Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “spherical harmonics”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 433 records · Page 24

Saturn's magnetosphere and its interaction with the solar wind

The paper deals with the Pioneer 11 vector helium magnetometer observations of Saturn's planetary magnetic field, magnetosphere, magnetopause, and bow shock. Models based on spherical harmonic analyses of measurements inside 8 Saturn radii show that the planetary field has a high degree of symmetry about the rotation axis. The vector dipole moment has a tilt angle of less than 1 deg and is offset along the polar axis by 0.04 plus or minus 0.02 Saturn radius. Equatorial offsets derived from the models show pronounced variability and could be consistent with a very small offset. Large impulsive field compressions are observed in the magnetosheath near noon. Multiple crossings of the bow shock are observed, and the absence of significant changes in field direction indicates that it is quasi-perpendicular.

Smith, E. J.↗

Material properties for mantle convection consistent with observed surface fields

An attempt is made to derive constraints on mantle convection from observed surface fields: plate velocities, gravity, topography and heat flow. The spherical harmonic spectra of the fields are expressed in terms of a spectral magnitude and slope, and requirements for the minimal representation of the equations for mantle convection are discussed. The effects of the boundary layer represented by the surface fields on convection at the mantle surface and at deeper levels are then examined, and a mean value of the effective mantle viscosity of approximately 10 to the 23rd g/cm per sec is obtained, together with values of 10 to the 8th and 10 to the 7th for the Rayleigh numbers of whole mantle and upper mantle convection, respectively. Consideration is then given to the compositional, thermal and rheological aspects of mantle convection, and it is pointed out that constraints on the depth and other properties of convection will require more detailed modeling using the relationships between the harmonic coefficients of the surface fields.

Kaula, W. M.↗

Numerical simulation of stratospheric sudden warmings with a primitive equation spectral model

A 26-level primitive equation spherical harmonic spectral model allowing for wave-wave and wave-zonal flow interactions is presented for the study of stratospheric sudden warmings. The warmings are simulated by the forcing of a single planetary wave at the tropopause. Four numerical experiments were performed. Nonlinear wave-wave interactions appear to play an important role in the evolution of the flow and temperature fields in the middle to upper stratosphere. In the case involving both wave-wave and wave-zonal flow interactions, this was manifested by the split in the initial polar vortex into a quasi-wave number 2 pattern. In the cases at 60 deg N, easterlies develop first in the upper mesosphere and descend gradually. About the same time or a little later, easterlies also develop in the mid-stratosphere. The linear cases exhibit warmings which are more shallow and more intense at 30 km than the nonlinear cases.

Lordi, N. J.↗

Large-angular-scale anisotropy in the cosmic background radiation

Results of an extended series of airborne measurements of large-angular-scale anisotropy in the 3-K cosmic background radiation are reported. A dual-antenna microwave radiometer operating at 33 GHz flown aboard a U-2 aircraft to 20-km altitude on 11 flights between December 1976 and May 1978 measured differential intensity between pairs of directions distributed over most of the Northern Hemisphere. Measurements show clear evidence of anisotropy that is readily interpreted as due to the solar motion relative to the sources of the radiation. The anisotropy is well fitted by a first order spherical harmonic of amplitude 3.6 + or - 0.5 mK, corresponding to a velocity of 360 + or - 50 km/s toward the direction 11.2 + or - 0.5 hours of right ascension and 19 deg + or - 8 deg declination.

Gorenstein, M. V.↗

Polarization of the cosmic background radiation

The technique and results of a measurement of the linear polarization of the cosmic background radiation at a wavelength of 9 mm are discussed. Data taken between 1978 May and 1980 February from both the Northern Hemisphere (Berkeley latitude 38 deg N) and the Southern Hemisphere (Lima latitude 12 deg S) over 11 declinations from -37 to +63 deg show the radiation to be essentially unpolarized over all areas surveyed. Fitting all data gives the 95% confidence level limit on a linearly polarized component of 0.3 mK for spherical harmonics through third order. A fit of all data to the anisotropic axisymmetric model of Rees (1968) yields a 95% confidence level limit of 0.15 mK for the magnitude of the polarized component. Constraints on various cosmological models are discussed in light of these limits.

Lubin, P. M.↗

A method of defining topographic datums of planetary bodies

Since no known planetary bodies in the solar system other than the earth have large bodies of water, a topographical datum other than a sea-level reference must be used as a zero-elevation reference surface. The present paper discusses the definition of the topographic datums of Mars and the moon in terms of a gravity-level surface. Planetary gravitational field potentials were represented by a spherical harmonic expansion in terms of gravity coefficients measured by planetary orbiters, and the topographical datum was taken as the sum of an arbitrarily selected radius of the mean sphere and the radial deviation from the mean sphere. The datum defined for Mars on the basis of Mariner 9 data can be approximated as a triaxial ellipsoid with semimajor axes of 3394.6 and 3393.3 km and semiminor axis of 3376.3 km, based on a mean radius of 3382.9 km. For the moon, Lunar Orbiter IV tracking and ranging data give a datum approximated by a triaxial figure with semimajor axes 1738.30 and 1738.18 km and semiminor axis 1737.65 km, based on a mean radius of 1738 km. A topographic datum of Venus is also planned based on Pioneer-Venus gravity data.

Wu, S. S. C.↗

Venus gravity fields

Results of Pioneer Venus Orbiter observations concerning the gravity field of Venus are presented. The gravitational data was obtained from reductions of Doppler radio tracking data for the Orbiter, which is in a highly eccentric orbit with periapsis altitude varying from 145 to 180 km and nearly fixed periapsis latitude of 15 deg N. The global gravity field was obtained through the simultaneous estimation of the orbit state parameters and gravity coefficients from long-period variations in orbital element rates. The global field has been described with sixth degree and order spherical harmonic coefficients, which are capable of resolving the three major topographical features on Venus. Local anomalies have been mapped using line-of-sight accelerations derived from the Doppler residuals between 40 deg N and 10 deg S latitude at approximately 300 km spatial resolution. Gravitational data is observed to correspond to topographical data obtained by radar altimeter, with most of the gravitational anomalies about 20-30 milligals. Simulations evaluating the isostatic states of two topographic features indicate that at least partial isostasy prevails, with the possibility of complete compensation.

Sjogren, W. L.↗

Geopotential resonance in a Landsat orbit

A Landsat 1 resonance analysis was conducted on the basis of almost continuous range-rate observations provided by the S-Band station at Greenbelt, MD for a twenty-four day period in September 1976. Constraints on the resonance effects of Landsat 1, determined directly from radar tracking data could be summarized in a number of equations for fully normalized geopotential coefficients. The coefficient values for the dominant resonance terms can be directly determined through the estimation scheme, as the resonance constraints are implicit in the spherical harmonic representation chosen for the geopotential. The degree of the constraint equation series may be arbitrarily increased with analytical expressions for the along-track orbital component in terms of Keplerian elements.

Dunn, P.↗

Geoid anomalies in the vicinity of subduction zones

In the considered investigation, attention is given to the line source model, a surface source model, an application of the model, and a model of the thermal lithosphere associated with marginal basins. It is found that undulations in the altimetrically observed geoid of the southwest Pacific are strongly controlled by positive density anomalies in the subducting slabs of the region and the effects of elevation of the geotherm in behind arc lithosphere (corresponding to young marginal basins). Finer details of slab geometry do not obviously manifest themselves in the observed geoid. Such gravitational effects are quite attenuated at sea level and are apparently mixed with crustal effects, oceanographic noise, etc. It appears that slabs in global composite may contribute substantially to intermediate and long wavelength portions (down to spherical harmonic degree 3 or 4) of the earth's gravity field.

Mcadoo, D. C.↗

N-stream approximations to radiative transfer

Schuster's two-stream approximation (1905) is first derived from Chandrasekhar's radiative transfer equation (1950), and then extended to an arbitrary number of streams. The resulting technique for solving the transfer function similar to the discrete ordinate and spherical harmonic methods, is useful for modeling atmospheres with complicated phase functions and moderate optical depths. The resulting n coupled linear differential equations are simple and consume less computer time than other approximations, yet have the same required accuracy. The approximation is also flexible with respect to the choice of patch functions, and no approximations are made on the form of the phase function, other than its expansion into Legendre polynomials. A four-stream approximation is evaluated for a Henyey-Greenstein phase function with an asymmetry factor equal to 0.5.

Acquista, C.↗

Early results from Magsat

Papers presented at the May 27, 1981 meeting of the American Geophysical Union concerning early results from the Magsat satellite program, which was designed to study the near-earth magnetic fields originating in the core and lithosphere, are discussed. The satellite was launched on October 30, 1979 into a sun-synchronous (twilight) orbit, and re-entered the atmosphere on June 11, 1980. Instruments carried included a cesium vapor magnetometer to measure field magnitudes, a fluxgate magnetometer to measure field components and an optical system to measure fluxgate magnetometer orientation. Early results concerned spherical harmonic models, fields due to ionospheric and magnetospheric currents, the identification and interpretation of fields from lithospheric sources. The preliminary results confirm the possibility of separating the measured field into core, crustal and external components, and represent significant developments in analytical techniques in main-field modelling and the physics of the field sources.

Langel, R. A.↗

Voyager 1 assessment of Jupiter's planetary magnetic field

An estimate of Jupiter's planetary magnetic field is obtained from the Voyager 1 observations of the Jovian magnetosphere. An explicit model for the magnetodisc current system is combined with a spherical harmonic model of the planetary field with both sets of parameters determined simultaneously using a nonlinear generalized inverse methodology. The resulting model fits the observations extremely well throughout the analysis interval (r 20 Jovian radii). The Jovian internal field model obtained from the Voyager 1 data is very similar to the octopole Pioneer 11 models. The best fitting magnetodisc lies in the centrifugal equator, 2/3 of the way between the rotational and magnetic equators, as appropriate for centrifugal loading of the magnetosphere by a cold plasma.

Connerney, J. E. P.↗

Preliminary models of the core field

Using the CHROFIN tapes containing MAGSAT data for the month of December, two spherical harmonic models were prepared. One of these models was specially designed to study the Bangui anomaly region. For this region an attempt was made to downward continue the data and to compare it with the existing ground level map.

Lemouel, J. L.↗

Resonances, radiation pressure and optical scattering phenomena of drops and bubbles

Acoustic levitation and the response of fluid spheres to spherical harmonic projections of the radiation pressure are described. Simplified discussions of the projections are given. A relationship between the tangential radiation stress and the Konstantinov effect is introduced and fundamental streaming patterns for drops are predicted. Experiments on the forced shape oscillation of drops are described and photographs of drop fission are displayed. Photographs of critical angle and glory scattering by bubbles and rainbow scattering by drops are displayed.

Marston, P. L.↗

Investigation of the effects of external current systems on the MAGSAT data utilizing grid cell modeling techniques

Efforts in support of the development of a model of the magnetic fields due to ionospheric and magnetospheric electrical currents are discussed. Specifically, progress made in reading MAGSAT tapes and plotting the deviation of the measured magnetic field components with respect to a spherical harmonic model of the main geomagnetic field is reported. Initial tests of the modeling procedure developed to compute the ionosphere/magnetosphere-induced fields at satellite orbit are also described. The modeling technique utilizes a liner current element representation of the large scale current system.

Klumpar, D. M.↗

The role of zonally asymmetric heating in the vertical and temporal structure of the global scale flow fields during FGGE SOP-1

By examining the vertical structure of the low order spherical harmonics of the divergence and vorticity fields, the relative contribution of tropical and monsoonal circulations upon the global wind fields was estimated. This indicates that the overall flow over North America and the Pacific between January and February is quite distinct both in the lower and upper troposphere. In these longitudes there is a stronger tropical overturning and subtropical jet stream in January than February. The divergent flow reversed between 850 and 200 mb. Poleward rotational flow at upper levels is associated with an equatorward rotational flow at low levels. This suggests that the monsoon and other tropical circulations project more amplitude upon low order (global scale) representations of the flow than do the typical midlatitude circulations and that their structures show conspicuous changes on a time scale of a week or less.

Paegle, J.↗

A stochastic-dynamic model for global atmospheric mass-field statistics

Global atmospheric mass field error correlations based on satellite observations and on numerical forecasts show strong and systematic latitude dependence. A model for the latitude dependent spatial correlation structure of mass field forecast errors is derived from dynamical considerations. Three methods of solution were tested. In the first method, the equation was solved by expansion in spherical harmonics, and the correlation function was computed analytically using the expansion coefficients. In the second method, the finite difference equivalent of the equation was solved using a fast poisson solver. The correlation function was computed using stratified sampling of the individual realizations. In the third method, a higher order equation was derived, and solved directly in finite differences by two successive applications of the fast poisson solver. The three methods were compared for accuracy and efficiency, and the third method was chosen as clearly superior.

Ghil, M.↗