. In a discrete-event simulation, the global simulation clock is the most natural choice for the oscillation index. However, past efforts to reference all frequencies to the simulation clock generally yielded unsatisfactory results. The reason for these unsatisfactory results is explained in this paper and a new methodology which uses the simulation clock as the oscillation index is presented. Techniques for implementing this new methodology are demonstrated by performing a frequency domain simulation experiment for a network of queues.

Mitra, Mousumi↗

NASA NTRS1993

An optimized finite-difference scheme for wave propagation problems

Two fully-discrete finite-difference schemes for wave propagation problems are presented, a maximum-order scheme and an optimized (or spectral-like) scheme. Both combine a seven-point spatial operator and an explicit six-stage time-march method. The maximum-order operator is fifth-order in space and is sixth-order in time for a linear problem with periodic boundary conditions. The phase and amplitude errors of the schemes obtained using Fourier analysis are given and compared with a second-order and a fourth-order method. Numerical experiments are presented which demonstrate the usefulness of the schemes for a range of problems. For some problems, the optimized scheme leads to a reduction in global error compared to the maximum-order scheme with no additional computational expense.

Zingg, D. W.↗

NASA NTRS1993

Direct calculations of waves in fluid flows using a high-order compact difference scheme

The solution of the unsteady Euler equations by a sixth-order compact difference scheme combined with a fourth-order Runge-Kutta method is investigated. Closed-form expressions for the amplification factors and their corresponding dispersion correlations are obtained by Fourier analysis of the fully discretized, two-dimensional Euler equations, and the numerical dissipation, dispersion, and anisotropic effects are assessed. It is found that the CFL limit for stable calculations is about 0.8. For a CFL number equal to 0.6, the smallest wavelength which is resolved without numerical damping is about 6 to 8 grid nodes. For phase speeds corresponding to acoustic waves, the corresponding time period is resolved by about 200 to 300 time steps. Three numerical examples of waves in compressible flow are included.

Yu, Sheng-Tao↗

NASA NTRS1993

Normal incidence X-ray telescope power spectra of X-ray emission from solar active regions. I - Observations. II - Theory

Fourier analysis is applied to very high resolution image of coronal active regions obtained by the Normal Incidence X-Ray Telescope is used to find a broad isotropic power-law spectrum of the spatial distribution of soft X-ray intensities. Magnetic structures of all sizes are present down to the resolution limit of the instrument. Power spectra for the X-ray intensities of a sample of topologically different active regions are found which fall off with increasing wavenumber as 1/k-cubed. A model is presented that relates the basic features of coronal magnetic fluctuations to the subphotospheric hydrodynamic turbulence that generates them. The model is used to find a theoretical power spectrum for the X-ray intensity which falls off with increasing wavenumber as 1/k-cubed. The implications of a turbulent regime in active regions are discussed.

Gomez, Daniel O.↗

NASA NTRS1992

Position and morphology of the compact non-thermal radio source at the Galactic Center

We have determined with VLBI the position of the compact nonthermal radio source at the Galactic Center, commonly referred to as SgrA*, in the J2000.0 reference frame of extragalactic radio sources. We have also determined the size of SgrA* at 1.3, 3.6, and 13 cm wavelengths and found that the apparent size of the source increases proportionally to the observing wavelength squared, as expected from source size broadening by interstellar scattering and as reported previously by other authors. We have also established an upper limit of about 8 mJy at 3.6 cm wavelength for any ultracompact component. The actual size of the source is less than 15 AU. Fourier analysis of our very sensitive 3.6 cm observations of this source shows no significant variations of correlated flux density on time scales from 12 to 700 s.

Marcaide, J. M.↗

NASA NTRS1952

Dynamic Response of Turbine-blade Temperature to Exhaust-gas Temperature for Gas-turbine Engines

The frequency of blade temperature to exhaust gas temperature is presented for two locations in the blade and at several operating conditions. The frequency response was determined by Fourier analysis of transient data. Two analytical methods are presented, and results are compared with experimental data. Dynamic response of turbine-blade temperature to exhaust-gas temperature exhibited the form of an approximate first-order lag. The results are used to predict blade temperature for a typical controlled and uncontrolled gas-turbine engine.

HEAT TRANSFER THEORY AND EXPERIMENT↗

NASA NTRS1958

On the statistical theory of turbulence

A study is made of the spectrum of isotropic turbulence with the aid of the customary method of Fourier analysis. The spectrum of the turbulent motion is derived to the smallest wave lengths, that is, into the laminar region, and correlation functions and pressure fluctuations are calculated. A comparison with experimental results is included. Finally, an attempt is made to derive the numerical value of a constant characteristic of the energy dissipation in isotropic turbulence.

Heisenberg, W↗