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All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

One-dimensional models of quasi-neutral parallel electric fields

Parallel electric fields can exist in the magnetic mirror geometry of auroral field lines if they conform to the quasineutral equilibrium solutions. Results on quasi-neutral equilibria and on double layer discontinuities were reviewed and the effects on such equilibria due to non-unique solutions, potential barriers and field aligned current flows using as inputs monoenergetic isotropic distribution functions were examined.

Stern, D. P.↗
NASA NTRS1981

The magnetic field of Jupiter - A generalized inverse approach

The estimation of planetary magnetic fields from observations of the magnetic field gathered along a spacecraft flyby trajectory is examined with the aid of generalized inverse techniques, with application to the internal magnetic field of Jupiter. Model non-uniqueness resulting from the limited spatial extent of the observations and noise on the data is explored and quantitative estimates of the model parameter resolution are found. The presence of a substantial magnetic field of external origin due to the currents flowing in the Jovian magnetodisc is found to be an important source of error in estimates of the internal Jovian field, and new models explicitly incorporating these currents are proposed. New internal field models are derived using the vector helium magnetometer observations and the high field fluxgate observations of Pioneer 11, and knowledge of the external current system gained from the Pioneer 10 and Voyagers 1 and 2 encounters.

Connerney, J. E. P.↗
NASA NTRS1985

Water-ice Clouds on Mars: Location and Seasonal Variation

Water-ice clouds were located on Mars using Viking infrared thermal mapper (IRTM) broadband spectral observations. The IRTM instrument had 5 thermal bands centered at 7, 9, 11, 15, and 20 microns. Clouds and hazes were consistently observed in four northern hemisphere regions centered over Tharsis, Arabia, Elysium, and along the boundary between the crater uplands and the northern plains. During the northern spring and summer when the atmosphere is relatively free of dust, there is a distinct difference between the cloud abundance in the Northern and Southern Hemispheres, with clouds and hazes being rare in the south. A second important class of water-ice clouds are those observed along the boundary of the retreating north polar cap. These clouds occur at all longitudes around the cap and are generally confined to within +/- 5 deg of the cap boundary. The cloud opacities can be estimated using a delta-Eddington radiative transfer model which incorporates Mie scattering and the electrical properties of water-ice. Assuming realistic, but non-unique, values for the ice particle size and cloud temperature, the derived opacities range from near-zero to 1.

Christensen, P. R.↗
NASA NTRS1983

Crack arrest in structural ceramics

The non-unique, dynamic stress intensity factor versus crack-velocity relation as well as the lack of a dynamic arrest stress intensity factor in reaction bonded silicon nitride are contrasted with the gamma-shaped, dynamic stress intensity factor versus crack velocity relation and the dynamic arrest stress intensity factor of structural steel. These differences in dynamic fracture responses resulted in fracture of a hypothetical reaction bonded silicon nitride disk during a simulated start up condition of a gas turbine engine. A larger initial crack in a similar steel disk was arrested after propagating into a decreasing stress field generated by a steady state thermal gradient.

Kobayashi, A. S.↗
NASA NTRS1988

Entropy and vorticity corrections for transonic flows

Different models for inviscid transonic flows are examined. The common assumptions that the flow is isentropic and irrotational are critically evaluated. Entropy and vorticity correction procedures for potential and stream function formulations are presented, together with the details of the treatment of shocks and wakes, and drag and lift calculations. The non-uniqueness problem of the potential formulation is studied using different artificial viscosity forms. Numerical results are compared with Euler solutions.

Hafez, M.↗
NASA NTRS1988

Numerical methods for turbulent flow

It has generally become accepted that the Navier-Strokes equations predict the dynamic behavior of turbulent as well as laminar flows of a fluid at a point in space away form a discontinuity such as a shock wave. Turbulence is also closely related to the phenomena of non-uniqueness of solutions of the Navier-Strokes equations. These second order, nonlinear partial differential equations can be solved analytically for only a few simple flows. Turbulent flow fields are much to complex to lend themselves to these few analytical methods. Numerical methods, therefore, offer the only possibility of achieving a solution of turbulent flow equations. In spite of recent advances in computer technology, the direct solution, by discrete methods, of the Navier-Strokes equations for turbulent flow fields is today, and in the foreseeable future, impossible. Thus the only economically feasible way to solve practical turbulent flow problems numerically is to use statistically averaged equations governing mean-flow quantities. The objective is to study some recent developments relating to the use of numerical methods to study turbulent flow.

Turner, James C., Jr.↗
NASA NTRS1989

On the Gortler vortex instability mechanism at hypersonic speeds

The linear instability of the hypersonic boundary layer on a curved wall is considered. As a starting point the viscosity of the fluid is taken to be a linear function of temperature and real-gas effects are ignored. It is shown that the flow is susceptible to Gortler vortices and that they are trapped in the logarithmically thin adjustment layer in which the temperature of the basic flow changes rapidly to its free stream value. The vortices decay exponentially in both directions away from this layer and are most unstable when their wavelength is comparable with the depth of the adjustment layer. The non-uniqueness of the neutral stability curve associated with incompressible Gortler vortices is shown to disappear at high Mach numbers if the appropriate fast streamwise dependence of the instability is built into the disturbance flow structure. It is shown that in the hypersonic limit wall-cooling has a negligible effect on the stability of a fluid with a given value of the Chapman constant.

Hall, Philip↗
NASA NTRS1990

Analytical solutions with Generalized Impedance Boundary Conditions (GIBC)

The diffraction by a material discontinuity in a thick dielectric/ferrite layer is considered by modeling the layer as a distributed current sheet obeying generalized sheet transition conditions (GSTC's). The sheet currents are then formulated and solved via the standard dual integral equation approach. This yields the diffracted field in terms of unknown constants which underscore the non-uniqueness of the GSTC current sheet representation. The constants are dependent on the geometry and properties of the discontinuity and are determined by enforcing field continuity across the material junction. This requires the field internal to the slab which are determined from the external ones via analytic continuity. Results are given which validate the solution and demonstrate the importance of the constants.

Ricoy, Mark A.↗
NASA NTRS1992

Full and reduced order observer based controller design for H2-optimization

The most general H2 control problem is considered. The authors derive necessary and sufficient conditions when the infimum is attained by state feedback. They do the same for the measurement feedback case where necessary and sufficient conditions are derived when the infimum is attained by proper dynamic compensator. Reduced-order compensators are investigated if some states are observable without noise. For all of these cases the freedom that the non-uniqueness of optimal compensators gives in assigning the closed-loop eigenvalues is discussed. The case when the infimum cannot be attained is investigated. A constructive algorithm is presented to find a minimizing sequence of stabilizing controllers and the freedom in the asymptotic locations of the closed-loop eigenvalues is discussed. This procedure is repeated for three different cases: static state feedback, full-order measurement feedback, and reduced-order measurement feedback.

Stoorvogel, Anton A.↗
NASA NTRS1988

Evaluation of a methodology for model identification in the time domain

A model identification methodology for structural dynamics has been applied to simulated vibrational data as a first step in evaluating its accuracy. The evaluation has taken into account a wide variety of factors which affect the accuracy of the procedure. The effects of each of these factors were observed in both the response time histories and the estimates of the parameters of the model by comparing them with the exact values of the system. Each factor was varied independently but combinations of these have also been considered in an effort to simulate real situations. The results of the tests have shown that for the chain model, the procedure yields robust estimates of the stiffness parameters under the conditions studied whenever uniqueness is ensured. When inaccuracies occur in the results, they are intimately related to non-uniqueness conditions inherent in the inverse problem and not to shortcomings in the methodology.

Beck, R. T.↗
NASA NTRS1996

A Numerical Study of Self-Similarity in a Turbulent Plane Wake Using Large-Eddy Simulation

Turbulent wakes are known to develop self-similarly sufficiently far downstream from obstacles that generate them. It has long been assumed that the spreading rate of the wake in the self-similar regime is independent of the details of the body generating the wake, being dependent only on the total drag (or momentum deficit). This assumption seems to be in contradiction with some recent experiments. In this study we attempt to complement these experimental investigations through a numerical study of a time-developing wake. A numerical study has the advantage of eliminating many of the uncontrolled factors present in experiments and allowing precise control of initial conditions. Large-eddy simulations employing the recently developed dynamic localization model are used to extend previous results from direct numerical simulations. The large-eddy simulation results are compared to the direct numerical simulation database, wherever such comparisons are feasible, as a check of the method. Like the experiments, the large-eddy simulations suggest that non-unique self-similar states, characterized by different spreading rates and turbulent statistics, are possible and that they can be maintained for significant time periods. The study also demonstrates the predictive capability of the dynamic localization subgrid model.

Ghosal, Sandip↗
NASA NTRS2000

A New Neural Network Approach Including First-Guess for Retrieval of Atmospheric Water Vapor, Cloud Liquid Water Path, Surface Temperature and Emissivities Over Land From Satellite Microwave Observations

The analysis of microwave observations over land to determine atmospheric and surface parameters is still limited due to the complexity of the inverse problem. Neural network techniques have already proved successful as the basis of efficient retrieval methods for non-linear cases, however, first-guess estimates, which are used in variational methods to avoid problems of solution non-uniqueness or other forms of solution irregularity, have up to now not been used with neural network methods. In this study, a neural network approach is developed that uses a first-guess. Conceptual bridges are established between the neural network and variational methods. The new neural method retrieves the surface skin temperature, the integrated water vapor content, the cloud liquid water path and the microwave surface emissivities between 19 and 85 GHz over land from SSM/I observations. The retrieval, in parallel, of all these quantities improves the results for consistency reasons. A data base to train the neural network is calculated with a radiative transfer model and a a global collection of coincident surface and atmospheric parameters extracted from the National Center for Environmental Prediction reanalysis, from the International Satellite Cloud Climatology Project data and from microwave emissivity atlases previously calculated. The results of the neural network inversion are very encouraging. The r.m.s. error of the surface temperature retrieval over the globe is 1.3 K in clear sky conditions and 1.6 K in cloudy scenes. Water vapor is retrieved with a r.m.s. error of 3.8 kg/sq m in clear conditions and 4.9 kg/sq m in cloudy situations. The r.m.s. error in cloud liquid water path is 0.08 kg/sq m . The surface emissivities are retrieved with an accuracy of better than 0.008 in clear conditions and 0.010 in cloudy conditions. Microwave land surface temperature retrieval presents a very attractive complement to the infrared estimates in cloudy areas: time record of land surface temperature will be produced.

Aires, F.↗
NASA NTRS2002

New Boundary Constraints for Elliptic Systems used in Grid Generation Problems

This paper discusses new boundary constraints for elliptic partial differential equations as used in grid generation problems in generalized curvilinear coordinate systems. These constraints, based on the principle of local conservation of thermal energy in the vicinity of the boundaries, are derived using the Green's Theorem. They uniquely determine the so called decay parameters in the source terms of these elliptic systems. These constraints' are designed for boundary clustered grids where large gradients in physical quantities need to be resolved adequately. It is observed that the present formulation also works satisfactorily for mild clustering. Therefore, a closure for the decay parameter specification for elliptic grid generation problems has been provided resulting in a fully automated elliptic grid generation technique. Thus, there is no need for a parametric study of these decay parameters since the new constraints fix them uniquely. It is also shown that for Neumann type boundary conditions, these boundary constraints uniquely determine the solution to the internal elliptic problem thus eliminating the non-uniqueness of the solution of an internal Neumann boundary value grid generation problem.

Kaul, Upender K.↗
NASA NTRS2002

Lightning Return-Stroke Current Waveforms Aloft, From Measured Field Change, Current, and Channel Geometry

Direct current measurements are available near the attachment point from both natural cloud-to-ground lightning and rocket-triggered lightning, but little is known about the rise time and peak amplitude of return-stroke currents aloft. We present, as functions of height, current amplitudes, rise times, and effective propagation velocities that have been estimated with a novel remote-sensing technique from data on 24 subsequent return strokes in six different lightning flashes that were triggering at the NASA Kennedy Space Center, FL, during 1987. The unique feature of this data set is the stereo pairs of still photographs, from which three-dimensional channel geometries were determined previously. This has permitted us to calculate the fine structure of the electric-field-change (E) waveforms produced by these strokes, using the current waveforms measured at the channel base together with physically reasonable assumptions about the current distributions aloft. The computed waveforms have been compared with observed E waveforms from the same strokes, and our assumptions have been adjusted to maximize agreement. In spite of the non-uniqueness of solutions derived by this technique, several conclusions seem inescapable: 1) The effective propagation speed of the current up the channel is usually significantly (but not unreasonably) faster than the two-dimensional velocity measured by a streak camera for 14 of these strokes. 2) Given the deduced propagation speed, the peak amplitude of the current waveform often must decrease dramatically with height to prevent the electric field from being over-predicted. 3) The rise time of the current wave front must always increase rapidly with height in order to keep the fine structure of the calculated field consistent with the observations.

Willett, J. C.↗
NASA NTRS2003

Analytic Solution to the Problem of Aircraft Electric Field Mill Calibration

It is by no means a simple task to retrieve storm electric fields from an aircraft instrumented with electric field mill sensors. The presence of the aircraft distorts the ambient field in a complicated way. Before retrievals of the storm field can be made, the field mill measurement system must be "calibrated". In other words, a relationship between impressed (i.e., ambient) electric field and mill output must be established. If this relationship can be determined, it is mathematically inverted so that ambient field can be inferred from the mill outputs. Previous studies have primarily focused on linear theories where the relationship between ambient field and mill output is described by a "calibration matrix" M. Each element of the matrix describes how a particular component of the ambient field is enhanced by the aircraft. For example the product M(sub ix), E(sub x), is the contribution of the E(sub x) field to the i(th) mill output. Similarly, net aircraft charge (described by a "charge field component" E(sub q)) contributes an amount M(sub iq)E(sub q) to the output of the i(th) sensor. The central difficulty in obtaining M stems from the fact that the impressed field (E(sub x), E(sub y), E(sub z), E(sub q) is not known but is instead estimated. Typically, the aircraft is flown through a series of roll and pitch maneuvers in fair weather, and the values of the fair weather field and aircraft charge are estimated at each point along the aircraft trajectory. These initial estimates are often highly inadequate, but several investigators have improved the estimates by implementing various (ad hoc) iterative methods. Unfortunately, none of the iterative methods guarantee absolute convergence to correct values (i.e., absolute convergence to correct values has not been rigorously proven). In this work, the mathematical problem is solved directly by analytic means. For m mills installed on an arbitrary aircraft, it is shown that it is possible to solve for a single 2m-vector that provides all other needed variables (i.e., the unknown fair weather field, the unknown aircraft charge, and the unknown matrix M). Numerical tests of the solution, effects of measurement errors, and studies of solution non-uniqueness are ongoing as of this writing.

Koshak, William↗
NASA NTRS2003

Reliability of CHAMP Anomaly Continuations

CHAMP is recording state-of-the-art magnetic and gravity field observations at altitudes ranging over roughly 300 - 550 km. However, anomaly continuation is severely limited by the non-uniqueness of the process and satellite anomaly errors. Indeed, our numerical anomaly simulations from satellite to airborne altitudes show that effective downward continuations of the CHAMP data are restricted to within approximately 50 km of the observation altitudes while upward continuations can be effective over a somewhat larger altitude range. The great unreliability of downward continuation requires that the satellite geopotential observations must be analyzed at satellite altitudes if the anomaly details are to be exploited most fully. Given current anomaly error levels, joint inversion of satellite and near- surface anomalies is the best approach for implementing satellite geopotential observations for subsurface studies. We demonstrate the power of this approach using a crustal model constrained by joint inversions of near-surface and satellite magnetic and gravity observations for Maude Rise, Antarctica, in the southwestern Indian Ocean. Our modeling suggests that the dominant satellite altitude magnetic anomalies are produced by crustal thickness variations and remanent magnetization of the normal polarity Cretaceous Quiet Zone.

vonFrese, Ralph R. B.↗
NASA NTRS2004

On the Measurement of Elemental Abundance Ratios in Inner Galaxy H II Regions

Although abundance gradients in the Milky Way Galaxy certainly exist, details remain uncertain, particularly in the inner Galaxy, where stars and H II regions in the Galactic plane are obscured optically. In this paper we revisit two previously studied, inner Galaxy H II regions: G333.6-0.2 and W43. We observed three new positions in G333.6-0.2 with the Kuiper Airborne Observatory and reobserved the central position with the Infrared Space Observatory's Long Wavelength Spectrometer in far-infrared lines of S++, N++, N+, and O++. We also added the N+ lines at 122 and 205 microns to the suite of lines measured in W43 by Simpson et al.. The measured electron densities range from approx. 40 to over 4000 per cu cm in a single HII region, indicating that abundance analyses must consider density variations, since the critical densities of the observed lines range from 40 to 9000 per cu cm. We propose a method to handle density variations and make new estimates of the S/H and N/H abundance ratios. We find that our sulfur abundance estimates for G333.6-0.2 and W43 agree with the S/H abundance ratios expected for the gradient previously reported by Simpson et al., with the S/H values revised to be smaller owing to changes in collisional excitation cross sections. The estimated N/H, S/H, and N/S ratios are the most reliable because of their small corrections for unseen ionization states (< or approx. 10%). The estimated N/S ratios for the two sources are smaller than what would be calculated from the N/H and S/H ratios in our previous paper. If all low excitation H II regions had similar changes to their N/S ratios as a result of adding measurements of N+ to previous measurements of N++, there would be no or only a very small gradient in N/S. This is interesting because nitrogen is considered to be a secondary element and sulfur is a primary element in galactic chemical evolution calculations. We compute models of the two H II regions to estimate corrections for the other unseen ionization states. We find, with large uncertainties, that oxygen does not, have a high abundance, with the result that the N/O ratio is as high (approx. 0.35) as previously reported. The reasons for the uncertainty in the ionization corrections for oxygen are both the non-uniqueness of the H II region models and the sensitivity of these models to different input atomic data and stellar atmosphere models. We discuss these predictions and conclude that only a few of the latest models adequately reproduce H II region observations, including the well-known, relatively-large observed Ne++/O++ ratios in low- and moderate-excitation H II regions.

Simpson, Janet P.↗
NASA NTRS2004

Meridional Variations of C2H2 and C2H6 in Jupiter's Atmosphere from Cassini CIRS Infrared Spectra

Hydrocarbons such as acetylene (C2H2) and ethane (C2H6) are important tracers in Jupiter's atmosphere, constraining our models of the chemical and dynamical processes. However, our knowledge of the vertical and meridional variations of their abundances has remained sparse. During the flyby of the Cassini spacecraft in December 2000, the Composite Infrared Spectrometer (CIRS) instrument was used to map the spatial variation of emissions from 10-1400 cm(sup -1) (1000-7 microns). In this paper we analyze a zonally-averaged set of CIRS spectra taken at the highest (0.5 cm(sup -1)) resolution, to infer atmospheric temperatures in the stratosphere at 0.5-20 mbar via the v4 band of CH4, and in the troposphere at 150-400 mbar, via the H2 absorption at 600-800 cm(sup -1). Simultaneously, we retrieve the abundances of C2H2 and C2H6 via the v5 and vg bands respectively. Tropospheric absorption and stratospheric emission are highly anti-correlated at the CIRS resolution, introducing a non-uniqueness into the retrievals, such that vertical gradient and column abundance cannot both be found without additional constraints. Assuming profile gradients from photochemical calculations, we show that the column abundance of C2H2 decreases sharply towards the poles by a factor approximately 4, while C2H6 is unchanged in the north and increasing in the south, by a factor approximately 1.8. An explanation for the meridional trends is proposed in terms of a combination of photochemistry and dynamics. Poleward, the decreasing UV flux is predicted to decrease the abundances of C2H2 and C2H6 by factors 2.7 and 3.5 respectively at a latitude 70 deg. However, the lifetime of C2H6 in the stratosphere (5 x 10(exp 9)) is much longer than the dynamical timescale for meridional motions inferred from SL-9 debris (5 x 10(exp 8 s)), and therefore the constant or rising abundance towards high latitudes likely indicates that meridional mixing dominates over photochemical effects. For C2H2, the opposite occurs, with the relatively short photochemical lifetime (3 x 10(exp 7 s)), compared to meridional mixing times, ensuring that the expected photochemical trends are visible.

Nixon, C. A.↗