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NASA NTRS1994

A note on windowing for the waveform relaxation

The technique of windowing has been often used in the implementation of the waveform relaxations for solving ODE's or time dependent PDE's. Its efficiency depends upon problem stiffness and operator splitting. Using model problems, the estimates for window length and convergence rate are derived. The electiveness of windowing is then investigated for non-stiff and stiff cases respectively. lt concludes that for the former, windowing is highly recommended when a large discrepancy exists between the convergence rate on a time interval and the ones on its subintervals. For the latter, windowing does not provide any computational advantage if machine features are disregarded. The discussion is supported by experimental results.

Zhang, Hong↗

NASA NTRS1994

A Note on the Wave Action Density of a Viscous Instability Mode on a Laminar Free-shear Flow

Using the assumptions of an incompressible and viscous flow at large Reynolds number, we derive the evolution equation for the wave action density of an instability wave traveling on top of a laminar free-shear flow. The instability is considered to be viscous; the purpose of the present work is to include the cumulative effect of the (locally) small viscous correction to the wave, over length and time scales on which the underlying base flow appears inhomogeneous owing to its viscous diffusion. As such, we generalize our previous work for inviscid waves. This generalization appears as an additional (but usually non-negligible) term in the equation for the wave action. The basic structure of the equation remains unaltered.

Balsa, Thomas F.↗

NASA NTRS1994

A note on singularities of the 3-D Euler equation

In this paper, we consider analytic initial conditions with finite energy, whose complex spatial continuation is a superposition of a smooth background flow and a singular field. Through explicit calculation in the complex plane, we show that under some assumptions, the solution to the 3-D Euler equation ceases to be analytic in the real domain in finite time.

Tanveer, S.↗

NASA NTRS1994

Notes on rotating turbulence

This work investigates the turbulent constitutive relation when turbulence is subjected to solid body rotation. Laws regarding spectra and asymptotic decay of rotating homogeneous turbulence were confirmed through large-eddy simulation (LES) computations. Rotating turbulent flows exist in many industrial, geophysical, and astrophysical applications. From Lagrangian analysis a relation between turbulent stress and strain in rotating homogeneous turbulence was inferred. This relation was used to derive the spectral energy flux and, ultimately, the energy spectrum form. If the rotation wavenumber k(sub Omega) lies in the inertial subrange, then for wavenumbers less than k(sub Omega) the turbulence motions are affected by rotation and the energy spectrum slope is modified. Energy decay laws inferred in other reports and the present results suggest a modification of the epsilon model equation and eddy viscosity in k-epsilon models.

Zeman, Otto↗

NASA NTRS1995

A note on the angular Fourier transformation

It is demonstrated that an angular Fourier transformation is obtained by making a rotation around the non-compact axis of So(2,1), the Lorentz group in three dimensions.

Santhanam, Balu↗

NASA NTRS1994

Notes and correspondence: An alternative form for potential vorticity

A form of potential vorticity is described that has conversation properties similar to those of Ertel's potential vorticity (EPV) but removes the exponential variation with height displayed by EPV. This form is thus more suitable for inspecting vertical cross sections of potential vorticity and for use (with potential temperature) as a quasi-conserved coordinate in the analysis of chemical constituent data.

Lait, Leslie R.↗

NASA NTRS1994

A note on two-dimensional asymptotic magnetotail equilibria

In order to understand, on the fluid level, the structure, the time evolution, and the stability of current sheets, such as the magnetotail plasma sheet in Earth's magnetosphere, one has to consider magnetic field configurations that are in magnetohydrodynamic (MHD) force equilibrium. Any reasonable MHD current sheet model has to be two-dimensional, at least in an asymptotic sense (B(sub z)/B (sub x)) = epsilon much less than 1. The necessary two-dimensionality is described by a rather arbitrary function f(x). We utilize the free function f(x) to construct two-dimensional magnetotail equilibria are 'equivalent' to current sheets in empirical three-dimensional models. We obtain a class of asymptotic magnetotail equilibria ordered with respect to the magnetic disturbance index Kp. For low Kp values the two-dimensional MHD equilibria reflect some of the realistic, observation-based, aspects of three-dimensional models. For high Kp values the three-dimensional models do not fit the asymptotic MHD equlibria, which is indicative of their inconsistency with the assumed pressure function. This, in turn, implies that high magnetic activity levels of the real magnetosphere might be ruled by thermodynamic conditions different from local thermodynamic equilibrium.

Voigt, Gerd-Hannes↗

NASA NTRS1994

Correlated environmental corrections in TOPEX/POSEIDON, with a note on ionospheric accuracy

Estimates of the effectiveness of an altimetric correction, and interpretation of sea level variability as a response to atmospheric forcing, both depend upon assuming that residual errors in altimetric corrections are uncorrelated among themselves and with residual sea level, or knowing the correlations. Not surprisingly, many corrections are highly correlated since they involve atmospheric properties and the ocean surface's response to them. The full corrections (including their geographically varying time mean values), show correlations between electromagnetic bias (mostly the height of wind waves) and either atmospheric pressure or water vapor of -40%, and between atmospheric pressure and water vapor of 28%. In the more commonly used collinear differences (after removal of the geographically varying time mean), atmospheric pressure and wave height show a -30% correlation, atmospheric pressure and water vapor a -10% correlation, both pressure and water vapor a 7% correlation with residual sea level, and a bit surprisingly, ionospheric electron content and wave height a 15% correlation. Only the ocean tide is totally uncorrelated with other corrections or residual sea level. The effectiveness of three ionospheric corrections (TOPEX dual-frequency, a smoothed version of the TOPEX dual-frequency, and Doppler orbitography and radiopositioning integrated by satellite (DORIS) is also evaluated in terms of their reduction in variance of residual sea level. Smooth (90-200 km along-track) versions of the dual-frequency altimeter ionosphere perform best both globally and within 20 deg in latitude from the equator. The noise variance in the 1/s TOPEX inospheric samples is approximately (11 mm) squared, about the same as noise in the DORIS-based correction; however, the latter has its error over scales of order 10(exp 3) km. Within 20 deg of the equator, the DORIS-based correction adds (14 mm) squared to the residual sea level variance.

Zlotnicki, V.↗

NASA NTRS1995

Notes on the diversity of the properties of radio bursts observed on the nightside of Venus

We report on further studies of radio wave bursts detected by the Orbiting Electric Field Detector (OEFD) on the Pioneer Venus Orbiter (PVO) in the nightside ionosphere of Venus. We have tested a total of 25 cases of wave burst activity for evidence of whistler-mode propagation to the spacecraft from impulsive subionospheric sources. As in a previous study of 11 of these cases (Sonwalkar et al., 1991) we find at least two distinct classes of events, one, mostly involving bursts at 100 Hz only, that passes certain tests for whistler-mode propagation, and another, mostly involving bursts in two or more of the four PVO narrowband channels (at 100 Hz, 730 Hz, 5.4 kHz, and 30 kHz), that fails to pass the tests. The subionospheric lightning hypothesis continues to be tenable as a candidate explanation for many of the 100 Hz-only events, but its number of 100 Hz-only cases that do no pass all the applicable whistler-mode tests, as well as the existence at a wide range of altitudes of multichannel cases that are clearly not propagating whistler-mode waves. The wideband bursts are often observed at altitudes above 1000 km and frequently occur in regions of locally reduced electron density. Those observed at high altitude (and possibly low altitude as well) are believed to be generated near the spacecraft, possibly by an as yet unknown mechanism responsible for similar burst observations made near Earth and other planets.

Sonwalkar, Vikas S.↗

NASA NTRS1995

Note on use of slope diffraction coefficients for aperture antennas on finite ground planes

The use of slope diffraction coefficients along with regular diffraction coefficients for calculating the radiation patterns of aperture antennas in a finite ground plane is investigated. Explicit expressions for regular diffraction coefficients and slope diffraction coefficients are presented. The expressions for the incident magnetic field in terms of the magnetic current in the aperture are given. The slope of the incident magnetic field is calculated and closed form expressions are presented.

Cockrell, C. R.↗

NASA NTRS1996

A Note on Interfacing Object Warehouses and Mass Storage Systems for Data Mining Applications

Data mining is the automatic discovery of patterns, associations, and anomalies in data sets. Data mining requires numerically and statistically intensive queries. Our assumption is that data mining requires a specialized data management infrastructure to support the aforementioned intensive queries, but because of the sizes of data involved, this infrastructure is layered over a hierarchical storage system. In this paper, we discuss the architecture of a system which is layered for modularity, but exploits specialized lightweight services to maintain efficiency. Rather than use a full functioned database for example, we use light weight object services specialized for data mining. We propose using information repositories between layers so that components on either side of the layer can access information in the repositories to assist in making decisions about data layout, the caching and migration of data, the scheduling of queries, and related matters.

Grossman, Robert L.↗

NASA NTRS1996

A Note on Substructuring Preconditioning for Nonconforming Finite Element Approximations of Second Order Elliptic Problems

In this paper an algebraic substructuring preconditioner is considered for nonconforming finite element approximations of second order elliptic problems in 3D domains with a piecewise constant diffusion coefficient. Using a substructuring idea and a block Gauss elimination, part of the unknowns is eliminated and the Schur complement obtained is preconditioned by a spectrally equivalent very sparse matrix. In the case of quasiuniform tetrahedral mesh an appropriate algebraic multigrid solver can be used to solve the problem with this matrix. Explicit estimates of condition numbers and implementation algorithms are established for the constructed preconditioner. It is shown that the condition number of the preconditioned matrix does not depend on either the mesh step size or the jump of the coefficient. Finally, numerical experiments are presented to illustrate the theory being developed.

Maliassov, Serguei↗

NASA NTRS1996

A Note on Multigrid Theory for Non-nested Grids and/or Quadrature

We provide a unified theory for multilevel and multigrid methods when the usual assumptions are not present. For example, we do not assume that the solution spaces or the grids are nested. Further, we do not assume that there is an algebraic relationship between the linear algebra problems on different levels. What we provide is a computationally useful theory for adaptively changing levels. Theory is provided for multilevel correction schemes, nested iteration schemes, and one way (i.e., coarse to fine grid with no correction iterations) schemes. We include examples showing the applicability of this theory: finite element examples using quadrature in the matrix assembly and finite volume examples with non-nested grids. Our theory applies directly to other discretizations as well.

Douglas, C. C.↗

NASA NTRS1998

A Note on Kinetic Energy, Dissipation and Enstrophy

The dissipation rate of a Newtonian fluid with constant shear viscosity can be shown to include three constituents: dilatation, vorticity, and surface strain. The last one is found to make no contributions to the change of kinetic energy. These dissipation constituents arc used to identify typical compact turbulent flow structures at high Reynolds numbers. The incompressible version of the simplified kinetic-energy equation is then cast to a novel form, which is free from the work rate done by surface stresses but in which the full dissipation re-enters.

Wu, Jie-Zhi↗

NASA NTRS1998

Programmable Logic Application Notes

This column will be provided each quarter as a source for reliability, radiation results, NASA capabilities, and other information on programmable logic devices and related applications. This quarter's column will include some announcements and some recent radiation test results and evaluations of interest. Specifically, the following topics will be covered: the Military and Aerospace Applications of Programmable Devices and Technologies Conference to be held at GSFC in September, 1998, proton test results, heavy ion test results, and some total dose results.

Katz, Richard↗

NASA NTRS1995

A Note on the Barotropic Response of Sea Level to Time-Dependent Wind Forcing

This study examines the extent to which sea level variations at periods between 30 days and 1 year and spatial scales greater than 1000 km can be described by the wind- driven linear barotropic vorticity dynamics. The TOPEX/POSEIDON altimetric observations of sea level and the wind products of the National Meteorological Center are used as the database for the study. Each term of the linear barotropic vorticity equation was evaluated by averaging over regions of 10 deg x 10 deg. In most of the open ocean the result of the analysis suggests that the sea level variabilities at the scales considered cannot be fully described by the equation; the apparent net vorticity change is more than what can be explained by the local wind stress curl. In the few regions where the wind stress curl is strong enough to balance the vorticity budget, predominantly in the northeast Pacific and the southeast Pacific, the balance is basically achieved in terms of the time-dependent topographic Sverdrup relation, namely, the balance between the advection of the planetary vorticity plus the topography-induced vorticity and the forcing by the wind stress curl.

Fu, Lee-Lueng↗

NASA NTRS1999

Programmable Logic Application Notes

This column will be provided each quarter as a source for reliability, radiation results, NASA capabilities, and other information on programmable logic devices and related applications. This quarter the focus is on some experimental data on low voltage drop out regulators to support mixed 5 and 3.3 volt systems. A discussion of the Small Explorer WIRE spacecraft will also be given. Lastly, we show take a first look at robust state machines in Hardware Description Languages (VHDL) and their use in critical systems. If you have information that you would like to submit or an area you would like discussed or researched, please give me a call or e-mail.

Katz, Richard↗

NASA NTRS1998

Programmable Logic Application Notes

Katz, Richard↗