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NASA NTRS1989

Finite element analysis in fluids; Proceedings of the Seventh International Conference on Finite Element Methods in Flow Problems, University of Alabama, Huntsville, Apr. 3-7, 1989

Recent advances in computational fluid dynamics are examined in reviews and reports, with an emphasis on finite-element methods. Sections are devoted to adaptive meshes, atmospheric dynamics, combustion, compressible flows, control-volume finite elements, crystal growth, domain decomposition, EM-field problems, FDM/FEM, and fluid-structure interactions. Consideration is given to free-boundary problems with heat transfer, free surface flow, geophysical flow problems, heat and mass transfer, high-speed flow, incompressible flow, inverse design methods, MHD problems, the mathematics of finite elements, and mesh generation. Also discussed are mixed finite elements, multigrid methods, non-Newtonian fluids, numerical dissipation, parallel vector processing, reservoir simulation, seepage, shallow-water problems, spectral methods, supercomputer architectures, three-dimensional problems, and turbulent flows.

Chung, T. J.↗
NASA NTRS1985

Some anticipated contributions to core fluid dynamics from the GRM

It is broadly maintained that the secular variation (SV) of the large scale geomagnetic field contains information on the fluid dynamics of Earth's electrically conducting outer core. The electromagnetic theory appropriate to a simple Earth model has recently been combined with reduced geomagnetic data in order to extract some of this information and ascertain its significance. The simple Earth model consists of a rigid, electrically insulating mantle surrounding a spherical, inviscid, and perfectly conducting liquid outer core. This model was tested against seismology by using truncated spherical harmonic models of the observed geomagnetic field to locate Earth's core-mantle boundary, CMB. Further electromagnetic theory has been developed and applied to the problem of estimating the horizontal fluid motion just beneath CMB. Of particular geophysical interest are the hypotheses that these motions: (1) include appreciable surface divergence indicative of vertical motion at depth, and (2) are steady for time intervals of a decade or more. In addition to the extended testing of the basic Earth model, the proposed GRM provides a unique opportunity to test these dynamical hypotheses.

Vanvorhies, C.↗
NASA NTRS2011

Geomagnetic Variability and Predictability

The Earth's magnetic field varies on time scales from seconds to millions of years. These variations can be measured directly by ground observatories and satellites, and indirectly through laboratories. They are from different electromagnetic processes in magnetosphere and ionosphere (external), ocean and crust (surface), and deep in the Earth's fluid outer core (internal). Of the measured magnetic signals, 95% is from the core, and is called the core field, or internal field. Variation of the core field, often called the geomagnetic secular variation (SV), is the manifestation of the magnetohydrodynamic processes in the core. Therefore, SV provides rich information on the core dynamical state that is then critical for understanding the geophysical mechanisms of the SV, the core-mantle interactions, and contribution of mass transport inside the core on Earth's gravity variation. Traditionally, the core state is probed via two independent methodologies: core flow inversion from the observed SV, and pure numerical dynamo simulation. The former is driven by observations, but does not include necessary interactions among physical variables; the latter is dynamically consistent, but is not constrained by any observation. Therefore, both are very limited in providing appropriate estimates of the core state. To avoid these limitations, a new approach, geomagnetic data assimilation, appears recently. In this approach, simulation results (model forecasts) are constantly corrected with observations, the corrected solutions (analysis), are then used as the initial conditions to make more accurate forecasts of future. Recent studies have demonstrated successfully that assimilation solutions are different from those of free running models. These new solutions are better estimates of the core state, and have been used to provide accurate prediction of SV for the period from 2010 to 2015. This prediction is part of the IGRF field model for international community applications.

Kuang, Weijia↗
NASA NTRS1999

A View of the Lunar Interior Through Lunar Laser Range Analysis

Laser ranges between observatories on the Earth and retroreflectors on the Moon started in 1969 and continue to the present. Recent range accuracies are 2 cm while earliest ranges are an C, order of magnitude less certain. Four retroreflectors are ranged: three located at the Apollo 11, 14, and 15 sites and one on the Lunakhod 2 rover. Accurate analysis of the range data determines a number of lunar science parameters. The lunar interior variables include a fluid core parameter. The Lunar Laser Ranging effort is reviewed elsewhere. Many parameters are detected through their influence on rotation. Also detected are solid-body tides and accurate selenocentric reflector locations. Determined through the rotation are moment-of-inertia differences, gravitational harmonics, potential Love number, and dissipation effects due to tides and molten core. The rotation of the Moon is not at its minimum energy state; some recently active process has caused free librations. The moment differences contributed to the recent improvement of the Moon's moment of inertia from the Lunar Prospector gravity field. The Love numbers provide bulk elastic properties. Future possibilities for measurement include oblateness of the core-mantle boundary and core moment. A study of dissipation signatures in the rotation determines tidal Q vs. frequency and concludes that the Moon has a molten core. At 1 month the tidal Q is 37 and at 1 yr it is 60. The core radius is < or = 352 km for Fe and < or = 374 km for the Fe-FeS eutectic. The core detection exceeds 3x its uncertainty. The spin of the core is not aligned with the spin of the mantle and torque arises from the velocity difference at the boundary. Yoder's turbulent boundary layer theory is used to compute the radii. The present heat generation from tides and core interaction is minor compared to radiogenic heating. The heating for ancient times is more interesting. Peale and Cassen investigated lunar tidal heating while the lunar orbit expanded due to tides on Earth. Their calculations predate the measurement of Q and should be multiplied by 3.45 to match the lunar-laser-determined Love number and monthly Q. Tidal-heating computations depend on how fast the lunar orbit evolved and whether the tidal dissipation is localized. Neither is known, but plausible assumptions lead to early central region temperature increases of several hundred degrees. Most of the energy is deposited early in the Moon's history. The turbulent boundary layer theory allows a prediction of energy dissipated at the core-mantle boundary during orbit evolution. Under the assumption that the properties of the early core are the same as at present, the energy dissipated by core-mantle interaction is about the same as for tidal dissipation, but it is deposited in a smaller volume. This source of energy is capable of promoting convection in an early fluid core and driving a dynamo. This is a transient phase with a duration depending on the rate of orbit evolution. Plausible assumptions lead to a duration of a few hundred million years. Thus, the remnant magnetization of many lunar rocks is compatible with a brief global magnetic field powered by dynamical energy dissipation. Analysis of the lunar laser ranges is providing information on lunar geophysics. Future data will improve accuracies of present solution parameters, and several more interior effects should be detectable.

Williams, J. G.↗
NASA NTRS2002

The Global Geophysical Fluids Center of IERS (and its Special Bureau for Mantle)

The Global Geophysical Fluids Center (GGFC) was established by the International Earth Rotation Service (IERS) on IERS's 10th anniversary day January 1, 1998, in an effort to expand IERS's services to the scientific community. Under the GGFC, eight Special Bureaus (SB) have been selected, each to be responsible for research and data service activities pertaining to mass transports and related geophysical processes in specific components of the Earth system, or "global geophysical fluids," including the atmosphere, oceans, solid Earth, core, and geophysical processes of gravity, loading, tides and hydrological cycles. GGFC and the SBs have the responsibility of supporting, facilitating, and providing services to the worldwide research community, in areas related to the variations in Earth rotation, gravity field and geocenter that are caused by mass transport in the global geophysical fluids. These minute variations have been observed by various space geodetic techniques, as effective remote sensing tools, with ever increasing precision/accuracy and temporal/spatial resolution. The GGFC and SBs have organized dedicated workshops and special sessions at international conferences, published articles, and held regular business meetings. The SBs also maintain individual website for data services and information exchanges. See URL . In particular, the SB for Mantle focuses on large-scale mass redistributions that occur in the mantle in association with various dynamic processes, including seismic activities, the post-glacial rebound, and mantle convections.

Chao, Benjamin F.↗
NASA NTRS1988

Geoid and topography for infinite Prandtl number convection in a spherical shell

Geoid anomalies and surface and lower-boundary topographies are calculated for numerically generated thermal convection for an infinite Prandtl number, Boussinesq, axisymmetric spherical fluid shell with constant gravity and viscosity, for heating both entirely from below and entirely from within. Convection solutions are obtained for Rayleigh numbers Ra up to 20 times the critical Ra in heating from below and 27 times critical for heating from within. Geoid parallels surface undulations, and boundary deformation generally increases with increasing cell wavelength. Dimensionless geoid and topography in heating from below are about 5 times greater than in heating from within. Values for heating from within correlate more closely with geophysical data than values from heating from below, suggesting a predominance of internal heating in the mantle. The study emphasizes that dynamically induced topography and geoid are sensitive to the mode of heating in the earth's mantle.

Bercovici, D.↗
NASA NTRS2003

Density Anomalies in the Mantle and the Gravitational Core-Mantle Interaction

Seismic studies suggest that the bulk of the mantle is heterogeneous, with density variations in depth as well as in horizontal directions (latitude and longitude). This density variation produces a three- dimensional gravity field throughout the Earth. On the other hand, the core density also varies in both time and space, due to convective core flow. Consequently, the fluid outer core and the solid mantle interact gravitationally due to the mass anomalies in both regions. This gravitational core-mantle interaction could play a significant role in exchange of angular momentum between the core and the mantle, and thus the change in Earth's rotation on time scales of decades and longer. Aiming at estimating the significance of the gravitational core-mantle interaction on Earth's rotation variation, we introduce in our MoSST core dynamics model a heterogeneous mantle, with a density distribution derived from seismic results. In this model, the core convection is driven by the buoyancy forces. And the density variation is determined dynamically with the convection. Numerical simulation is carried out with different parameter values, intending to extrapolate numerical results for geophysical implications.

Kuang, Weijia↗
NASA NTRS1999

Mass Transport in Global Geophysical Fluids

Mass transports occurring in the atmosphere-hydrosphere-solid Earth-core system (the "global geophysical fluids") are important geophysical phenomena. They occur on all temporal and spatial scales. Examples include air mass and ocean circulations, tides, hydrological water redistribution, mantle processes such as post-glacial rebound, earthquakes and tectonic motions, and core geodynamo activities. With only a few exceptions on the Earth surface, the temporal history and spatial pattern of such mass transport are often not amenable to direct observations. Space geodesy techniques, however, have the capability of monitoring certain direct consequences of the mass transport, including Earth's rotation variations, gravitational field variations, and the geocenter motion. These techniques include the very-long-baseline interferometry, satellite laser ranging and Doppler tracking, and the Global Positioning System, all entail global observational networks. While considerable advances have been made in observing and understanding of the dynamics of Earth's rotation, only the lowest-degree gravitational variations have been observed and limited knowledge of geocenter motion obtained. New space missions, projects and initiatives promise to further improve the measurements and hence our knowledge about the global mass transports. The latter contributes to our understanding and modeling capability of the geophysical processes that produce and regulate the mass transports, as well as the solid Earth's response to such changes in constraining the modeling of Earth's mechanical properties.

Chao, B. F.↗
NASA NTRS1993

Investigation of Mars Rotational Dynamics Using Earth-based Radio Tracking of Mars Landers

The development of space geodetic techniques over the past two decades has made it possible to measure the rotational dynamics of the Earth at the milliarcsecond level, improving our geophysical models of the Earth 's interior and the interactions between the solid Earth and its atmosphere. We have found that the rotational dynamics of Mars can be determined to nearly the same level of accuracy by acquiring Earth-based two-way radio tracking observations of three or more landers globally distributed on the surface of Mars. Our results indicate that the precession and long-term obliquity changes of the Mars pole direction can be determined to an angular accuracy corresponding to about 15 cm/yr at the planet's surface. In addition, periodic nutations of the pole and seasonal variations in the spin rate of the planet can be determined to 10 cm or less. Measuring the rotation of Mars at this accuracy would greatly improve the determination of the planet' s moment of inertia and would resolve the size of a planetary fluid core, providing a valuable constraint on Mars interior models. Detecting seasonal variations in the spin rate of Mars would provide global constraints on atmospheric angular momentum changes due to sublimation of the Mars CO2 polar ice caps. Finally, observation of quasisecular changes in Mars obliquity would have significant implications for understanding long-term climatic change. The key to achieving these accuracies is a globally distributed network of Mars landers with stable, phase-coherent radio transponders. By simultaneously acquiring coherent two-way carrier phase observations between a single Earth tracking station and multiple Mars landers, Earth media errors are essentially eliminated, providing an extremely sensitive measure of changes in the differential path lengths between the Earth tracking station and the Mars landers due to Mars rotation. Time variability of the instrumental phase delay through the radio transponder may represent the limiting error source for this technique. Calibration of the transponder stability to about 0.1 ns or less, over a single tracking arc of up to 12 hr, is sufficient to provide the decimeter-level determination of Mars orientation parameters quoted above. We will provide a detailed description of the multilander tracking technique and the requirements it imposes on both the lander radio system and the Earth-based ground-tracking system. This concept is currently part of the strawman science plan for the Mars Environmental Survey (MESUR) mission and complements many of the other MESUR science goals.

Edwards, C. D., Jr.↗
NASA NTRS1988

Dynamic compensation in the central Pacific Ocean

The intermediate-wavelength geoid (lambda similar to 2000 km) and sea-floor topography fields in the central Pacific Ocean were studied in terms of static and dynamic compensation models. Topographic features on the sea-floor with lambda less than 1000 km were found to be compensated both regionally, by the elastic strength of the lithosphere, and locally, by displacing mantle material to reach isostatic adjustment. The larger-scale sea-floor topography and the corresponding geoid anomalies with lambda similar to 2000 km cannot be explained by either local or regional compensation. The topography and the resulting geoid anomaly at this wavelength were modeled by considering the dynamic effects arising from viscous stresses in a layer of fluid with a highly temperature-dependent viscosity for the cases of: (1) surface cooling, and (2) basal heating. In this model, the mechanical properties of the elastic part of the lithosphere were taken into account by considering an activation energy of about 520 kJ/mol in the Arrhenius law for the viscosity. Numerical predictions of the topography, total geoid anomaly, and admittance were obtained, and the results show that the thermal perturbation in the layer, which accounts for the mass deficit, must be located close to the surface to compensate the gravitational effect of the surface deformation. For the case of basal heating, the temperature dependence of viscosity results in a separation of the upper, quasi-rigid lid from the lower mobile fluid, hence inhibiting the development of a compensating thermal perturbation at shallow depths. The results clearly rule out small-scale, upper-mantle convection as the source of these anomalies. Instead, the geophysical observables can be well explained by a shallow, transient thermal perturbation.

Hinojosa, Juan Homero↗
NASA NTRS2006

Constraining Numerical Geodynamo Modeling with Surface Observations

Numerical dynamo solutions have traditionally been generated entirely by a set of self-consistent differential equations that govern the spatial-temporal variation of the magnetic field, velocity field and other fields related to dynamo processes. In particular, those solutions are obtained with parameters very different from those appropriate for the Earth s core. Geophysical application of the numerical results therefore depends on correct understanding of the differences (errors) between the model outputs and the true states (truth) in the outer core. Part of the truth can be observed at the surface in the form of poloidal magnetic field. To understand these differences, or errors, we generate new initial model state (analysis) by assimilating sequentially the model outputs with the surface geomagnetic observations using an optimal interpolation scheme. The time evolution of the core state is then controlled by our MoSST core dynamics model. The final outputs (forecasts) are then compared with the surface observations as a means to test the success of the assimilation. We use the surface geomagnetic data back to year 1900 for our studies, with 5-year forecast and 20-year analysis periods. We intend to use the result; to understand time variation of the errors with the assimilation sequences, and the impact of the assimilation on other unobservable quantities, such as the toroidal field and the fluid velocity in the core.

Kuang, Weijia↗
NASA NTRS2003

Time-Variable Gravity from Space: Quarter Century of Observations, Mysteries, and Prospects

Any large mass transport in the Earth system produces changes in the gravity field. Via the space geodetic technique of satellite-laser ranging in the last quarter century, the Earth s dynamic oblateness J2 (the lowest-degree harmonic component of the gravity field) has been observed to undergo a slight decrease - until around 1998, when it switched quite suddenly to an increase trend which has continued to date. The secular decrease in J2 has long been attributed primarily to the post-glacial rebound in the mantle; the present increase signifies an even larger change in global mass distribution whose J2 effect overshadows that of the post-glacial rebound, at least over interannual timescales. Intriguing evidences have been found in the ocean water distribution, especially in the extratropical Pacific basins, that may be responsible for this 52 change. New techniques based on satellite-to-satellite tracking will yield greatly improved observations for time-variable gravity, with much higher precision and spatial resolution @e., much higher harmonic degrees). The most important example is the GRACE mission launched in March 2002, following the success of the CHAMP mission. Such observations are becoming a new and powerful tool for remote sensing of geophysical fluid processes that involve larger-scale mass transports.

Chao, Benjamin F.↗
NASA NTRS2017

Extratropical Weather Systems on Mars: Radiatively-Active Water Ice Effects

Extratropical, large-scale weather disturbances, namely transient, synoptic-period,baroclinic barotropic eddies - or - low- (high-) pressure cyclones (anticyclones), are components fundamental to global circulation patterns for rapidly rotating, differentially heated, shallow atmospheres such as Earth and Mars. Such "wave-like" disturbances that arise via (geophysical) fluid shear instability develop, mature and decay, and travel west-to-east in the middle and high latitudes within terrestrial-like planetary atmospheres. These disturbances serve as critical agents in the transport of heat and momentum between low and high latitudes of the planet. Moreover, they transport trace species within the atmosphere (e.g., water vapor/ice, other aerosols (dust), chemical species, etc). Between early autumn through early spring, middle and high latitudes on Mars exhibit strong equator-to-pole mean temperature contrasts (i.e., "baroclinicity"). Data collected during the Viking era and observations from both the Mars Global Surveyor (MGS) and Mars Reconnaissance Orbiter (MRO) indicate that such strong baroclinicity supports vigorous, large-scale eastward traveling weather systems [Banfield et al., 2004; Barnes et al., 1993]. A good example of traveling weather systems, frontal wave activity and sequestered dust activity from MGS/MOC image analyses is provided in Figure 1 (cf. Wang et al. [2005]). Utilizing an upgraded and evolving version of the NASA Ames Research Center (ARC) Mars global climate model, investigated here are key dynamical and physical aspects of simulated northern hemisphere (NH) large-scale extratropica lweather systems,with and without radiatively-active water ice clouds. Mars Climate Model:

cyclones↗
NASA NTRS2003

Time-Variable Gravity from Space: Quarter Century of Observations, Mysteries, and Prospects

Any large mass transport in the Earth system produces changes in the gravity field. Via the space geodetic technique of satellite-laser ranging in the last quarter century, the Earth's dynamic oblateness J2 (the lowest-degree harmonic component of the gravity field) has been observed to undergo a slight decrease -- until around 1998, when it switched quite suddenly to an increase trend which has continued to 2001 before sharply turning back to the value which it is "supposed to be"!. The secular decrease in J2 has long been attributed primarily to the post-glacial rebound in the mantle; the present increase signifies an even larger change in global mass distribution whose J2 effect overshadows that of the post-glacial rebound, at least over interannual timescales. Intriguing evidences have been found in the ocean water distribution, especially in the extratropical Pacific basins, that may be responsible for this J2 change. New techniques based on satellite-to-satellite tracking will yield greatly improved observations for time-variable gravity, with much higher precision and spatial resolution (i.e., much higher harmonic degrees). The most important example is the GRACE mission launched in March 2002, following the success of the CHAMP mission. Such observations are becoming a new and powerful tool for remote sensing of geophysical fluid processes that involve larger-scale mass transports.

Chao, Benjamin F.↗
NASA NTRS2003

Time-Variable Gravity from Space: Quarter Century of Observations, Mysteries, and Prospects

Any large mass transport in the Earth system produces changes in the gravity field. Via the space geodetic technique of satellite-laser ranging in the last quarter century, the Earth's dynamic oblateness J2 (the lowest-degree harmonic component of the gravity field) has been observed to undergo a slight decrease -- until around 1998, when it switched quite suddenly to an increase trend which has continued to date. The secular decrease in J2 has long been attributed primarily to the post-glacial rebound in the mantle; the present increase signifies an even larger change in global mass distribution whose J2 effect overshadows that of the post-glacial rebound, at least over interannual timescales. Intriguing evidences have been found in the ocean water distribution, especially in the extratropical Pacific basins, that may be responsible for this J2 change. New techniques based on satellite-to-satellite tracking will yield greatly improved observations for time-variable gravity, with much higher precision and spatial resolution (i.e., much higher harmonic degrees). The most important example is the GRACE mission launched in March 2002, following the success of the CHAMP mission. In addition, although less precise than GRACE, the GPS/Meteorology constellation mission COSMIC, with 6 mini-satellites to be launched in late 2005, is expected to provide continued and complementary time-variable gravity observations. Such observations are becoming a new and powerful tool for remote sensing of geophysical fluid processes that involve larger-scale mass transports.

Chao, Benjamin F.↗
NASA NTRS2003

Numerical Simulation of Protoplanetary Vortices

The fluid dynamics within a protoplanetary disk has been attracting the attention of many researchers for a few decades. Previous works include, to list only a few among many others, the well-known prescription of Shakura & Sunyaev, the convective and instability study of Stone & Balbus and Hawley et al., the Rossby wave approach of Lovelace et al., as well as a recent work by Klahr & Bodenheimer, which attempted to identify turbulent flow within the disk. The disk is commonly understood to be a thin gas disk rotating around a central star with differential rotation (the Keplerian velocity), and the central quest remains as how the flow behavior deviates (albeit by a small amount) from a strong balance established between gravitational and centrifugal forces, transfers mass and momentum inward, and eventually forms planetesimals and planets. In earlier works we have briefly described the possible physical processes involved in the disk; we have proposed the existence of long-lasting, coherent vortices as an efficient agent for mass and momentum transport. In particular, Barranco et al. provided a general mathematical framework that is suitable for the asymptotic regime of the disk; Barranco & Marcus (2000) addressed a proposed vortex-dust interaction mechanism which might lead to planetesimal formation; and Lin et al. (2002), as inspired by general geophysical vortex dynamics, proposed basic mechanisms by which vortices can transport mass and angular momentum. The current work follows up on our previous effort. We shall focus on the detailed numerical implementation of our problem. We have developed a parallel, pseudo-spectral code to simulate the full three-dimensional vortex dynamics in a stably-stratified, differentially rotating frame, which represents the environment of the disk. Our simulation is validated with full diagnostics and comparisons, and we present our results on a family of three-dimensional, coherent equilibrium vortices.

Lin, H.↗