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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
NASA NTRS2012

The Validity Chlorophyll-a Estimation by Sun Induced Fluorescence in Estuarine Waters: An Analysis of Long-term (2003-2011) Water Quality Data from Tampa Bay, Florida (USA)

Satellite observation of phytoplankton concentration or chlorophyll-a is an important characteristic, critically integral to monitoring coastal water quality. However, the optical properties of estuarine and coastal waters are highly variable and complex and pose a great challenge for accurate analysis. Constituents such as suspended solids and dissolved organic matter and the overlapping and uncorrelated absorptions in the blue region of the spectrum renders the blue-green ratio algorithms for estimating chlorophyll-a inaccurate. Measurement of sun-induced chlorophyll fluorescence, on the other hand, which utilizes the near infrared portion of the electromagnetic spectrum, may provide a better estimate of phytoplankton concentrations. While modelling and laboratory studies have illustrated both the utility and limitations of satellite baseline algorithms based on the sun induced chlorophyll fluorescence signal, few have examined the empirical validity of these algorithms using a comprehensive long term in situ data set. In an unprecedented analysis of a long term (2003-2011) in situ monitoring data from Tampa Bay, Florida (USA), we assess the validity of the FLH product from the Moderate Resolution Imaging Spectrometer (MODIS) against chlorophyll ]a and a suite of water quality parameters taken in a variety of conditions throughout a large optically complex estuarine system. A systematic analysis of sampling sites throughout the bay is undertaken to understand how the relationship between FLH and in situ chlorophyll-a responds to varying conditions within the estuary including water depth, distance from shore and structures and eight water quality parameters. From the 39 station for which data was derived, 22 stations showed significant correlations when the FLH product was matched with in situ chlorophyll-alpha data. The correlations (r2) for individual stations within Tampa Bay ranged between 0.67 (n=28, pless than 0.01) and-0.457 (n=12, p=.016), indicating that for some areas within the Bay, FLH can be a good predictor of chlorophyll-alpha concentration and hence a useful tool for the analysis of water quality. Overall, the results show a 106% increase in the validity of chlorophyll -a concentration estimates using FLH over the standard the blue-green OC3M algorithm. This analysis also illustrates that the correlations between FLH and in situ chlorophyll -a measurements increases with increasing water depth and distance of the monitoring sites from both the shore and structures. However, due to confounding factors related to the complexity of the estuarine system, a linear improvement in the FLH to chlorophyll ]a relationship was not clearly noted with increasing depth and distance from shore alone. Correlations of FLH with turbidity, nutrients (total nitrogen and total phosphorous) biological oxygen demand, salinity, sea surface temperature correlated positively with FLH concentrations, while dissolved oxygen and pH showed negative correlations. Principle component analyses are employed to further describe the relationships between the multivariate water quality parameters and the FLH product. The majority of sites with higher and very significant correlations (pless than 0.01) also showed high correlation values for nutrients, turbidity and biological oxygen demand. These sites were on average in greater than seven meters of water and over five kilometers from shore. A thorough understanding of the relationship between the MODIS FLH product and in situ water quality parameters will enhance our understanding of the accuracy MODIS fs global FLH algorithm and assist in optimizing its calibration for use in monitoring the quality of estuarine and coastal waters worldwide.

Moreno-Madrinan, Max Jacobo↗
NASA NTRSDate not supplied

Novel Turbulence Model Tailored for Complex Rocket Motor Exhaust Jets

This paper describes a new RANS turbulence model intended to give improved accuracy in turbulence that is affected by compressibility, rotation and curvature, and variable density, making it well-suited to complex rocket motor exhaust jets. Four key elements of the model are: the use of simple-averaged (not mass-averaged) turbulence decomposition; a second-order Taylor series for the equilibrated turbulent fluxes; empirical modeling that accounts for the combined effects of aforementioned turbulence modifiers; and model tuning on large-eddy simulation data for mixing layers for a wide range of these turbulence modifiers. The model is implemented as an extension of the k-w SST model. Results include comparisons to detached eddy simulation results for hot and cold co-flowing exhaust jets, and to experimental data for supersonic retropropulsion on the CobraMRV Mars-lander concept vehicle. The model is named TMRC for its constituents elements, the Taylor series with Mach number, rotation and curvature effects.

turbulence modeling↗
NASA NTRS1999

Aerodynamic Analysis of Multistage Turbomachinery Flows in Support of Aerodynamic Design

This paper summarizes the state of 3D CFD based models of the time average flow field within axial flow multistage turbomachines. Emphasis is placed on models which are compatible with the industrial design environment and those models which offer the potential of providing credible results at both design and off-design operating conditions. The need to develop models which are free of aerodynamic input from semi-empirical design systems is stressed. The accuracy of such models is shown to be dependent upon their ability to account for the unsteady flow environment in multistage turbomachinery. The relevant flow physics associated with some of the unsteady flow processes present in axial flow multistage machinery are presented along with procedures which can be used to account for them in 3D CFD simulations. Sample results are presented for both axial flow compressors and axial flow turbines which help to illustrate the enhanced predictive capabilities afforded by including these procedures in 3D CFD simulations. Finally, suggestions are given for future work on the development of time average flow models.

Adamczyk, John J.↗
NASA NTRS2024

Turbulence Model Validation through Joint Experimental / Computational Studies of Separated Flow Over a Three-Dimensional Tapered Bump: Part II - Computational Investigation

This report serves as documentation of activities related to Computational Fluid Dynamics (CFD) analysis applied to the Smooth Body Separation Experiment designed to produce validation-quality experimental data from wind-tunnel tests performed at the University of Notre Dame. All CFD analysis utilized the Boeing CFD (BCFD) flow solver. BCFD was used to analyze flow over the Boeing Speed Bump with second-order accuracy in space and time. Inviscid fluxes were computed using the HLLE scheme for steady-state simulations, and the Low-Dissipation Roe scheme for time-accurate simulations. The working fluid was modeled as calorically perfect air using Sutherland's law for viscosity. Thermal diffusivity was determined by assuming a constant molecular Prandtl number of 0.72, and a turbulent Prandtl number of 0.9. Reynolds Averaged Navier-Stokes (RANS) simulations were conducted using the one-equation Spalart-Allmaras turbulence model with rotation correction3 and the quadratic constitutive relation (SA-RC-QCR), as well as Menter's two-equation, Shear-Stress Transport (SST) model. Time-accurate computations were conducted using Delayed Detached eddy Simulation (DDES) with the one-equation RANS model, and Large Eddy Stress balance (LESb) with the two-equation RANS model. Implicit dual-time stepping was used to achieve second-order temporal accuracy. The experimental investigation conducted during the course of this study is described in detail in an accompanying report.

Flow separation↗
NASA NTRS1973

A numerical method for determining the temperature structure of planetary atmospheres.

A numerical method for calculating the time-average, vertical temperature structure of planetary atmospheres is presented. It is assumed that the atmospheres are in radiative-convective equilibrium, which is a good first approximation to many situations. Numerical tests of the rate of convergence and accuracy of the answer are presented. The method can readily handle molecular sources of opacity. Accurate results can be obtained with a minimum of computer time, because the number of iterations needed (about 4) is small and the number of pressure levels at which the net flux needs to be evaluated (about 10) is small. As an application of this procedure, some model atmospheres of Jupiter are calculated.

Pollack, J. B.↗
NASA NTRS1975

Monitoring physical and chemical parameters of Delaware Bay waters with an ERTS-1 data collection platform

The author has identified the following significant results. Results of the analysis of data collected during the summer of 1974 demonstrate that the ERTS Data Collection Platform (DCP) is quite responsive to changing water parameters and that this information can be successfully transmitted under all weather conditions. The monitoring of on-site probe outputs reveals a rapid response to changing water temperature, salinity, and turbidity conditions on incoming tides as the tidal salt wedge passes the probe location. The changes in water properties were corroborated by simultaneously sampling the water for subsequent laboratory analysis. Fluctuations observed in the values of salinity, conductivity, temperature and water depth over short time intervals were extremely small. Due to the nature of the probe, 10% to 20% fluctuations were observed in the turbidity values. The use of the average of the values observed during an overpass provided acceptable results. Good quality data was obtained from the satellite on each overpass regardless of weather conditions. Continued use of the DCP will help provide an indication of the accuracy of the probes and transmission system during long term use.

Klemas, V.↗
NASA NTRS1976

Signature extension through the application of cluster matching algorithms to determine appropriate signature transformations

Signature extension is intended to increase the space-time range over which a set of training statistics can be used to classify data without significant loss of recognition accuracy. A first cluster matching algorithm MASC (Multiplicative and Additive Signature Correction) was developed at the Environmental Research Institute of Michigan to test the concept of using associations between training and recognition area cluster statistics to define an average signature transformation. A more recent signature extension module CROP-A (Cluster Regression Ordered on Principal Axis) has shown evidence of making significant associations between training and recognition area cluster statistics, with the clusters to be matched being selected automatically by the algorithm.

Lambeck, P. F.↗
NASA NTRS1986

Precision attitude determination and control using gyros and earth sensor

A novel scheme to estimate the biases present in the gyros and the attitude of three-axis stabilized earth pointing spacecraft using the outputs of gyros and earth sensor is presented. The earth sensor pitch output is averaged every orbit to provide pitch gyro bias correction. Roll and yaw gyro biases are determined by averaging the earth sensor roll output every quarter orbit and suitably combining the four quarter orbit averages obtained in each orbit. Yaw attitude information is also required once every orbit. Simulation studies including error sources due to earth sensor, gyros, yaw sensor and horizon radiance uncertainty in the winter poles showed that attitude determination accuracy of 0.01-0.03 deg (3 sigma) can be achieved about all the axes.

Rajaram, S.↗
NASA NTRS1987

A task-based metric for telerobotic performance assessment

A methodology is described for developing a task complexity index based on combining the six basic motion primitives (three translation, three orientation) with force control and accuracy requirements. The result of this development is a set of complexity values that can be assigned to the high-level task primitives derived from a relatively shallow top-down mission analysis. These values are then averaged to arrive at total average mission complexities, such as for the mission of exchanging the Hubble Space Telescope (HST) battery modules. Application of this metric to a candidate set of NASA Flight Telerobotic Servicer evaluation tasks is discussed using the HST battery module mission for an in-depth example.

Barnes, J. F.↗
NASA NTRS2004

The Southern Hemisphere Additional Ozonesondes (SHADOZ) 1998-2002 Tropical Ozone Climatology: Instrumentation and Station-to-Station Variability - 3

Abstract: Since 1998 the Southern Hemisphere ADditional OZonesondes (SHADOZ) project has collected more than 2000 ozone profiles from a dozen tropical and subtropical sites using balloon-borne electrochemical concentration cell (ECC) ozonesondes. The data (with accompanying pressure-temperature-humidity soundings) are archived. Analysis of ozonesonde imprecision within the SHADOZ dataset revealed that variations in ozonesonde technique could lead to station-to-station biases in the measurements. In this paper imprecisions and accuracy in the SHADOZ dataset are examined in light of new data. When SHADOZ total ozone column amounts are compared to version 8 TOMS (2004 release), discrepancies between sonde and satellite datasets decline 1-2 percentage points on average, compared to version 7 TOMS. Variability among stations is evaluated using total ozone normalized to TOMS and results of laboratory tests on ozonesondes (JOSE-2O00, Julich Ozonesonde Intercomparison Experiment). Ozone deviations from a standard instrument in the JOSE flight simulation chamber resemble those of SHADOZ station data relative to a SHADOZ-defined climatological reference. Certain systematic variations in SHADOZ ozone profiles are accounted for by differences in solution composition, data processing and instrument (manufacturer). Instrument bias leads to a greater ozone measurement above 25 km over Nairobi and to lower total column ozone at three Pacific sites compared to other SHADOZ stations at 0-20 deg.S.

Thompson, Anne M.↗
NASA NTRS2018

How Can TOLNet Help to Better Understand Tropospheric Ozone? A Satellite Perspective

Potential sources of a priori ozone (O3) profiles for use in Tropospheric Emissions: Monitoring of Pollution (TEMPO) satellite tropospheric O3 retrievals are evaluated with observations from multiple Tropospheric Ozone Lidar Network (TOLNet) systems in North America. An O3 profile climatology (tropopause-based O3 climatology (TB-Clim), currently proposed for use in the TEMPO O3 retrieval algorithm) derived from ozonesonde observations and O3 profiles from three separate models (operational Goddard Earth Observing System (GEOS-5) Forward Processing (FP) product, reanalysis product from Modern-Era Retrospective analysis for Research and Applications version 2 (MERRA2), and the GEOS-Chem chemical transport model (CTM)) were: 1) evaluated with TOLNet measurements on various temporal scales (seasonally, daily, hourly) and 2) implemented as a priori information in theoretical TEMPO tropospheric O3 retrievals in order to determine how each a priori impacts the accuracy of retrieved tropospheric (0-10 km) and lowermost tropospheric (LMT, 0-2 km) O3 columns. We found that all sources of a priori O3 profiles evaluated in this study generally reproduced the vertical structure of summer-averaged observations. However, larger differences between the a priori profiles and lidar observations were observed when evaluating inter-daily and diurnal variability of tropospheric O3. The TB-Clim O3 profile climatology was unable to replicate observed inter-daily and diurnal variability of O3 while model products, in particular GEOS-Chem simulations, displayed more skill in reproducing these features. Due to the ability of models, primarily the CTM used in this study, on average to capture the inter-daily and diurnal variability of tropospheric and LMT O3 columns, using a priori profiles from CTM simulations resulted in TEMPO retrievals with the best statistical comparison with lidar observations. Furthermore, important from an air quality perspective, when high LMT O3 values were observed, using CTM a priori profiles resulted in TEMPO LMT O3 retrievals with the least bias. The application of time-specific (non-climatological) hourly/daily model predictions as the a priori profile in TEMPO O3 retrievals will be best suited when applying this data to study air quality or event-based processes as the standard retrieval algorithm will still need to use a climatology product. Follow-on studies to this work are currently being conducted to investigate the application of different CTM-predicted O3 climatology products in the standard TEMPO retrieval algorithm. Finally, similar methods to those used in this study can be easily applied by TEMPO data users to recalculate tropospheric O3 profiles provided from the standard retrieval using a different source of a priori.

Satellite↗
NASA NTRS2020

Passive Thermal Control of the Primordial Inflation Polarization Explorer (PIPER) Flight Electronics

The scientific balloon program at NASA offers an exciting and open area of opportunity for testing new technologies and for conducting meaningful experimentation at a fraction of the cost of a space mission. This paper outlines a simple thermal model developed and employed for the Primordial Inflation Polarization ExplorER (PIPER). The sub-orbital environment that PIPER operates in hosts an interesting mix of atmospheric and space thermal challenges. The work done was to mitigate thermal loads and passively cool the payload's exterior mounted electronics at an altitude of 36.6 km. This was done by characterizing the thermal environment and then designing solutions for the heat loads through a combined radiation and conduction passive cooling radiator system thermal model. Despite the simplicity and subsequent limitations of the model, as well as some unexpected payload operational events, the model produced results between 0.31% and 11.8% difference between the predicted values and measured average temperatures. From these results, the model was able to successfully provide estimates for the electronics temperatures. Additional flights will be needed to eliminate unknowns encountered in this flight in order to further refine the model for higher accuracy.

Walts, Alexander R.↗
NASA NTRSDate not supplied

USM3D-ME Contributions to the 5th AIAA High Lift Prediction Workshop

This paper presents the results of Reynolds-averaged Navier-Stokes (RANS) simulations conducted by the NASA flow solver, mixed-element USM3D (USM3D-ME), for the 5th AIAA High-Lift Prediction Workshop. As part of the Fixed-Grid RANS Technology Focus Group (TFG), these simulations were performed to assess the accuracy and efficiency of the USM3D-ME solutions in predicting high-lift flows. The High-Lift Common Research Model (CRM-HL) served as the primary geometry. Several CRM-HL configurations were used for three case studies: a verification study (Case 1), a configuration buildup study (Case 2), and a Reynolds-number variation study (Case 3). Overall, USM3D-ME RANS results aligned with the solutions selected by the Fixed-Grid RANS TFG and available wind tunnel data. Simulations for Case 1 and Configuration 2.1 achieved machine-zero residual convergence, with aerodynamic coefficients converging to steady-state values. However, Configurations 2.2-2.4 and Case 3 encountered iterative- and grid-convergence challenges, particularly at high angles of attack. Compared with the experimental data available for Configurations 2.2-2.4, close agreement was demonstrated at low angles of attack. However, for angles of attack approaching the maximum lift conditions, the predicted lift coefficient and pitching moment deviated from experimental values. The drag-coefficient predictions were in relatively good agreement, however, slight overpredictions were observed at the highest angle of attack corresponding to the maximum-lift condition. Although iterative convergence for Configurations 2.2-2.4 at high angles of attack remains a persistent challenge, averaging aerodynamic coefficients over the last 5000 iterations yielded satisfactory agreement with the available wind tunnel experimental data. During the workshop, the lack of iterative convergence was attributed to the vortex structures emanating from the slat brackets. To investigate this issue further, post-workshop simulations were conducted on Configuration 2.2. In one study, RANS simulations were performed on a simplified geometry with the slat brackets removed. The second study focused on performing unsteady RANS (URANS) simulations on the original Configuration 2.2 geometry. Preliminary results from both studies are presented and compared with wind tunnel data for Configuration 2.2. Consistent with the findings of other participants in the Fixed-Grid RANS TFG, this study emphasizes the necessity for further exploration and advancement in RANS technology for predicting high-lift flows.

Aerodynamics↗
NASA NTRSDate not supplied

USM3D-ME Contributions to the 5th AIAA High Lift Prediction Workshop

This paper presents the results of Reynolds-averaged Navier-Stokes (RANS) simulations conducted by NASA’s flow solver, mixed-element USM3D (USM3D-ME), for the 5th AIAA High-Lift Prediction Workshop. As part of the Fixed-Grid RANS Technology Focus Group (TFG), these simulations were performed to assess the accuracy and efficiency of the USM3D-ME solutions in predicting high-lift flows. The High-Lift Common Research Model (CRM-HL) served as the primary geometry. Several CRM-HL configurations were used for three case studies: a verification study (Case 1), a configuration buildup study (Case 2), and a Reynolds-number variation study (Case 3). Overall, USM3D-ME RANS results aligned with the solutions selected by the Fixed-Grid RANS TFG and available wind tunnel data Simulations for Cases 1 and Configuration 2.1 achieved machine-zero residual convergence, with aerodynamic coefficients converging to steady-state values. However, Configurations 2.2-2.4 and Case 3 encountered iterative- and grid-convergence challenges, particularly at high angles of attack. Compared with the experimental data available for Configurations 2.2-2.4, close agreement was demonstrated at low angles of attack. However, for angles of attack approaching the maximum lift conditions, the predicted lift coefficient and pitching moment deviated from experimental values. The drag-coefficient predictions were in a relatively good agreement, however, slight overpredictions were observed at the highest angle of attack corresponding to the maximum-lift condition. Although iterative convergence for Configurations 2.2-2.4 at high angles of attack remains a persistent challenge, averaging aerodynamic coefficients over the last 5000 iterations yielded satisfactory agreement with the available wind tunnel experimental data. During the workshop, the lack of iterative convergence was attributed to the vortex structures emanating from the slat brackets. To investigate this issue further, post-workshop simulations were conducted on Configuration 2.2. In one study, RANS simulations were performed on a simplified geometry with the slat brackets removed. The second study focused on performing URANS simulations on the original Configuration 2.2 geometry. Preliminary results from both studies are presented and compared with wind tunnel data for Configuration 2.2. Consistent with the findings of other participants in the Fixed-Grid RANS TFG, this study emphasizes the necessity for further exploration and advancement in RANS technology for predicting high-lift flows.

CFD↗
NASA NTRS2016

Soil Moisture Active Passive Mission L4_SM Data Product Assessment (Version 2 Validated Release)

During the post-launch SMAP calibration and validation (Cal/Val) phase there are two objectives for each science data product team: 1) calibrate, verify, and improve the performance of the science algorithm, and 2) validate the accuracy of the science data product as specified in the science requirements and according to the Cal/Val schedule. This report provides an assessment of the SMAP Level 4 Surface and Root Zone Soil Moisture Passive (L4_SM) product specifically for the product's public Version 2 validated release scheduled for 29 April 2016. The assessment of the Version 2 L4_SM data product includes comparisons of SMAP L4_SM soil moisture estimates with in situ soil moisture observations from core validation sites and sparse networks. The assessment further includes a global evaluation of the internal diagnostics from the ensemble-based data assimilation system that is used to generate the L4_SM product. This evaluation focuses on the statistics of the observation-minus-forecast (O-F) residuals and the analysis increments. Together, the core validation site comparisons and the statistics of the assimilation diagnostics are considered primary validation methodologies for the L4_SM product. Comparisons against in situ measurements from regional-scale sparse networks are considered a secondary validation methodology because such in situ measurements are subject to up-scaling errors from the point-scale to the grid cell scale of the data product. Based on the limited set of core validation sites, the wide geographic range of the sparse network sites, and the global assessment of the assimilation diagnostics, the assessment presented here meets the criteria established by the Committee on Earth Observing Satellites for Stage 2 validation and supports the validated release of the data. An analysis of the time average surface and root zone soil moisture shows that the global pattern of arid and humid regions are captured by the L4_SM estimates. Results from the core validation site comparisons indicate that "Version 2" of the L4_SM data product meets the self-imposed L4_SM accuracy requirement, which is formulated in terms of the ubRMSE: the RMSE (Root Mean Square Error) after removal of the long-term mean difference. The overall ubRMSE of the 3-hourly L4_SM surface soil moisture at the 9 km scale is 0.035 cubic meters per cubic meter requirement. The corresponding ubRMSE for L4_SM root zone soil moisture is 0.024 cubic meters per cubic meter requirement. Both of these metrics are comfortably below the 0.04 cubic meters per cubic meter requirement. The L4_SM estimates are an improvement over estimates from a model-only SMAP Nature Run version 4 (NRv4), which demonstrates the beneficial impact of the SMAP brightness temperature data. L4_SM surface soil moisture estimates are consistently more skillful than NRv4 estimates, although not by a statistically significant margin. The lack of statistical significance is not surprising given the limited data record available to date. Root zone soil moisture estimates from L4_SM and NRv4 have similar skill. Results from comparisons of the L4_SM product to in situ measurements from nearly 400 sparse network sites corroborate the core validation site results. The instantaneous soil moisture and soil temperature analysis increments are within a reasonable range and result in spatially smooth soil moisture analyses. The O-F residuals exhibit only small biases on the order of 1-3 degrees Kelvin between the (re-scaled) SMAP brightness temperature observations and the L4_SM model forecast, which indicates that the assimilation system is largely unbiased. The spatially averaged time series standard deviation of the O-F residuals is 5.9 degrees Kelvin, which reduces to 4.0 degrees Kelvin for the observation-minus-analysis (O-A) residuals, reflecting the impact of the SMAP observations on the L4_SM system. Averaged globally, the time series standard deviation of the normalized O-F residuals is close to unity, which would suggest that the magnitude of the modeled errors approximately reflects that of the actual errors. The assessment report also notes several limitations of the "Version 2" L4_SM data product and science algorithm calibration that will be addressed in future releases. Regionally, the time series standard deviation of the normalized O-F residuals deviates considerably from unity, which indicates that the L4_SM assimilation algorithm either over- or under-estimates the actual errors that are present in the system. Planned improvements include revised land model parameters, revised error parameters for the land model and the assimilated SMAP observations, and revised surface meteorological forcing data for the operational period and underlying climatological data. Moreover, a refined analysis of the impact of SMAP observations will be facilitated by the construction of additional variants of the model-only reference data. Nevertheless, the “Version 2” validated release of the L4_SM product is sufficiently mature and of adequate quality for distribution to and use by the larger science and application communities.

SMAP L4_SM↗
NASA NTRS1976

Earth rotation measured by lunar laser ranging

The estimated median accuracy of 194 single-day determinations of the earth's angular position in space is 0.7 millisecond (0.01 arc second). Comparison with classical astronomical results gives agreement to about the expected 2-millisecond uncertainty of the 5-day averages obtained by the Bureau International de l'Heure. Little evidence for very rapid variations in the earth's rotation is present in the data.

Stolz, A.↗
NASA NTRS1982

High-accuracy linear and circular polarization measurements at 21 cm

New high-accuracy linear and circular polarization measurements have been obtained for 27 small-diameter radio sources, using the Westerbork Synthesis Radio Telescope at 21 cm (1415 MHz). From these and other observed properties of the sources, estimates of the average internal magnetic field strengths in the sources are made by applying the uniform synchrotron emission model to the measured circular polarization and by using equipartition arguments. These two values are compared and found to be in agreement to within an order of magnitude, as was previously found by Weiler and de Pater (1980). Also, the magnetic fields estimated from circular polarization measurements at two different wavelengths (49 and 21 cm) are compared and found to be in rough agreement, but with indications of differences between variable and nonvariable sources. A comparison of the magnitudes of linear and circular polarization in sources shows no correlations.

De Pater, I.↗
NASA NTRS1993

On the cross-stream spectral method for the Orr-Sommerfeld equation

Cross-stream models are defined as solutions to the Orr-Sommerfeld equation which are propagating normal to the flow direction. These models are utilized as a basis for a Hilbert space to approximate the spectrum of the Orr-Sommerfeld equation with plane Poiseuille flow. The cross-stream basis leads to a standard eigenvalue problem for the frequencies of Poiseuille flow instability waves. The coefficient matrix in the eigenvalue problem is shown to be the sum of a real matrix and a negative-imaginary diagonal matrix which represents the frequencies of the cross-stream modes. The real coefficient matrix is shown to approach a Toeplitz matrix when the row and column indices are large. The Toeplitz matrix is diagonally dominant, and the diagonal elements vary inversely in magnitude with diagonal position. The Poiseuille flow eigenvalues are shown to lie within Gersgorin disks with radii bounded by the product of the average flow speed and the axial wavenumber. It is shown that the eigenvalues approach the Gersgorin disk centers when the mode index is large, so that the method may be used to compute spectra with an essentially unlimited number of elements. When the mode index is large, the real part of the eigenvalue is the product of the axial wavenumber and the average flow speed, and the imaginary part of the eigen value is identical to the corresponding cross-stream mode frequency. The cross-stream method is numerically well-conditioned in comparison to Chebyshev based methods, providing equivalent accuracy for small mode indices and superior accuracy for large indices.

Zorumski, William E.↗