Engineering topics
Publications and source records attributed to Schubert, G..
Simulated radio tracking data from one flyby of Europa, two flybys of Ganymede, and two flybys of Callisto by the Galileo Orbiter yield estimates of the standard errors in the gravitational coefficient J*** of 44, 8.5, and 12 (in units of 10***) for Europa, Ganymede, and Callisto, respectively; errors in C***(in units of 10***) are 12, 1.7 and 2.1.
Numerical calculations have been carried out of steady, symmetric, 3D modes of convection in internally heated, infinite Prandtl number, Boussinesq fluids at a Rayleigh number of 1.4 x 10 exp 4 in a spherical shell with inner/outer radius of 0.55 and in a 3 x 3 x 1 rectangular box. Multiple patterns of convection occur in both geometries. In the Cartesian geometry, the patterns are dominated by cylindrical cold downflows and a broad hot upwelling. In the spherical geometry the patterns consist of cylindrical cold downwellings centered either at the vertices of a tetrahedron or the centers of the faces of a cube. The cold downflow cylinders are immersed in a background of upwelling within which there are cylindrical hot concentrations (plumes) and hot halos around the downflows. The forced hot upflow return plumes of internally heated spherical convection are fundamentally different from the buoyancy-driven plumes of heated from below convection.
The wave-driven fluctuations in the O2(0-1) atmospheric nightglow is modeled and the parameter (eta) is calculated using a model that accounts for either three-body recombination of atomic oxygen atoms alone to form the O2(b exp 1 Sigma(g)(+)) state directly, or by the further inclusion of the process that allows the formation of the O2(c exp 1 Sigma(u)(-)) intermediate state. The calculations are performed for a latitude of 18 deg N and for the months of March and June. The general results, which display how (eta) varies with wave period, horizontal wavelength, season, and chemical scheme, show that for given values of wave period and horizontal wavelength it is not possible to discriminate between seasonal effects and between the effects of different chemical schemes at evanescent and short gravity wave periods. It is shown that, when quenching by atomic oxygen is ignored, the resulting values of (eta) calculated with the complete chemistry are similar to those obtained from the three-body recombination scheme alone.
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The thermal evolution of Mars is governed by subsolidus mantle convection beneath a thick lithosphere. Models of the interior evolution are developed by parameterizing mantle convective heat transport in terms of mantle viscosity, the superadiabatic temperature rise across the mantle and mantle heat production. Geological, geophysical, and geochemical observations of the composition and structure of the interior and of the timing of major events in Martian evolution, such as global differentiation, atmospheric outgassing and the formation of the hemispherical dichotomy and Tharsis, are used to constrain the model computations. Isotope systematics of SNC meteorites suggest core formation essentially contemporaneously with the completion of accretion. Other aspects of this investigation are discussed.
Earth, Moon, Mars, and Venus all have centers of mass (C.M.) that are displaced from their centers of figure (C.F.) by amounts which range from 340 meters (Venus) to 2.5 km (Mars). These offsets have all been calculated from the first degree terms in spherical harmonic expansions of topography. We describe an alternate method for calculating C.M. - C.F. offsets directly from a global topographic data set and apply it to Venus. Using Magellan altimetry, we find that Venus' C.F. is displaced approximately 280 meters from its C.M. in the direction of Western Aphrodite Terra (4.4 deg S, 135.8 deg E). We investigate several simple models for this offset and find that it is most consistent with thickened crust in Ovda and Thetis Regiones (which constitute most of W. Aphrodite). The location of the C.F. offset also places constraints on the degree of crustal thickening in Western Ishtar Terra and/or this highland's mode of origin. We favor a model in which offset due to thick crust in Western Ishtar Terra is balanced by an opposing offset due to cold, downwelling mantle material beneath the highland.
A model which incorporates extended OH-layer emission and gravity-wave dynamics with eddy diffusivities is set forth to analyze seasonal and latitudinal variations in the OH nightglow. The 2D analysis is aimed at determining the nature of the relationship between the oscillation in intensity about a mean intensity and the oscillation in temperature of the emission region about a mean temperature. Competing eddy diffusivities modify the local values and altitudes of maximum wave amplitude, so long-period characterization of the relationship is imprecise. Seasonal trends in the relationship are noted for periods of several hrs or less that are primarily related to seasonal changes in the mesopause undisturbed temperature. Latitudinal trends are shown to be less pronounced, and trends that exist at intermediate periods are difficult to isolate due to interference effects.
Differentiation of a planet can have profound consequences for its structure and thermal evolution, including core formation and crystal growth. Recent theories for the origin and evolution of the terrestrial planets and the Moon have all these bodies forming hot and cooling thereafter. Early core formation, and in the cases of Earth and Moon, a deep magma ocean possibly encompassing the entire mantle are characteristic features of these models. Secular cooling of Mars from a hot origin and cooling of Moon from a hot initial state with a deep magma ocean have been criticized on the basis of their tectonic implications. The cases of Mars and the Moon are discussed.
An overview of numerical methods describing the structure and dynamics of the mantle is presented with attention given to novel 3D modeling techniques. The paper reviews 3D spherical and Cartesian models for constant viscosity emphasizing the assumptions regarding style of convection, time dependence, and implications for the mantle. Similarly treated are 3D Cartesian models with temperature-dependent viscosities, and briefly examined are models that are based on compressibility, nonlinear viscosity, or plates. Extensive illustrations are presented detailing: (1) temperature variations from models of 3D thermal convection in spherical shells; (2) thermal anomalies in equatorial cross sections; and (3) temperature variations in a spherical shell heated from within. The discussion relates the numerical results of the models with real mantle-convection events, and the simulations are shown to yield increasingly realistic representations of material behavior.
Coronae on Venus are large, generally circular surface features that have distinctive tectonic, volcanic, and topographic expressions. They range in diameter from less than 200 km to at least 1000 km. Data from the Magellan spacecraft have now allowed complete global mapping of the spatial distribution of coronae on the planet. Unlike impact craters, which show a random (i.e., Poisson) spatial distribution, the distribution of coronae appears to be nonrandom. We investigate the distribution here in detail, and explore its implications in terms of mantle convection and surface modification processes.
A two-dimensional, fully nonlinear, nonhydrostatic, gravity wave model is used to study the evolution of gravity waves generated near the surface of Venus. The model extends from near the surface to well above the cloud layers. Waves are forced by applying a vertical wind at the bottom boundary. The boundary vertical wind is determined by the product of the horizontal wind and the gradient of the surface height. When wave amplitudes are small, the near-surface horizontal wind is the zonally averaged basic-state zonal wind, and the length scales of the forcing that results are characteristic of the surface height variation. When the forcing becomes larger and wave amplitudes affect the near-surface horizontal wind field, the forcing spectrum becomes more complicated, and a spectrum of waves is generated that is not a direct reflection of the spectrum of the surface height variation. Model spatial resolution required depends on the amplitude of forcing; for very nonlinear cases considered, vertical resolution was 250 m, and horizontal resolution was slightly greater than 1 km. For smaller forcing amplitudes, spatial resolution was much coarser, being 1 km in the vertical and about 10 km in the horizontal. Background static stability and mean wind are typical of those observed in the Venus atmosphere.
The thermal evolution of Mars is governed by subsolidus mantle convection beneath a thick lithosphere. Models of the interior evolution are developed by parameterizing mantle convective heat transport in terms of mantle viscosity, the superadiabatic temperature rise across the mantle, and mantle heat production. Geological, geophysical, and geochemical observations of the composition and structure of the interior and of the timing of major events in Martian evolution are used to constrain the model computations. Such evolutionary events include global differentiation, atmospheric outgassing, and the formation of the hemispherical dichotomy and Tharsis. Numerical calculations of fully three-dimensional, spherical convection in a shell the size of the Martian mantle are performed to explore plausible patterns of Martian mantel convection and to relate convective features, such as plumes, to surface features, such as Tharsis. The results from the model calculations are presented.
A thermal evolution model for the cooling of a terrestrial planet, a prescribed fraction of which is melted during a giant impact, is described. Two model geometries are considered, one having a laterally inhomogeneous distribution of melt and solid through a mega-crater geometry and the other having a global magma ocean. It is found that almost the whole planet may melt if the impact originally melted half of the planet and if the first melt temperature was double a typical planet melting temperature. For reasonable choices of parameter values it is determined that thermal equilibration of the earth occurs on a time-scale of 1 to ten million years.
The paper theoretically examines the modification of the characteristics of OH nightglow from an extended emission region by eddy momentum and eddy thermal diffusivities. The reactions that account for OH decay are presented with the additional modifications demonstrating the importance of the upper limit of vertical integration of the extended source. When the vertical wavelengths are smaller than the thickness of the main OH emission region, oscillations cause the effects, particularly at long wavelengths. Eddy diffusion increases the vertical wavelength, and therefore the interference effects related to a finite range of vertical integration can be reduced by accounting for eddy diffusion. It is determined that the effects of eddy momentum and thermal diffusivities are important elements of gravity wave dynamics and should be considered when calculating OH emission perturbations and related variables.
Internal heat flow from radioactive decay in Triton's interior along with absorbed thermal energy from Neptune total 5 to 20 percent of the isolation absorbed by Triton, thus comprising a significant fraction of Triton's surface energy balance. These additional energy inputs can raise Triton's surface temperature between about 0.5 and 1.5 K above that possible with absorbed sunlight alone, resulting in an increase of about a factor of about 1.5 to 2.5 in Triton's basal atmospheric pressure. If Triton's internal heat flow is concentrated in some areas, as is likely, local effects such as enhanced sublimation with subsequent modification of albedo could be quite large. Furthermore, indications of recent global albedo change on Triton suggest that Triton's surface temperature and pressure may not now be in steady state, further suggesting that atmospheric pressure on Triton was as much as ten times higher in the recent past.
The manner of the mantle convection in planets with rigid lids, such as Venus and Mars, is investigated using a numerical method. The effect of the rigid upper boundary condition on mantle convection was examined by comparing the convection in planets with rigid lids with results for planets with shear stress-free upper surfaces. The results for convection in models of the mantles of Mars and Venus show that the cylindrical plume is the prominent form of upwelling as long as sufficient heat enters the mantle from the core.
It is proposed that western Ishtar Terra formed due to compression and crustal thickening above a cylindrical mantle downwelling. A model for crustal deformation due to downwelling successfully reproduces many observed characteristics of western Ishtar. Although axisymmetric downwelling occur in numerical models of constant-viscosity mantle convection, there is no evidence for their existence in earth's mantle, where downwellings are sheet-like. Either modes of downflow in Venus and earth are fundamentally different, or differences in near-surface conditions and material behavior selectively emphasize surface expressions of the different downwelling modes.
A global topography is presently calculated for two multilayer Io models in which dissipation occurs in a viscous asthenosphere and a solid mantle: (1) a 'thermal swell' model, in which topography and heat flow are positively correlated, and (2) a 'differentiated lithosphere' model, in which topography and heat flow are negatively correlated. Both the polar topography and the hypsometric distribution of elevations in the differentiated lithosphere model are better matched with observations than the thermal swell model. The shift of the equatorial basin-swell pattern indicates a recent zonal rotation of about 25 deg for Io's lithosphere.