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Schubert, G.

Publications and source records attributed to Schubert, G..

At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

Infinite Prandtl number thermal convection in a spherical shell

A Galerkin technique is used to calculate the steady-state axisymmetric nonlinear convective motions in an infinite-Prandtl-number Boussinesq fluid in a relatively thick spherical shell heated from below. A reasonably complete study of the properties of the even and general axisymmetric steady states is carried out for a range of moderately supercritical Rayleigh numbers. In addition, stability analyses are conducted to determine which form of axisymmetric steady convection is the preferred one and whether the axisymmetric steady flows are unstable to azimuthal perturbations.

Zebib, A.↗
NASA NTRS1980

Thermal convection of an internally heated infinite Prandtl number fluid in a spherical shell

A Galerkin technique is used to study the finite-amplitude axisymmetric steady convective motions of an infinite Prandtl number Boussinesq fluid in a spherical shell. Two types of heating are considered: in one case, convection is driven both by internal heat sources in the fluid and by an externally imposed temperature drop across the shell boundaries; in the other case, only internal heat sources drive convection and the lower boundary of the shell is adiabatic. Two distinct classes of axisymmetric steady states are found to be possible: states characterized by temperature and radial velocity fields that are symmetric about an equatorial plane; and a class of solutions that does not possess any symmetry properties about the equatorial plane.

Schubert, G.↗
NASA NTRS1979

Core cooling by subsolidus mantle convection

Although vigorous mantle convection early in the thermal history of the earth is shown to be capable of removing several times the latent heat content of the core, a thermal evolution model of the earth in which the core does not solidify can be constructed. The large amount of energy removed from the model earth's core by mantle convection is supplied by the internal energy of the core which is assumed to cool from an initial high temperature given by the silicate melting temperature at the core-mantle boundary. For the smaller terrestrial planets, the iron and silicate melting temperatures at the core-mantle boundaries are more comparable than for the earth; the models incorporate temperature-dependent mantle viscosity and radiogenic heat sources in the mantle. The earth models are constrained by the present surface heat flux and mantle viscosity and internal heat sources produce only about 55% of the earth model's present surface heat flow.

Schubert, G.↗
NASA NTRS1979

Acoustic-gravity waves in the thermosphere of Venus

The paper studies the properties of acoustic-gravity waves in the upper atmosphere of Venus by means of a two fluid model which includes the effects of wave-induced diffusion in a diffusively separated atmosphere. It is maintained that in conjunction with neutral mass spectrometer data from the Pioneer Venus orbiter, the theory should provide information on the distribution of wave sources in the Venus upper atmosphere. In addition observed wave structure in species density measurements should generally have periods less than or equal to 30-35 min, small N2, CO, and O amplitudes, and highly variable phase shifts relative to CO2. Finally, it is noted that large-density oscillations in stratospheric cloud layer constituents are also possible and may be detectable by the Pioneer Venus large probe neutral mass spectrometer.

Del Genio, A. D.↗
NASA NTRS1979

Gravity wave propagation in a diffusively separated atmosphere with height-dependent collision frequencies

Numerical calculations of gravity wave propagation through a two-component thermosphere with vertically-varying inter-species collision frequencies are performed using a direct integration method. Reflection of upgoing gravity wave energy into downgoing gravity waves appears to be small though nonnegligible at typical thermospheric periods and wavelengths. Coupling into diffusion waves is completely insignificant in most cases and may be determined in part by the relative abundance of the minor species. Temperature perturbation differences between species can be greater than 10% above 300 km altitude even though coupling into diffusion waves is small. Diffusive dissipation of gravity wave energy can be significant in the lower thermosphere and may be comparable to dissipation by viscosity and heat conduction below about 225 km altitude. Heating by diffusive dissipation may also be comparable to direct heating by solar radiation in the lower thermosphere. As a result of dissipative filtering of long-period and short-wavelength waves and the sensitivity of He-N2 density perturbation phase differences to diffusion, the AE-C satellite wave observations can only be fit by internal gravity waves with periods no greater than about 25 min and horizontal wavelengths no less than about 200 km.

Del Genio, A. D.↗
NASA NTRS1979

Inhibition of solar wind impingement on Mercury by planetary induction currents

Analytic methods are developed for taking into account finite planetary conductivity in modeling departures from equilibrium of a magnetospheric boundary caused by solar wind stagnation pressure variations. Using the lowest suggested value of the planetary dipole moment (2.4 x 10 to the 22nd G cu cm), it is estimated that a minimum pressure of about 38 P sub 0 (where P sub 0 is the external stagnation pressure in the steady state) is required to force the standoff distance down to the subsolar surface of Mercury if the pressure change persists for at least 1 day. This value is 4.3 times that which would be predicted if Mercury had no core, and it is larger than the maximum pressure predicted at Mercury's orbit (about 25 P sub 0) on the basis of hourly averaged solar wind statistics at 1 AU.

Hood, L. L.↗
NASA NTRS1979

Subsolidus convective cooling histories of terrestrial planets

The subsolidus convective cooling histories of terrestrial planets evolving from hot initial states are investigated quantitatively. A simple analytic model simulating average heat flux from a vigorously convecting mantle and incorporating a mantle viscosity proportional to mantle temperature and a lithosphere which thickens as the planet cools is employed. Heat flux from the convecting mantle is calculated on the basis of a power law relation between Nusselt number and Rayleigh number. The temperature distribution in the lithosphere is assumed to be linear throughout the cooling history of the planet. Cooling histories have been determined for the earth, Mars, Mercury and the moon and the mantle temperature decreases, mantle viscosity increases and decreases of heat flux to the surface and to the base of the lithosphere and of Nusselt and Rayleigh numbers are illustrated for each planet. It is found that primordial heat can contribute substantially to the present surface heat flux of a planet.

Schubert, G.↗
NASA NTRS1979

Characteristics of acoustic-gravity waves in a diffusively separated atmosphere

The effects of wave-induced diffusion on the characteristics of plane acoustic gravity waves in the earth's thermosphere are investigated by means of a two fluid model atmosphere in diffusive equilibrium. At wave periods greater than the shortest characteristic diffusion time for the minor gas, diffusion induced by the wave is considered to act to eliminate amplitude and phase differences between the wave-induced density fluctuations of individual gases and restore the perturbed fluid to diffusive equilibrium. Vertical diffusion is most important at large scale sizes, but horizontal diffusion dominates for horizontal wavelengths of less than several hundred kilometers. As a result of wave-induced diffusion, AE-C satellite measurements of neutral density fluctuations of thermospheric constituents are only compatible with relatively small scale internal gravity waves. Velocity and temperature differences for acoustic-gravity waves are greatest at periods near the mean collision time and diffusion time and lead to the dissipation of wave energy. The predictions of the theory are consistent with a high latitude, low altitude source for the medium scale waves and a more localized random source for the waves observed by AE-C.

Del Genio, A. D.↗
NASA NTRS1979

Studies of oceanic tectonics based on GEOS-3 satellite altimetry

Using statistical analysis, geoidal admittance (the relationship between the ocean geoid and seafloor topography) obtained from GEOS-3 altimetry was compared to various model admittances. Analysis of several altimetry tracks in the Pacific Ocean demonstrated a low coherence between altimetry and seafloor topography except where the track crosses active or recent tectonic features. However, global statistical studies using the much larger data base of all available gravimetry showed a positive correlation of oceanic gravity with topography. The oceanic lithosphere was modeled by simultaneously inverting surface wave dispersion, topography, and gravity data. Efforts to incorporate geoid data into the inversion showed that the base of the subchannel can be better resolved with geoid rather than gravity data. Thermomechanical models of seafloor spreading taking into account differing plate velocities, heat source distributions, and rock rheologies were discussed.

Poehls, K. A.↗
NASA NTRS1979

Subsolidus convection in the mantles of terrestrial planets

The role of heat transport by solid state mantle convection in determining the past and present thermal states of terrestrial planets is examined. Mantle convection models have relied on two-dimensional and axisymmetric three-dimensional numerical calculations incorporating the temperature and pressure dependence of mantle rheology and its non-Newtonian nature. Convection at high Rayleigh numbers has been investigated through theoretical scaling arguments and boundary layer theories; nevertheless, computational limits prevent modeling of the fully three-dimensional, time-dependent, very high Rayleigh number convection which probably prevails in terrestrial planets. Radar measurements of Venus, as well as Voyager exploration of the Galilean satellites, should also provide information on mantle convection.

Schubert, G.↗
NASA NTRS1978

Mantle flow pressure and the angle of subduction - Non-Newtonian corner flows

Corner flows of Newtonian and non-Newtonian fluids are used to model the flow in a subduction zone which is viscously driven by the motions of the converging plates and the descending slab. The pressures induced by the flow tend to lift the slab up beneath the overriding plate thereby offsetting the tendency of gravity to align the slab with the vertical. The low angles of subduction observed in Peru and Central Chile may be the result of strong dynamic pressures forcing the slab up against the overriding plate. Viscous coupling between the overriding plate and the downgoing slab is essential if the nonvertical dips of slabs are a consequence of the balance between gravitational and pressure torques. For a Newtonian mantle, shear stresses and pressures on the top of the slab are comparable. If the mantle is non-Newtonian, however, the pressures greatly exceed the shear stresses, for most acute dip angles. Thus frictional forces on the top and bottom surfaces of slabs are less important in resisting slab descent into a non-Newtonian mantle than they are in resisting penetration into a Newtonian mantle.

Tovish, A.↗
NASA NTRS1978

Effects of wave-induced diffusion on thermospheric acoustic-gravity waves

When wave-induced diffusion is included in the equations governing acoustic-gravity wave propagation in an atmosphere in diffusive equilibrium, it is found that phase and amplitude relationships between the density fluctuations of individual atmospheric constituents agree with AE-C satellite observations of wavelike structure only over a narrow range of wave periods. For a 400-km horizotal wavelength, the observations are consistent with internal gravity waves of periods 11.5-22 minutes propagating at phase speeds 300-600 m/sec.

Del Genio, A. D.↗
NASA NTRS1978

The distortion of the moon due to convection

Numerical calculations of the dynamical ellipticity of the moon due to finite-amplitude solid-state convection indicate that convection could be the cause of the nonhydrostatic gravitational figure, but only if the lunar lithosphere is capable of resisting global scale deformation. Thus lithospheric inhomogeneities and surface loads could also contribute substantially to the disequilibrium of the gravity figure. The calculations also show that it is unlikely that the geometrical distortion is due to convection.

Cassen, P.↗
NASA NTRS1978

Shear flow beneath oceanic plates - Local nonsimilarity boundary layers for olivine rheology

The principle of local similarity, which has been used to model the two-dimensional boundary layers in the oceanic upper mantle, permits calculation of the temperature, velocity, and stress fields with essentially analytic techniques. Finite difference numerical methods are hard pressed to resolve the detail required by the large variation of viscosity between the lithosphere and the asthenosphere. In this paper the local similarity approximation has been justified by quantitatively evaluating the effect of nonsimilarity due to viscous heating, nonlinear temperature- and pressure-dependent rheology, buoyancy, adiabatic cooling, etc. Nonsimilar effects produce only small modifications of the locally similar boundary layers; important geophysical observables such as surface heat flux and ocean floor topography are given to better than 10 percent by the locally similar solution. A posteriori evaluations of the terms neglected in the boundary layer simplification of the complete equations have been conducted on the locally similar temperature and velocity profiles close to the spreading ridge. The boundary layer models are valid to depths of 100 km at 3 m.y. and 10 km at 0.3 m.y.

Yuen, D. A.↗
NASA NTRS1978

A magnetohydrodynamic theory for the lunar response to time variations in a spatially uniform ambient magnetic field

An analytic theory based on principles of magnetohydrodynamics is derived for interpreting the lunar magnetic response to magnetic field fluctuations in the lobes of the geomagnetic tail. Only the case of magnetic perturbations parallel to a spatially uniform ambient magnetic field is treated. The theoretical frequency-dependent MHD transfer function depends on both the lunar electrical conductivity profile and the Alfven speed of the tail lobe plasma. For circular frequencies much less than the Alfven speed/lunar radius, the MHD transfer function reduces to the vacuum transfer function, while at higher frequencies the finite propagation speed of magnetic disturbances affects the response. These characteristics of the MHD transfer function are in qualitative agreement with observation. A carefully selected set of magnetic field transient events could be used together with this theory to infer lunar electrical conductivity profiles and the tail lobe plasma density (via its dependence on the Alfven speed).

Hood, L. L.↗
NASA NTRS1977

Crater evolutionary tracks

The technique proposed in the present paper for studying planetary surface processes is based on the measurement of crater rim height, h, depth, d, and diameter, D. The h/d and d/D ratios provide a quantitative description of crater morphology as well as a quantitative method for assessing the relative importance of competing crater modification processes (since h, d, and D change as a crater is degraded by surface processes, and h/d and d/D change with time). Different classes of processes produce distinctive evolutionary tracks on an h/d versus d/D diagram. Tracks for three general classes of crater modification (processes adding material to the crater; processes redistributing the material within the crater vicinity; and processes removing the material from the crater vicinity) are calculated, and h/d and d/D ratios for craters on the earth, moon, and Mars are compared.

Schubert, G.↗
NASA NTRS1977

Dynamics, winds, circulation and turbulence in the atmosphere of Venus

With the possible exception of the lowest one or two scale heights, the dominant mode of circulation of Venus' atmosphere is a rapid, zonal, retrograde motion. Global albedo variations in the ultraviolet may reflect planetary scale waves propagating relative to the zonal winds. Other special phenomena such as cellular convection in the subsolar region and internal gravity waves generated in the interaction of the zonal circulation with the subsolar disturbance may also be revealed in ultraviolet imagery of the atmosphere. We discuss the contributions of experiments on the Orbiter and Entry Probes of Pioneer Venus toward unravelling the mystery of the planet's global circulation and the role played by waves, instabilities and convection therein

Schubert, G.↗