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NASA NTRS1979

Shallow moonquakes - Depth, distribution and implications as to the present state of the lunar interior

The observed seismic amplitudes of HFT (high-frequency teleseismic) events do not vary with distance as expected for surface sources, but are consistent with sources in the upper mantle of the moon. Thus, the upper mantle of the moon is the only zone where tectonic stresses deriving from differential thermal contraction and expansion of the lunar interior are presently high enough to cause moonquakes. The distribution of shallow moonquake epicenters suggests a possible correlation with impact basins, implying a lasting tectonic influence of impact basins long after their formation. The finite depths now assigned to these shallow moonquakes necessitate further revision to the seismic structural model of the lunar interior.

Nakamura, Y.↗

NASA NTRS1979

Explicit large time-step schemes for the shallow water equations

Modifications to explicit finite difference schemes for solving the shallow water equations for meteorological applications by increasing the time step for the fast gravity waves are analyzed. Terms associated with the gravity waves in the shallow water equations are treated on a coarser grid than those associated with the slow Rossby waves, which contain much more of the available energy and must be treated with higher accuracy, enabling a several-fold increase in time step without degrading the accuracy of the solution. The method is presented in Cartesian and spherical coordinates for a rotating earth, using generalized leapfrog, frozen coefficient, and Fourier filtering finite difference schemes. Computational results verify the numerical stability of the approach.

Turkel, E.↗

NASA NTRS1979

An energy and potential enstrophy conserving scheme for the shallow water equations

A three-dimensional finite difference scheme for the solution of the shallow water momentum equations which accounts for the conservation of potential enstrophy in the flow of a homogeneous incompressible shallow atmosphere over steep topography as well as for total energy conservation is presented. The scheme is derived to be consistent with a reasonable scheme for potential vorticity advection in a long-term integration for a general flow with divergent mass flux. Numerical comparisons of the characteristics of the present potential enstrophy-conserving scheme with those of a scheme that conserves potential enstrophy only for purely horizontal nondivergent flow are presented which demonstrate the reduction of computational noise in the wind field with the enstrophy-conserving scheme and its convergence even in relatively coarse grids.

Arakawa, A.↗

NASA NTRS1980

GaAs shallow-homojunction solar cells

With the objective of demonstrating the feasibility of fabricating 2 x 2 cm efficient, shallow homojunction GaAs solar cells for space applications, this program addresses the basic problems of material preparation and device fabrication. Significant progress was made and conversion efficiencies close to 16 percent at AM0 were obtained on 2 x 2 cm cells. Measurements and computer analyses on the n(+)/p/p(+) shallow homojunction cells indicate that such cell configuration should be very resistant to 1 MeV electron irradiation.

Fan, J. C.↗

NASA NTRS1983

Reduction of rms-error in shallow faceted large space antennas

This paper examines the potential for reducing root-mean-square surface error in shallow faceted reflectors by replacing flat facets with membrane facets. Exact solutions are obtained for the small lateral deflections of equilateral triangular and rectangular membranes subject to isotropic tension and parabolic edge deflections. These solutions are used to minimize the rms-error between a facet of a shallow paraboloidal surface and its approximating membrane facet. The resulting optimum placements and edge curvatures yield membrane facets which have significantly lower rms-errors than the corresponding best-fit flat facets. The rms-error reductions are about 55 percent for equilateral triangles and 25 percent to 93 percent for rectangles, depending on aspect ratio. The results suggest that the use of membrane facets conforming to curved structural members could yield reflectors with lower rms-error, or comparable error with larger facets and, hence, fewer structural members.

Fichter, W. B.↗

NASA NTRS1983

Development of ion-implantation confined, shallow mesa stripe (Pn,Sn)Te/Pb(Te,Se) DH laser diodes

Preliminary results of a program to develop ion implantation confined, shallow mesa stripe (Pb,Sn)Te laser diodes are presented. The practicality of using a shallow mesa stripe to produce single mode laser output and to increase the single mode tuning range are demonstrated. The first results of p-type ion implantation in the lead-tin salts are also reported. It is shown that sodium and lithium both can be used to convert n-type Pb(Te,Se) to p-type. The implant and anneal procedures are described, and electrical characteristics of Li-implanted layers are presented.

Fonstad, C. G.↗

NASA NTRS1985

High stress shallow moonquakes - Evidence for an initially totally molten moon

Thermoelastic stress calculations show that if the moon was initially molten only in the outer few hundred kilometers, as in the magma ocean model of the moon, the highlands crust should be aseismic. In contrast, if the moon was initially totally molten, high stress (1 to more than about 3 kbar), shallow (0 to about 6 km deep), compressional moonquakes should be occurring in the highlands crust. Calculations of the minimum stress drops made for the 28 observed shallow moonquakes suggest that 3 of them probably have stress drops in the kbar range. Thus, these very limited seismic data are consistent with the model that the moon was initially totally molten.

Binder, A. B.↗

NASA NTRS1987

Optimization of shallow arches against instability using sensitivity derivatives

The author discusses the problem of optimization of shallow frame structures which involve a coupling of axial and bending responses. A shallow arch of a given shape and of given weight is optimized such that its limit point load is maximized. The cross-sectional area, A(x) and the moment of inertia, I(x) of the arch obey the relationship I(x) = rho A(x) sup n, n = 1,2,3 and rho is a specified constant. Analysis of the arch for its limit point calculation involves a geometric nonlinear analysis which is performed using a corotational formulation. The optimization is carried out using a second-order projected Lagrangian algorithm and the sensitivity derivatives of the critical load parameter with respect to the areas of the finite elements of the arch are calculated using implicit differentation. Results are presented for an arch of a specified rise to span ratio under two different loadings and the limitations of the approach for the intermediate rise arches are addressed.

Kamat, Manohar P.↗

NASA NTRS1985

A Lagrangian method for the shallow water equations based on a Voronoi mesh - Flows on a rotating sphere

A Lagrangian scheme using the Voronoi mesh is applied to study shallow water flow on a sphere. Discrete approximations to the shallow water equations are obtained for the surfaces of a nonrotating and a rotating sphere, and discrete differential operators are defined for the gradient and the divergence on the sphere. Dissipation is put into the model, when needed, by merging fluid points when they get too close to each other. The full numerical scheme is described and results of numerical computations on various test cases are given, including zonal flow and the Riemann problem.

Augenbaum, J. M.↗

NASA NTRS1988

Unsteady viscous calculations of supersonic flows past deep and shallow three-dimensional cavities

Computational simulations were performed for supersonic, turbulent flows over deep and shallow three-dimensional cavities. The width and the depth of these cavities were fixed at 2.5 in. and 0.5 in., respectively. Length-to-depth ratio of the deep cavity was 6 and that of the shallow cavity was 16. Freestream values of Mach number and Reynolds number were 1.50 and 2.0 x 10 to the 6th/ft., respectively, at a total temperature of 585 R. The thickness of the turbulent boundary layer at the front lip of the cavity was 0.2 in. Simulations of these oscillatory flows were generated through time-accurate solutions of Reynolds-averaged full Navier-Stokes equations using the explicit MacCormack scheme. The solutions are validated through comparisons with experimental data. The features of open and closed cavity flows and effects of the third dimension are illustrated through computational graphics.

Baysal, O.↗

NASA NTRS1990

Recurrence in truncated Boussinesq models for nonlinear waves in shallow water

The rapid spatial recurrence of weakly nonlinear and weakly dispersive progressive shallow-water waves is examined using a numerical integration technique on the discretized and truncated form of the Boussinesq equations. This study primarily examines recurrence in wave fields with Ursell number O(1) and characterizes the sensitivity of recurrence to initial spectral shape and number of allowed frequency modes. It is shown that the rapid spatial recurrence is not an inherent property of the considered Boussinesq systems for evolution distances of 10-50 wavelengths. The main result of the study is that highly truncated Boussinesq models of resonant shallow-water ocean surface gravity waves predict rapid multiple recurrence cycles, but that this is an artifact dependent on the number of allowed modes. For initial conditions consisting of essentially all energy concentrated in a single mode, damping of the recurrence cycles increases as the number of low-power background modes increases. When more than 32 modes are allowed, the recurrence behavior is relatively insensitive to the number of allowed modes.

Elgar, Steve↗

NASA NTRS1989

A shear deformable theory of laminated composite shallow shell-type panels and their response analysis. I - Free vibration and buckling

This paper deals with the substantiation of a shear deformable theory of cross-ply laminated composite shallow shells. While the developed theory preserves all the advantages of the first order transverse shear deformation theory it succeeds in eliminating some of its basic shortcomings. The theory is further employed in the analysis of the eigenvibration and static buckling problems of doubly curved shallow panels. In this context, the state space concept is used in conjunction with the Levy method, allowing one to analyze these problems in a unified manner, for a variety of boundary conditions. Numerical results are presented and some pertinent conclusions are formulated.

Librescu, L.↗

NASA NTRS1992

Wrinkle ridges on Venusian plains: Indicators of shallow crustal stress orientations at local and regional scales

The plains regions of Venus exhibit a complex array of structural features, including deformation belts of various types, wrinkle ridges, grabens, and enigmatic radar-bright linears. Probably the most pervasive of these structures are the wrinkle ridges, which appear to be morphologically identical to their counterparts on the Moon and Mars. Almost all workers agree that wrinkle ridges result from horizontal compressive stresses in the crust; they either are explained as flexural fold structures, or alternatively as scarps or folds related to reverse faults. Wrinkle ridges generally are narrow, have small amplitudes, and commonly are closely spaced as well, characteristics that imply a shallow crustal origin. If wrinkle ridges are due to horizontally directed compressive stresses in the shallow crust, as generally has been inferred, then the trends of these features provide a means to map both local and regional orientations of principal stresses in the uppermost part of the venusian crust: maximum compressive stress is normal to the ridges, minimum compressive stress is normal to the topographic surface, and thus the wrinkle ridge trends trace the orientation of the intermediate principal stress. Because there are few plains areas on Venus totally devoid of wrinkle ridges, it should be possible to establish a number of interesting relationships on a near-global scale by mapping the trends of wrinkle ridges wherever they occur. The present study is addressing three questions: (1) Do the trends of wrinkle ridges define domains that are large relative to the sizes of individual plains regions? If so, can these domains be related to large-scale topographic or geologic features? (2) Are regional trends of wrinkle ridges affected by local features such as coronae? If so, is it possible to determine the relative ages of the far-field and local stresses from detailed study of trend inheritance or superposition relationships? (3) What is the relationship between wrinkle ridges and the larger ridges that make up ridge belts?

Mcgill, George E.↗

NASA NTRS1954

A Nonlinear Theory of Bending and Buckling of Thin Elastic Shallow Spherical Shells

The problem of the finite displacement and buckling, of a shallow spherical dome is investigated both theoretically and experimentally. Experimental results seem to indicate that the classical criterion of buckling is applicable to very shallow spherical domes for which the theoretical calculation was made. A transition to energy criterion for higher domes is also indicated.

Kaplan, A↗

NASA NTRS1993

Shallow crustal discontinuities and graben and scarp formation in the Tharsis region of Mars

We recently obtained photoclinometric profiles across all simple grabens and erosional landforms (e.g., troughs, pits, wall-valley heads, and scarps that are bounded above and below by flat surfaces) that occur within Tempe Terra. These data, together with similar data that we obtained for Syria, Sinai, and Lunae Plana and the Alba Patera region, allow regional examination of shallow crust Al discontinuities between latitude 30 deg. S and 50 deg. N and longitude 50 deg. W and 112 deg. W. The profile for each simple graben was used with an appropriate structural model to estimate the depth to the base of the faulted layer. The depths of erosional wall scarps may also indicate the depths of mechanical discontinuities such as a local lithologic or cryospheric boundary. Examination of these data indicates a surprisingly consistent set of shallow crust Al discontinuities for the Tharsis region at depths of 0.4-0.6 km, 1.0-1.4 km, and 2 km; the maximum depth of the features in most study areas appears to be about 4 km. The concentration of values between 0.4 and 0.6 km in most scarp and some faulted-layer depth data is similar to the range in estimated thicknesses of individual exposed Noachian and Hesperian plains units in the Tharsis region. The regional depth data also show two modes near 1 and 2 km in some study areas and a maximum depth near 4 km in most study areas; the faulted-layer depths in excess of 4 km at Alba Patera occur near the summit of the caldera and could be attributed to volcanic loading. Our detailed examination of these depth data includes the following observations: (1) The mode at 1.0-1.4 km depth transcends age and geologic setting in this broad study area; (2) The 2-km mode is most obvious at Alba Patera and moderately well developed at Syria and Sinai Plana, but it is muted at Tempe Terra, which is in the same latitude range as Alba Patera but older; and (3) The 2-km-depth mode is not present in all areas that have features of Amazonian age. We suggest two possible explanations for our observations in the Tharsis region.

Davis, P. A.↗

NASA NTRS1993

Earth's partial pressure of CO2 over the past 100-500 Ma; evidence from Ce anomalies in mostly shallow seas (less than 200 m) as recorded in carbonate sediments, 2

We reported the direct relationship of Ce anomalies recorded in 0.2-119 Ma CaCO3 sediments (Ce(sup A*)) to the Ce anomalies in the parental Pacific deep seawater (Ce(sup A)) and their relationship to atmospheric P(CO2) relative to present P(CO2). We have analyzed continental CaCO3 samples that were deposited in ancient oceans and shallow sea platforms less than 200 m over central USA, central Europe, China, and Saudi-Arabia/Oman. We have plotted Ce(sup A*) over the 75-470 Ma interval. For P(CO2) calculations, we assumed as a reference standard the less than 200 m mixed Pacific Ocean with a Ce(sup A) geometric mean of 0.22 and a range of 0.10-0.43. Because P(CO2) values obtained from reliable deep Pacific Ocean carbonates in the 67-119 Ma interval were similar to the present P(CO2) values, we have drawn a 1.0 ratio for that interval. Although there is considerable scatter among the approximately 150 Ma carbonates, the average Ce(sup A*) value suggests that P(CO2) increased during the early Cretaceous, from 1.0X at approximately 120 Ma to about 1.4X at approximately 150 Ma. At approximately 250 Ma, the average Ce(sup A*) in 13 shallow sea China carbonates agrees well with the single and more reliable approximately 250 Ma China carbonate deposited in deeper open platform. We suggest that P(CO2) ranged from 1.4-1.7X over the Jurassic and Triassic periods. At approximately 280 Ma, three China carbonates deposited in deeper open platforms and therefore considered more reliable are consistent with a European carbonate, which indicate Ce(sup A) and P(CO2) values similar to the present. The minimum at this time corresponds to the great Permo-Carboniferous glaciation. From 280 Ma to 470 Ma, the trend favors increasing Ce(sup A*) and corresponding P(CO2) values between 1.9-2.7X, with a more reliable value closer to 2.7X at 430 Ma because of the unknown higher temperature in the less than 100 m seawater over continental USA which was located just south of the equator at approximately 430 Ma.

Liu, Y.-G.↗

NASA NTRS1994

Structural and stratigraphic features and ERS 1 synthetic aperture radar backscatter characteristics of ice growing on shallow lakes in NW Alaska, winter 1991-1992

Changes in Earth Remote-Sensing Satellite (ERS) 1 C band synthetic aperture radar (SAR) backscatter intensity (sigma(exp 0)) from ice growing on shallow tundra lakes at three locations in NW Alaska are described. Ice core analysis shows that all lakes on the coast at Barrow the ice, whether floating or frozen to the bottom, includes an inclusion-free layer overlying a layer of ice with tubular bubbles oriented parallel to the direction of growth. The clear ice may also be overlain by a discontinuous layer of bubbly snow ice. Backscatter is low (-16 to -22 dB) at the time of initial ice formation, probably due to the specular nature of the upper and lower ice surfaces causing the radar pulse to be reflected away from the radar. As the ice thickens during the autumn, backscatter rises steadily. Once the ice freezes to the lake bottom, regardless of the presence of foward scattering tubular bubbles, low backscatter values of -17 to -18 dB are caused by absorption of the radar signal in the lake bed. For ice that remains afloat all winter the ice-water interface and the tubular bubbles combine, presumably via an incoherent double-bounce mechanism, to cause maximum backscatter values of the order of -6 to -7 dB. The sigma(exp 0) saturates at -6 to -7 dB before maximum ice thickness and tubular bubble content are attained. A simple ice growth model suggests that the layer of ice with tubular bubbles need be only a few centimeters thick midway through the growth season to cause maximum backscatter from floating ice. During the spring thaw a previously unreported backscatter reversal is observed on the floating and grounded portions of the coastal lakes but not on the lakes farther inland. This reversal may be related to the ice surface topography and wetness plus the effects of a longer, cooler melt period by the coast. Time series of backscatter variations from shallow tundra lakes are a record of (1) the development of tubular bubbles in the ice and, by association, changes in the gas content of the underlying water and (2) the freezing of ice to the bottoms of the lakes and therefore lake bathymetry and water availability. SAR is also able to detect the onset of lake ice growth in autumn and the initiation of the spring thaw and thus has potential for monitoring high-altitude lake ice growth and decay processes in relation to climate variability.

Jeffries, M. O.↗

NASA NTRS1994

Impact of land-surface moisture variability on local shallow convective cumulus and precipitation in large-scale models

Numerical experiments using state-of-the-art high-resolution mesoscale cloud model showed that land-surface moisture significantly affects the timing of onset of clouds and the intensity and distribution of precipitation. In general, landscape discontinuity enhances shallow convective precipitation. Two mechanisms that are strongly modulated by land-surface moisture-namely, random turbulent thermal cells and organized sea-breeze-like mesoscale circulations-also determine the horizontal distribution of maximum precipitation. However, interactions between shallow cumulus and land-surface moisture are highly nonlinear and complicated by different factors, such as atmospheric thermodynamic structure and large-scale background wind. This analysis also showed that land-surface moisture discontinuities seem to play a more important role in a relatively dry atmsophere, and that the strongest precipitation is produced by a wavelength of land-surface forcing equivalent to the local Rossby radius of deformation. A general trend between the maximum precipitation and the normalized maximum latent heat flux was identified. In general, large values of mesoscale latent heat flux imply strongly developed mesoscale circulations and intense cloud activity, accompanied by large surface latent heat fluxes that transport more water vapor into the atmosphere.

Chen, Fei↗