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NASA NTRS1985

A model of the polarization position-angle swings in BL Lacertae objects

The polarization position-angle swings that have been measured in a number of BL Lacertae objects and highly variable quasars are interpreted in terms of shock waves which illuminate (by enhanced synchrotron radiation) successive transverse cross sections of a magnetized, relativistic jet. The jet is assumed to have a nonaxisymmetric magnetic field configuration of the type discussed in the companion paper on the equilibria of force-free jets. For a jet that is viewed at a small angle to the axis, the passage of a shock will give rise to an apparent rotation of the polarization position angle whose amplitude can be substantially larger than 180 deg. The effects of freely propagating shocks are compared with those of bow shocks which form in front of dense obstacles in the jet, and specific applications to 0727 - 115 and BL Lacertae are considered. In the case of 0727 - 115, it is pointed out that the nonuniformity of the swing rate and the apparent oscillations of the degree of polarization could be a consequence of relativistic aberration.

Konigl, A.↗
NASA NTRS2003

Turbulent Plane Wakes Subjected to Successive Strains

Six direct numerical simulations of turbulent time-evolving strained plane wakes have been examined to investigate the response of a wake to successive irrotational plane strains of opposite sign. The orientation of the applied strain field has been selected so that the flow is the time-developing analogue of a spatially developing wake evolving in the presence of either a favourable or an adverse streamwise pressure gradient. The magnitude of the applied strain rate a is constant in time t until the total strain e(sup at) reaches about four. At this point, a new simulation is begun with the sign of the applied strain being reversed (the original simulation is continued as well). When the total strain is reduced back to its original value of one, yet another simulation is begun with the sign of the strain being reversed again back to its original sign. This process is done for both initially "favourable" and initially "adverse" strains, providing simulations for each of these strain types from three different initial conditions. The evolution of the wake mean velocity deficit and width is found to be very similar for all the adversely strained cases, with both measures rapidly achieving exponential growth at the rate associated with the cross-stream expansive strain e(sup at). In the "favourably" strained cases, the wake widths approach a constant and the velocity deficits ultimately decay rapidly as e(sup -2at). Although all three of these cases do exhibit the same asymptotic exponential behaviour, the time required to achieve this is longer for the cases that have been previously adversely strained (by at approx. equals 1). These simulations confirm the generality of the conclusions drawn in Rogers (2002) regarding the response of plane wakes to strain. The evolution of strained wakes is not consistent with the predictions of classical self-similar analysis; a more general equilibrium similarity solution is required to describe the results. At least for the cases considered here, the wake Reynolds number and the ratio of the turbulent kinetic energy to the square of the wake mean velocity deficit are determined nearly entirely by the total strain. For these measures the order in which the strains are applied does not matter and the changes brought about by the strain are nearly reversible. The wake mean velocity deficit and width, on the other hand, differ by about a factor of three when the total strain returns to one, depending on whether the wake was first "favourably" or "adversely" strained. The strain history is important for predicting the evolution of these quantities.

Rogers, Michael M.↗
NASA NTRS2012

The Atacama Cosmology Telescope: Data Characterization and Map Making

We present a description of the data reduction and mapmaking pipeline used for the 2008 observing season of the Atacama Cosmology Telescope (ACT). The data presented here at 148 GHz represent 12% or the 90 TB collected by ACT from 2007 to 2010. In 2008 we observed for 136 days, producing a total of 142h of data (11 TB for the 148 GHz band only), with a daily average of 10.5 h of observation. From these, 108.5 h were devoted to 850 sq deg stripe (11.2 h by 9 deg.1) centered on a declination of -52 deg.7, while 175 h were devoted to a 280 square deg stripe (4.5 h by 4 deg.8) centered at the celestial equator. We discuss sources of statistical and systematic noise, calibration, telescope pointing and data selection. Out of 1260 survey hours and 1024 detectors per array, 816 h and 593 effective detectors remain after data selection for this frequency band, yielding a 38 % survey efficiency. The total sensitivity in 2008, determined from the noise level between 5 Hz and 20 Hz in the time-ordered data stream (TOD), is 32 muK square root of s in CMB units. Atmospheric brightness fluctuations constitute the main contaminant in the data and dominate the detector and noise covariance at low frequencies in the TOD. The maps were made by solving the lease squares problem using the Preconditioned Conjugate Gradient method, incorporating the details of the detector and noise correlations. Cross-correlation with WMAP sky maps as well as analysis from simulations reveal the our maps are unbiased at l > 300. This paper accompanies the public release of the 148 GHz southern stripe maps from 2008. The techniques described here will be applied to future maps and data releases.

Duenner, Rolando↗
NASA NTRS2019

Impact of Assimilating Adaptively Thinned AIRS Cloud-Cleared Radiances in the GEOS

This work examines the assimilation of AIRS (Atmospheric Infrared Sounder) radiances from two points of view: the thinning strategy and the use of cloud-cleared radiances as opposed to clear-sky. Previous published work by this team, based on a very large set of Observing System Experiments performed with a 2014 3DVAR version of the GEOS (Goddard Earth Observing System), has shown that the assimilation of adaptively thinned AIRS cloud-cleared radiances (CCRs) improves the representation of tropical cyclones (TCs) without damaging the global forecast skill. The simple adaptive methodology is based on denser AIRS coverage in moving domains centered on TCs, and sparser coverage everywhere else. Subsequent experiments showed that the adaptive methodology produces good results also when applied to clear-sky CrIS (Cross-track Infrared Sounder) and IASI (Infrared Atmospheric Sounding Interferometer) radiances. In addition, the results indicate that the density of all hyperspectral data assimilated over meteorologically inactive areas is excessive, probably because of horizontal error correlation, suggesting that the global thinning should be more aggressive. More recent work focused on the polar regions has shown another positive impact of assimilating cloud-cleared AIRS radiances instead of clear-sky. The results show that high latitude atmospheric dynamics is very sensitive to the representation of the lower tropospheric temperature structure over the Arctic region. Specifically, assimilation of CCRs over areas that are data poor and also affected by broken stratus clouds, and as such minimally observed by AIRS clear-sky radiances, changes substantially the temperature structure over the Arctic low troposphere. Ingestion of CCRs over the region propagates, through hydrostatic adjustments, to mid-tropospheric geopotential height, allowing for better prediction of mid-latitude waves. In addition, adaptively thinned CCRs also improve the representation of mesoscale convective cyclones at high latitudes. An example of an Antarctic low is provided. Finally, recent ongoing work with the hybrid 4DenVAR GEOS, investigating the 2017 boreal TC season, has confirmed the previous results: namely that aggressively thinned cloud-cleared radiances improve TC structure with no loss of global skill.

CCR↗
NASA NTRS2003

Parameters Describing Earth Observing Remote Sensing Systems

The Earth science community needs to generate consistent and standard definitions for spatial, spectral, radiometric, and geometric properties describing passive electro-optical Earth observing sensors and their products. The parameters used to describe sensors and to describe their products are often confused. In some cases, parameters for a sensor and for its products are identical; in other cases, these parameters vary widely. Sensor parameters are bound by the fundamental performance of a system, while product parameters describe what is available to the end user. Products are often resampled, edge sharpened, pan-sharpened, or compressed, and can differ drastically from the intrinsic data acquired by the sensor. Because detailed sensor performance information may not be readily available to an international science community, standardization of product parameters is of primary performance. Spatial product parameters described include Modulation Transfer Function (MTF), point spread function, line spread function, edge response, stray light, edge sharpening, aliasing, ringing, and compression effects. Spectral product parameters discussed include full width half maximum, ripple, slope edge, and out-of-band rejection. Radiometric product properties discussed include relative and absolute radiometry, noise equivalent spectral radiance, noise equivalent temperature diffenence, and signal-to-noise ratio. Geometric product properties discussed include geopositional accuracy expressed as CE90, LE90, and root mean square error. Correlated properties discussed include such parameters as band-to-band registration, which is both a spectral and a spatial property. In addition, the proliferation of staring and pushbroom sensor architectures requires new parameters to describe artifacts that are different from traditional cross-track system artifacts. A better understanding of how various system parameters affect product performance is also needed to better ascertain the utility of existing datasets and products as well as to specify the performance of new sensors and products. Examples of simulations performed for the Landsat Data Continuity Mission illustrate how various parameters affect system and product performance. Specific examples include the effects of ground sample distance, MTF, and band-to-band registration on various products.

Zanoni, Vicki↗
NASA NTRS1992

Meteoroid and debris special investigation group; status of 3-D crater analysis from binocular imagery

During the 3 month deintegration of the LDEF, the M&D SIG generated approximately 5000 digital color stereo image pairs of impact related features from all space exposed surfaces. Currently, these images are being processed at JSC to yield more accurate feature information. Work is currently underway to determine the minimum number of data points necessary to parametrically define impact crater morphologies in order to minimize the man-hour intensive task of tie point selection. Initial attempts at deriving accurate crater depth and diameter measurements from binocular imagery were based on the assumption that the crater geometries were best defined by paraboloid. We made no assumptions regarding the crater depth/diameter ratios but instead allowed each crater to define its own coefficients by performing a least-squares fit based on user-selected tiepoints. Initial test cases resulted in larger errors than desired, so it was decided to test our basic assumptions that the crater geometries could be parametrically defined as paraboloids. The method for testing this assumption was to carefully slice test craters (experimentally produced in an appropriate aluminum alloy) vertically through the center resulting in a readily visible cross-section of the crater geometry. Initially, five separate craters were cross-sectioned in this fashion. A digital image of each cross-section was then created, and the 2-D crater geometry was then hand-digitized to create a table of XY position for each crater. A 2nd order polynomial (parabolic) was fitted to the data using a least-squares approach. The differences between the fit equation and the actual data were fairly significant, and easily large enough to account for the errors found in the 3-D fits. The differences between the curve fit and the actual data were consistent between the caters. This consistency suggested that the differences were due to the fact that a parabola did not sufficiently define the generic crater geometry. Fourth and 6th order equations were then fitted to each crater cross-section, and significantly better estimates of the crater geometry were obtained with each fit. Work is presently underway to determine the best way to make use of this new parametric crater definition.

Sapp, Clyde A.↗
NASA NTRS1993

Earth-based measurement of lunar topography using delayed radar interferometry

Radar interferometry has been applied to radar mapping of the surface of Venus to resolve the ambiguity in the backscatter from the areas with the same delay-Doppler coordinates. For observations of the Moon these points are usually isolated by the small extent of the area illuminated by the radar beam so that interferometric techniques can be used to determine a third dimension to the location of the radar backscatter. Recent observations of Sinus Iridum (41.5 deg N, 31.0 deg W) using the Arecibo Observatory S-Band radar system (12.6 cm wavelength) in Apr. and Aug. 1992 have yielded a pair of images viewed with a very small 0.0420 deg difference in incidence angle. These images can be used as a delay interferometric pair and have been correlated to generate phase fringes that are related to topography. The spatial resolution of the images are 18 m in delay and 33 m in cross range (Doppler). The anticipated topographic resolution once the phase fringes have been unwrapped is approximately +/- 10 m.

Stacy, N. J. S.↗
NASA NTRSDate not supplied

Dose, LET, time and strain dependence of radiation-induced 53BP1 foci in 15 mouse strains ex vivo and associations to in vivo radiation susceptibility

We present a comparative analysis on the repair of radiation-induced DNA damage ex vivo in 15 strains of mice, including 5 inbred reference strains and 10 collaborative-cross strains, of both sexes. Non-immortalized primary skin fibroblasts derived from 76 mice were subjected to both low- and high-LET radiation (0.1, 1 and 4 Gy of X rays; 1.1 and 3 particles/100μm2 of 350 MeV/n 40Ar and 600 MeV/n 56Fe). Automated image quantification of 53BP1 radiation-induced foci (RIF) during the first 4-48 h post-irradiation was performed as a function of dose and LET. Similarly to what we had previously reported for immortalized human cell lines [1], we observed a saturation of RIF number with dose at 4h post-irradiation, with more RIF/Gy for lower LET (X rays and 40Ar) compared to 56Fe. However at later time points (24h and above), the trend was inverted with more RIF/Gy for higher LET. Our data suggest that multiple DSBs cluster into RIF: as the linear density of DSBs increases with LET, so does the probability of having more DSBs per RIF, which makes it more difficult for cells to fully resolve high-LET-induced RIF, explaining the hypersensitivity to high-LET radiation despite a low number of RIF. Taking into account the amount of clustering at a given dose and LET, but also the kinetics of DNA damage repair, we introduced a novel mathematical formalism to evaluate the number of remaining RIF over time. We showed that the newly introduced kinetic metrics can be used as surrogate biomarkers for in vivo radiation toxicity, with potential applications in radiotherapy and human space exploration. In particular, we observed an association between the repairable fraction of RIF measured in vitro and survival levels of immune cells collected from irradiated mice. Moreover, the speed of DNA damage repair correlated with spontaneous cancer incidence data collected from the Mouse Tumor Biology database, suggesting a relationship between the efficiency of DSB repair after irradiation and cancer risk. In addition to the efficacy of repair and persistent RIF levels, even the amount of spontaneous foci without irradiation was shown to be strain dependent, indicating that these phenotypes are at least partially driven by genetics, and supporting their potential as indicators of individual radiation sensitivity. [1] Neumaier, T., et al., PNAS, 2012 (8) 109:443

Radiation, DNA damage, repair kinetics↗
NASA NTRSDate not supplied

Polarimeter + Lidar Derived Aerosol Particle Number Concentration

In this study, we propose a simple method to derive vertically resolved aerosol particle number concentration (Na) using combined polarimetric and lidar remote sensing observations. This method relies on accurate polarimeter retrievals of the fine-mode column-averaged aerosol particle extinction cross section and accurate lidar measurements of vertically resolved aerosol particle extinction coefficient such as those provided by multiwavelength high spectral resolution lidar. We compare the resulting lidar + polarimeter vertically resolved Na product to in situ Na data collected by airborne instruments during the NASA aerosol cloud meteorology interactions over the western Atlantic experiment (ACTIVATE). Based on all 35 joint ACTIVATE flights in 2020, we find a total of 32 collocated in situ and remote sensing profiles that occur on 11 separate days, which contain a total of 322 cloud-free vertically resolved altitude bins of 150 m resolution. We demonstrate that the lidar + polarimeter Na agrees to within 106% for 90% of the 322 vertically resolved points. We also demonstrate similar agreement to within 121% for the polarimeter-derived column-averaged Na. We find that the range-normalized mean absolute deviation (NMAD) for the polarimeter-derived column-averaged Na is 21%, and the NMAD for the lidar + polarimeter-derived vertically resolved Na is 16%. Taken together, these findings suggest that the error in the polarimeter-only column-averaged Na and the lidar + polarimeter vertically resolved Na are of similar magnitude and represent a significant improvement upon current remote sensing estimates of Na.

Aerosol number concentration↗
NASA NTRS1974

A computer program for plotting stress-strain data from compression, tension, and torsion tests of materials

A computer program for plotting stress-strain curves obtained from compression and tension tests on rectangular (flat) specimens and circular-cross-section specimens (rods and tubes) and both stress-strain and torque-twist curves obtained from torsion tests on tubes is presented in detail. The program is written in FORTRAN 4 language for the Control Data 6000 series digital computer with the SCOPE 3.0 operating system and requires approximately 110000 octal locations of core storage. The program has the capability of plotting individual strain-gage outputs and/or the average output of several strain gages and the capability of computing the slope of a straight line which provides a least-squares fit to a specified section of the plotted curve. In addition, the program can compute the slope of the stress-strain curve at any point along the curve. The computer program input and output for three sample problems are presented.

Greenbaum, A.↗
NASA NTRS1973

Inelastic Light Scattering Processes

Five different inelastic light scattering processes will be denoted by, ordinary Raman scattering (ORS), resonance Raman scattering (RRS), off-resonance fluorescence (ORF), resonance fluorescence (RF), and broad fluorescence (BF). A distinction between fluorescence (including ORF and RF) and Raman scattering (including ORS and RRS) will be made in terms of the number of intermediate molecular states which contribute significantly to the scattered amplitude, and not in terms of excited state lifetimes or virtual versus real processes. The theory of these processes will be reviewed, including the effects of pressure, laser wavelength, and laser spectral distribution on the scattered intensity. The application of these processes to the remote sensing of atmospheric pollutants will be discussed briefly. It will be pointed out that the poor sensitivity of the ORS technique cannot be increased by going toward resonance without also compromising the advantages it has over the RF technique. Experimental results on inelastic light scattering from I(sub 2) vapor will be presented. As a single longitudinal mode 5145 A argon-ion laser line was tuned away from an I(sub 2) absorption line, the scattering was observed to change from RF to ORF. The basis, of the distinction is the different pressure dependence of the scattered intensity. Nearly three orders of magnitude enhancement of the scattered intensity was measured in going from ORF to RF. Forty-seven overtones were observed and their relative intensities measured. The ORF cross section of I(sub 2) compared to the ORS cross section of N2 was found to be 3 x 10(exp 6), with I(sub 2) at its room temperature vapor pressure.

Fouche, Daniel G.↗
NASA NTRSDate not supplied

Cross-Measurement Comparisons for a CFD Validation Dataset on Mach 2.5 Axisymmetric Turbulent Shock-Wave/Boundary-Layer Interactions

Experimental data for a shock-wave/boundary-layer interaction has been collected using multiple measurement techniques. Unfortunately, diversity of methods for acquisition begets an aggregation of data which does not directly quantify the same properties of the flowfield. The objective in this paper was to (a) present the collection of flowfield measurements in one venue in a format more usable for those validating CFD models against the data, (b) evaluate the degree to which the experimental data support each other, and (c) highlight the differences and relative advantages/shortcomings of each measurement techniques. To present the various measured quantities into common format, CFD results from a companion paper also submitted for presentation at this meeting are utilized. For the case where the boundary layer remains attached, there is agreement between the various measurements as well as with Reynolds-averaged Navier-Stokes simulation solutions. As the impinging shock strength is increased beyond the point of separating the boundary layer, the congruity of the data wanes. Generally, agreement among the measurements exceeds the degree to which the CFD solutions agree with experiments. This suggests that unmodeled physical phenomena, such as transient motion of the reflected shock and separation bubble, give rise to the discrepancies observed in the computational results.

Shock-wave Boundary-layer interaction↗
NASA NTRS2003

Extratropical Stratosphere-Troposphere Mass Exchange

Global net mass flux between the troposphere and the stratosphere can be computed simply by estimating the heating rate along the 380K isentropic surface and the time rate of change of the lower most stratosphere (region between the tropopause and 380K). Given the net tropopause mass flux and the cross tropopause diabatic flux, the residual adiabatic mass flux can be estimated. These fluxes have been computed using three different meteorological data sets, the FVGCM and two assimilation data sets, FVDAS, and UKMO, using the 3.5 PVU defined tropopause. For all three data sets, the extratropical diabatic flux across the tropopause is generally to be larger than the net flux cross tropopause flux implying that there is a net extra-tropical adiabatic flux of air from the troposphere into the middle world stratosphere. This adiabatic flux is four to five times larger than the flux into the stratosphere across the tropical tropopause. For the FVDAS, the tropopause diabatic flux is smaller than UKMO as a result of colder tropopause temperatures. The difference in the diabatic mass fluxes by almost a factor of two between the two data assimilation meteorological analyses is much larger than the interannual variability in the UKMO or FVGCM data sets. Compared to radiosonde estimated tropopause temperatures, both data assimilation tropopause temperatures are warm biased due to a low bias in the tropopause heights. These comparisons point to the PV determination of the tropopause height as the source of the differences in the mass fluxes.

Schoeberl, Mark↗
NASA NTRS2012

Stereo and IMU-Assisted Visual Odometry for Small Robots

This software performs two functions: (1) taking stereo image pairs as input, it computes stereo disparity maps from them by cross-correlation to achieve 3D (three-dimensional) perception; (2) taking a sequence of stereo image pairs as input, it tracks features in the image sequence to estimate the motion of the cameras between successive image pairs. A real-time stereo vision system with IMU (inertial measurement unit)-assisted visual odometry was implemented on a single 750 MHz/520 MHz OMAP3530 SoC (system on chip) from TI (Texas Instruments). Frame rates of 46 fps (frames per second) were achieved at QVGA (Quarter Video Graphics Array i.e. 320 240), or 8 fps at VGA (Video Graphics Array 640 480) resolutions, while simultaneously tracking up to 200 features, taking full advantage of the OMAP3530's integer DSP (digital signal processor) and floating point ARM processors. This is a substantial advancement over previous work as the stereo implementation produces 146 Mde/s (millions of disparities evaluated per second) in 2.5W, yielding a stereo energy efficiency of 58.8 Mde/J, which is 3.75 better than prior DSP stereo while providing more functionality.

Source record↗
NASA NTRS2019

Forbush Decreases and < 2 Day GCR Flux Non-recurrent Variations Studied with LISA Pathfinder

Non-recurrent short-term variations of the galactic cosmic-ray (GCR) flux above 70 MeV n−1 were observed between 2016 February 18 and 2017 July 3 on board the European Space Agency LISA Pathfinder (LPF) mission orbiting around the Lagrange point L1 at 1.5 × 106 km from Earth. The energy dependence of three Forbush decreases is studied and reported here. A comparison of these observations with others carried out in space down to the energy of a few tens of MeV n−1 shows that the same GCR flux parameterization applies to events of different intensity during the main phase. FD observations in L1 with LPF and geomagnetic storm occurrence are also presented. Finally, the characteristics of GCR flux non-recurrent variations (peaks and depressions) of duration <2 days and their association with interplanetary structures are investigated. It is found that, most likely, plasma compression regions between subsequent corotating high-speed streams cause peaks, while heliospheric current sheet crossing causes the majority of the depressions.

M. Armano↗
NASA NTRS2022

Polarimeter + Lidar–Derived Aerosol Particle Number Concentration

In this study, we propose a simple method to derive vertically resolved aerosol particle number concentration (Na) using combined polarimetric and lidar remote sensing observations. This method relies on accurate polarimeter retrievals of the fine-mode column-averaged aerosol particle extinction cross section and accurate lidar measurements of vertically resolved aerosol particle extinction coefficient such as those provided by multiwavelength high spectral resolution lidar. We compare the resulting lidar + polarimeter vertically resolved N(a) product to in situ N(a) data collected by airborne instruments during the NASA aerosol cloud meteorology interactions over the western Atlantic experiment (ACTIVATE). Based on all 35 joint ACTIVATE flights in 2020, we find a total of 32 collocated in situ and remote sensing profiles that occur on 11separate days, which contain a total of 322 cloud-free vertically resolved altitude bins of 150 m resolution. We demonstrate that the lidar + polarimeter N(a) agrees to within 106% for 90% of the 322 vertically resolved points. We also demonstrate similar agreement to within 121% for the polarimeter-derived column-averaged N(a). We find that the range-normalized mean absolute deviation (NMAD) for the polarimeter-derived column-averaged Na is 21%, and the NMAD for the lidar + polarimeter-derived vertically resolved Na is 16%. Taken together, these findings suggest that the error in the polarimeter-only column-averaged N(a) and the lidar + polarimeter vertically resolved N(a) are of similar magnitude and represent a significant improvement upon current remote sensing estimates of N(a).

RSP↗
NASA NTRS1993

Structured adaptive grid generation using algebraic methods

The accuracy of the numerical algorithm depends not only on the formal order of approximation but also on the distribution of grid points in the computational domain. Grid adaptation is a procedure which allows optimal grid redistribution as the solution progresses. It offers the prospect of accurate flow field simulations without the use of an excessively timely, computationally expensive, grid. Grid adaptive schemes are divided into two basic categories: differential and algebraic. The differential method is based on a variational approach where a function which contains a measure of grid smoothness, orthogonality and volume variation is minimized by using a variational principle. This approach provided a solid mathematical basis for the adaptive method, but the Euler-Lagrange equations must be solved in addition to the original governing equations. On the other hand, the algebraic method requires much less computational effort, but the grid may not be smooth. The algebraic techniques are based on devising an algorithm where the grid movement is governed by estimates of the local error in the numerical solution. This is achieved by requiring the points in the large error regions to attract other points and points in the low error region to repel other points. The development of a fast, efficient, and robust algebraic adaptive algorithm for structured flow simulation applications is presented. This development is accomplished in a three step process. The first step is to define an adaptive weighting mesh (distribution mesh) on the basis of the equidistribution law applied to the flow field solution. The second, and probably the most crucial step, is to redistribute grid points in the computational domain according to the aforementioned weighting mesh. The third and the last step is to reevaluate the flow property by an appropriate search/interpolate scheme at the new grid locations. The adaptive weighting mesh provides the information on the desired concentration of points to the grid redistribution scheme. The evaluation of the weighting mesh is accomplished by utilizing the weight function representing the solution variation and the equidistribution law. The selection of the weight function plays a key role in grid adaptation. A new weight function utilizing a properly weighted boolean sum of various flowfield characteristics is defined. The redistribution scheme is developed utilizing Non-Uniform Rational B-Splines (NURBS) representation. The application of NURBS representation results in a well distributed smooth grid by maintaining the fidelity of the geometry associated with boundary curves. Several algebraic methods are applied to smooth and/or nearly orthogonalize the grid lines. An elliptic solver is utilized to smooth the grid lines if there are grid crossings. Various computational examples of practical interest are presented to demonstrate the success of these methods.

Yang, Jiann-Cherng↗
NASA NTRS1995

Three-dimensional position and shape of the bow shock and their variation with Alfvenic, sonic and magnetosonic Mach numbers and interplanetary magnetic field orientation

A large set of bow shock crossings (i.e., 1392) observed by 17 spacecraft has been used to explore the three-dimensional shape and location of the Earth's bow shock and its dependence on solar wind and interplanetary magnetic field (IMF) conditions. This study investigates deviations from gas dynamic flow models associated with the magnetic terms in the magnetohydrodynamic (MHD) equations. Empirical models predicting the statistical position and shape of the bow shock for arbitrary values of the solar wind pressure, IMF, and Alfvenic Mach number (M(sub A)) have been derived. The resulting data set has been used to fit three-dimensional bow shock surfaces and to explore the variations in these surfaces with sonic (M(sub S)), Alfvenic (M(sub A)) and magnetosonic (M(sub MS)) Mach numbers. Analysis reveals that among the three Mach numbers, M(sub A) provides the best ordering of the least square bow shock curves. The subsolar shock is observed to move Earthward while the flanks flare outward in response to decreasing M(sub A); the net change represents a 6-10% effect. Variations due to changes in the IMF orientation were investigated by rotating the crossings into geocentric interplanetary medium coordinates. Past studies have suggested that the north-south extent of the bow shock surface exceeds the east-west dimension due to asymmetries in the fast mode Mach cone. This study confirms such a north-south versus east-west asymmetry and quantifies its variation with M(sub S), M(sub A), M(sub MS), and IMF orientation. A 2-7% effect is measured, with the asymmetry being more pronounced at low Mach numbers. Combining the bow shock models with the magnetopause model of Roelof and Sibeck (1993), variations in the magnetosheath thickness at different local times are explored. The ratio of the bow shock size to the magnetopause size at the subpolar point is found to be 1.46; at dawn and dusk, the ratios are found to be 1.89 and 1.93, respectively. The subsolar magnetosheath thickness is used to derive the polytropic index gamma according to the empirical relation of Spreiter et al. (1966). The resulting gamma = 2.3 suggests the empirical formula is inadequate to describe the MHD interaction between the solar wind and the magnetosphere.

Peredo, M.↗