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NASA NTRS1986

Time-dependent profiles of lava flows

This work investigates the combined effects of a time-dependent effusion rate and a spatially varying viscosity on the thickness profile of a flowing lava. Relatively simple governing equations are formulated as a primitive dynamical model for these two influences on lava flow morphology. Free boundary solutions for the profile of the flow and its extent are presented and analyzed for different boundary conditions at the source of the flow and several models for the spatial dependence of the viscosity. The results presented here suggest that time dependence in the flow depth at the source and the form of the viscosity variation are significant influences on the morphology and dimensions of lava flows. Moreover, this analysis implies that time-dependent source conditions may contribute to the scatter in plots of eruption rate versus flow length and disparities between field and laboratory estimates of lava viscosity.

Baloga, Stephen↗
NASA NTRS1980

Time-dependent difference theory for noise propagation in a two-dimensional duct

A time-dependent numerical formulation is derived for sound propagation in a two-dimensional straight soft-walled duct in the absence of mean flow. The time-dependent governing acoustic-difference equations and boundary conditions are developed along with the maximum stable time increment. Example calculations are presented for sound attenuation in hard- and soft-wall ducts. The time-dependent analysis has been found to be superior to the conventional steady numerical analysis because of much shorter solution times and the elimination of matrix storage requirements.

Baumeister, K. J.↗
NASA NTRS1990

Time-dependent shock acceleration of energetic electrons including synchrotron losses

The present investigation of the time-dependent particle acceleration problem in strong shocks, including synchrotron radiation losses, solves the transport equation analytically by means of Laplace transforms. The particle distribution thus obtained is then transformed numerically into real space for the cases of continuous and impulsive injections of particles at the shock. While in the continuous case the steady-state spectrum undergoes evolution, impulsive injection is noted to yield such unpredicted features as a pile-up of high-energy particles or a steep power-law with time-dependent spectral index. The time-dependent calculations reveal varying spectral shapes and more complex features for the higher energies which may be useful in the interpretation of outburst spectra.

Fritz, Klaus-Dieter↗
NASA NTRS1975

UV stars and the interstellar medium - A statistical time-dependent model

A statistical time-dependent model for the effects on the interstellar gas of the ionizing radiation from UV stars is presented. The radiation from the stars is assumed to be emitted as monochromatic bursts at random times and locations. The thermal and ionization history of the gas is followed in a Monte Carlo simulation. Probability densities as well as mean values for the ionization fraction, temperature, and other observable quantities are derived. The fluctuations in observed quantities due to the stochastic nature of the model are estimated. Models of the interstellar medium perpendicular to the galactic plane are developed and compared with observations. The action of the UV stars can explain the bulk properties of the interstellar gas toward the galactic poles and is consistent with the Copernicus satellite observations toward lambda Scorpii.

Lyon, J.↗
NASA NTRS2001

Parametric Study of a YAV-8B Harrier in Ground Effect Using Time-Dependent Navier-Stokes Computations

Flow simulations using the time-dependent Navier-Stokes equations remain a challenge for several reasons. Principal among them are the difficulty to accurately model complex flows, and the time needed to perform the computations. A parametric study of such complex problems is not considered practical due to the large cost associated with computing many time-dependent solutions. The computation time for each solution must be reduced in order to make a parametric study possible. With successful reduction of computation time, the issue of accuracy, and appropriateness of turbulence models will become more tractable.

Shishir, Pandya↗
NASA NTRS1995

The large discretization step method for time-dependent partial differential equations

A new method for the acceleration of linear and nonlinear time dependent calculations is presented. It is based on the Large Discretization Step (LDS) approximation, defined in this work, which employs an extended system of low accuracy schemes to approximate a high accuracy discrete approximation to a time dependent differential operator. Error bounds on such approximations are derived. These approximations are efficiently implemented in the LDS methods for linear and nonlinear hyperbolic equations, presented here. In these algorithms the high and low accuracy schemes are interpreted as the same discretization of a time dependent operator on fine and coarse grids, respectively. Thus, a system of correction terms and corresponding equations are derived and solved on the coarse grid to yield the fine grid accuracy. These terms are initialized by visiting the fine grid once in many coarse grid time steps. The resulting methods are very general, simple to implement and may be used to accelerate many existing time marching schemes.

Haras, Zigo↗
NASA NTRS1983

The Eddington limit and supercritical accretion. II - Time-dependent calculations

Spherically symmetric, time-dependent accretion of an ionized hydrogen plasma onto a neutron star is calculated for accretion rates in excess of the Eddington limit. The coupled hydrodynamic and frequency integrated radiative transfer equations are solved on an Eulerian grid for these supercritical accretion flows. Our results indicate that steady state flows are limited to rates at or below the critical rate, with emergent luminosities equal to or less than the Eddington luminosity. Initially supercritical accretion rates generate a large pulse of radiation which reduces the accretion rate to the critical value and produces an extended quasi-static envelope.

Burger, H. L.↗
NASA NTRS1986

High spatial resolution models of time-dependent, layered mantle convection

Time-dependent models of Boussinesq convection are analyzed in order to determine the potential existence of the transient phase of multiple layered convection initially described by Ross and Sacks (1982, 1984). The initial thermal profile for subsolidus mantle convection is examined in terms of an adiabatic or a conductive profile. The effects of varied spatial resolution, aspect ratio, Rayleigh number, initial buoyancy, and supersolidus temperature cutoffs on mantle convection are investigated. It is observed that the data supports the existence of the transient phase of multiple layered convection.

Boss, A. P.↗
NASA NTRS1992

Time dependent heat transfer rates in high Reynolds number hypersonic flowfields

Time dependent heat transfer rates have been calculated from time dependent temperature measurements in the vicinity of shock-wave boundary-layer interactions due to conical compression ramps on an axisymmetric body. The basic model is a cylindrical body with a 10 degree conical nose. Four conical ramps, 20, 25, 30, and 35 degrees serve as shock wave generators. Flowfield surveys have been made in the vicinity of the conical ramp vertex, the separation point, and the reattachment point. A significant effort was made to characterize the natural frequencies and relative powers of the resulting fluctuations in heat transfer rates. This research effort, sponsored jointly by NASA and the Air Force, was conducted in the Air Force Flight Dynamics Directorate High Reynolds Facility. The nominal freestream Mach number was 6, and the freestream Reynolds numbers ranged from 2.2 million/ft to 30.0 million/ft. Experimental results quantify temperature response and the resulting heat transfer rates as a function of ramp angle and Reynolds number. The temperature response within the flowfield appears to be steady-state for all compression ramp angles and all Reynolds numbers, and hence, the heat transfer rates appear to be steady-state.

Flanagan, Michael J.↗
NASA NTRS1992

The simulated features of heliospheric cosmic-ray modulation with a time-dependent drift model. IV - The role of heliospheric neutral sheet deformation

Previous calculations with a time-dependent drift model revealed the model to be less successful in describing time-dependent modulation during periods of moderate to large solar activity. In this paper, it is argued that a major reason for this is that the previously used wavy heliospheric neutral sheet (HNS) description was based on an idealized HNS not subject to any spatial evolution while propagating radially outward. It is suggested that the deformation and compression of HNS wave peaks will lead to significant increases in the crossfield diffusion across these peaks (short-circuiting). The cosmic rays will effectively experience reduced tilt angles and therefore a reduction in the integrated HNS modulation effect between an observer and the heliospheric boundary. During periods of moderate to large solar activity these HNS deformation processes are progressively more frequent and should lead to a significant reduction in time-dependent modulation as predicted by drift models. Calculations done with radially propagating tilt angles that effectively decrease with radial distance give the expected reduction which improves the general description of modulation from 1987-1988.

Le Roux, J. A.↗
NASA NTRS1983

Theory of time-dependent intense-field collisional resonance fluorescence

The time-dependent theory of Courtens and Szoke (1977) is generalized using the approach of Burnett et al. (1982) to derive time-dependent spectral intensities of resonance fluorescence from atoms driven by a pulsed laser in the presence of collisions. These results are valid both for laser detunings inside and outside the usual impact region of the spectrum, including Zeeman degeneracy effects. This theory is applied to a simple but important example (J = 0 to J = 1) to obtain quantitative predictions for the observable scattered-light spectrum which can be directly compared with recent experiments.

Kleiber, P. D.↗
NASA NTRS1975

A time-dependent diffusion-convection model for the long-term modulation of cosmic rays

The model considered incorporates, to first order, the direct effects of the time-dependent diffusive propagation of interstellar cosmic rays in a slowly changing interplanetary medium. A one-dimensional model is discussed along with a three-dimensional radial wind. An evaluation is conducted of average diffusive propagation times. It is found that the effects of time-dependent diffusive propagation can be quite significant. A rigidity-dependent time delay or 'lag' in the modulated spectra is predicted.

Ogallagher, J. J.↗
NASA NTRS1992

Time-dependent mapping of the magnetic field at the core-mantle boundary

We consider the problem of constructing a time-dependent map of the magnetic field at the core-mantle boundary. We use almost all the available data from the last 300 years to produce two maps, one for the period 1690-1840 and the other for 1840-1990. We represent the spatial dependency of the field using spherical harmonics, the time dependency using a cubic B-spline basis, and seek the smoothest solutions compatible with the observations. We argue that, for observations from permanent magnetic observatories, the most efficient strategy is to use the first differences of annual means; for satellite data, the most efficient strategy is simply to limit the number of data used so as to minimize any tendency to map the crustal field into the core field. The resulting model fits the observatory data better than any previous model. The resulting time-dependent field map exhibits much of the same structure in the field and its secular variation identified in earlier studies.

Bloxham, Jeremy↗
NASA NTRS1998

Pulsed-field-gradient measurements of time-dependent gas diffusion

Pulsed-field-gradient NMR techniques are demonstrated for measurements of time-dependent gas diffusion. The standard PGSE technique and variants, applied to a free gas mixture of thermally polarized xenon and O2, are found to provide a reproducible measure of the xenon diffusion coefficient (5.71 x 10(-6) m2 s-1 for 1 atm of pure xenon), in excellent agreement with previous, non-NMR measurements. The utility of pulsed-field-gradient NMR techniques is demonstrated by the first measurement of time-dependent (i.e., restricted) gas diffusion inside a porous medium (a random pack of glass beads), with results that agree well with theory. Two modified NMR pulse sequences derived from the PGSE technique (named the Pulsed Gradient Echo, or PGE, and the Pulsed Gradient Multiple Spin Echo, or PGMSE) are also applied to measurements of time dependent diffusion of laser polarized xenon gas, with results in good agreement with previous measurements on thermally polarized gas. The PGMSE technique is found to be superior to the PGE method, and to standard PGSE techniques and variants, for efficiently measuring laser polarized noble gas diffusion over a wide range of diffusion times. Copyright 1998 Academic Press.

NASA Discipline Environmental Health↗