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At least 253 records · Page 14

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NASA NTRS1982

Focusing of waves in turbulent inhomogeneous media

A stochastic method using geometrical acoustics is employed to investigate the growth of a large fluctuation in the amplitude of high-frequency waves or shocks propagating through turbulent, inhomogeneous media. Nonlinear terms are retained in the analysis to correctly model focusing and growth of singular fluctuations in the amplitude. A two-dimensional analysis reveals that fluctuations in the ray-tube area grow exponentially and every ray displays caustics. Probability densities for the appearance of caustics are provided, and moments of the ray-tube area distribution and amplitude-related statistics are formulated for distances far into the region of caustic formation. Finally, a relationship is defined between theoretical predictions and measurements on an image plane.

Kulkarny, V. A.↗

NASA NTRS1982

Turbulent solution of the Navier-Stokes equations for an inhomogenous developing shear layer

To study the nonlinear physics of inhomogeneous turbulent shear flow, the unaveraged Navier-Stokes equations are solved numerically. For initial conditions a three-dimensional cosine velocity fluctuation and a mean-velocity profile with a step are used. Although the initial conditions are nonrandom. The flow soon becomes turbulent. Concentrated turbulent energy develops near the plane where the mean velocity gradient is initially infinite. The terms in the one-point correlation equation for turbulent energy, including those for the diffusion and production of turbulence, are calculated, the diffusion terms tend to make the turbulence more homogeneous.

Deissler, R. G.↗

NASA NTRS1982

Evidence for inhomogeneous thermal sources of two similar solar spike event of 1978, May 5 and December 4

Two short duration single spike events of 1978 May 5 and December 4 exhibit similar time profiles in the microwave and hard X-ray ranges, indicating emission from compact sources. Microwave spectral observations exhibit inhomogeneities present in the source parameters. The existence of fine time structures in the microwave time profiles at 10.4 GHz from Berne are interpreted as a signature of the dynamics of a disturbance travelling through the souce at the ion-sound speed. Stereoscopic observations with the hard X-ray detector on the solar orbiter, Helios-2, and the Berne microwave antennae do not indicate any time lag or differences in the time profiles during the impulsive phase. This is taken as evidence for the absence of directionality of emission making beam models unlikely for short duration single spike events.

Wiehl, H. J.↗

NASA NTRS1983

Transient difference solutions of the inhomogeneous wave equation: Simulation of the Green's function

A time-dependent finite difference formulation to the inhomogeneous wave equation is derived for plane wave propagation with harmonic noise sources. The difference equation and boundary conditions are developed along with the techniques to simulate the Dirac delta function associated with a concentrated noise source. Example calculations are presented for the Green's function and distributed noise sources. For the example considered, the desired Fourier transformed acoustic pressures are determined from the transient pressures by use of a ramping function and an integration technique, both of which eliminates the nonharmonic pressure associated with the initial transient.

Baumeiste, K. J.↗

NASA NTRS1983

Scatter of elastic waves by a thin flat elliptical inhomogeneity

Elastodynamic fields of a single, flat, elliptical inhomogeneity embedded in an infinite elastic medium subjected to plane time harmonic waves are studied. Scattered displacement amplitudes and stress intensities are obtained in series form for an incident wave in an arbitrary direction. The cases of a penny shaped crack and an elliptical crack are given as examples. The analysis is valid for alpha a up to about two, where alpha is longitudinal wave number and a is a typical geometric parameter.

Fu, L. S.↗

NASA NTRS1983

Transient difference solutions of the inhomogeneous wave equation - Simulation of the Green's function

Baumeister, K. J.↗

NASA NTRS1982

Forces acting on free carriers in semiconductors of inhomogeneous composition I, II

An investigation shows that the extended Wannier-Slater theorem with its position-dependent effective mass m cannot be considered a viable description of a semiconductor with compositional changes. The correct description of the behavior of the electron or hole flow in semiconductors in which the chemical composition changes gradually from position to position is more difficult. It is necessary to find a model Hamiltonian. This model Hamiltonian is to some extent arbitry, but it must be representative of a homogeneous sample. The difference between the true and the model Hamiltonian should be small in the sense that this difference may be considered a perturbation. However, a Hamiltonian with the required specifications can always be found provided that the compositional inhomogeneities do not change drastically over the distances of interest.

Von Roos, O.↗

NASA NTRS1983

Evidence for inhomogeneous thermal sources of two similar solar spike events of 1978 May 5 and December 4

Two short duration single spike solar events of 1978 May 5 and December 4 exhibit similar time profiles in the microwave and hard X-ray ranges, indicating emission from compact sources. Microwave spectral observations exhibit inhomogeneities present in the source parameters. The existence of fine time structures in the microwave time profiles at 10.4 GHz from Berne are interpreted as a signature of the dynamics of a disturbance traveling through the source at the ion-sound speed. Stereoscopic observations with the hard X-ray detector on the solar orbiter, Helios-2, and the Berne microwave antenna do not indicate any time lag or differences in the time profiles during the impulsive phase. This is taken as evidence for the absence of directionality of emission making beam models unlikely for short duration single spike events. Previously announced in STAR as N83-13047

Desai, U.↗

NASA NTRS1983

The collapse of the local, Spitzer-Haerm formulation and a global-local generalization for heat flow in an inhomogeneous, fully ionized plasma

The breakdown of the classical (CBES) field aligned transport relations for electrons in an inhomogeneous, fully ionized plasma as a mathematical issue of radius of convergence is addressed, the finite Knudsen number conditions when CBES results are accurate is presented and a global-local (GL) way to describe the results of Coulomb physics moderated conduction that is more nearly appropriate for astrophysical plasmas are defined. This paper shows the relationship to and points of departure of the present work from the CBES approach. The CBES heat law in current use is shown to be an especially restrictive special case of the new, more general GL result. A preliminary evaluation of the dimensionless heat function, using analytic formulas, shows that the dimensionless heat function profiles versus density of the type necessary for a conduction supported high speed solar wind appear possible.

Scudder, J. D.↗

NASA NTRS1983

Volume integrals associated with the inhomogeneous Helmholtz equation. Part 1: Ellipsoidal region

Problems of wave phenomena in fields of acoustics, electromagnetics and elasticity are often reduced to an integration of the inhomogeneous Helmholtz equation. Results are presented for volume integrals associated with the Helmholtz operator, nabla(2) to alpha(2), for the case of an ellipsoidal region. By using appropriate Taylor series expansions and multinomial theorem, these volume integrals are obtained in series form for regions r 4' and r r', where r and r' are distances from the origin to the point of observation and source, respectively. Derivatives of these integrals are easily evaluated. When the wave number approaches zero, the results reduce directly to the potentials of variable densities.

Fu, L. S.↗

NASA NTRS1983

Finite element methods for the inhomogeneous Navier-Stokes equations

A conforming mixed finite element method for the stationary Navier-Stokes equations with inhomogeneous boundary conditions is considered. Estimates for the error in the velocity and pressure approximations are derived. A computational example is provided to illustrate the implementation of the method.

Peterson, J. S.↗

NASA NTRS1984

Atmospheric transfer of radiation above an inhomogeneous non-Lambertian reflective ground. I - Theory

A method for solving the three-dimensional equation of transfer for a vertically inhomogeneous atmosphere bounded by a reflecting surface of non-uniform bidirectional reflectance is presented. The technique incorporates a two-dimensional spatial Fourier transform of the transfer equation and solution of the resulting expressions for each Fourier component of the radiation field using the method of Gauss-Seidel iteration. The intensity field in the spatial domain, which is calculated for a variety of altitudes, zenith angles, and azimuths, is reconstructed using the inverse Fourier transform. An empirical surface bidirectional reflectance function is employed, permitting the consideration of non-Lambertian reflective properties.

Diner, D. J.↗

NASA NTRS1984

S-P wave travel time residuals and lateral inhomogeneity in the mantle beneath Tibet and the Himalaya

S-P wave travel time residuals were measured in earthquakes in Tibet and the Himalaya in order to study lateral inhomogeneities in the earth's mantle. Average S-P residuals, measured with respect to Jeffrey-Bullen (J-B) tables for 11 earthquakes in the Himalaya are less than +1 second. Average J-B S-P from 10 of 11 earthquakes in Tibet, however, are greater than +1 second even when corrected for local crustal thickness. The largest values, ranging between 2.5 and 4.9 seconds are for five events in central and northern Tibet, and they imply that the average velocities in the crust and upper mantle in this part of Tibet are 4 to 10 percent lower than those beneath the Himalaya. On the basis of the data, it is concluded that it is unlikely that a shield structure lies beneath north central Tibet unless the S-P residuals are due to structural variations occurring deeper than 250 km.

Molnar, P.↗

NASA NTRS1985

Resistive wave dissipation on magnetic inhomogeneities Normal modes and phase mixing

Numerical solutions of the linearized, resistive MHD equations indicate the presence of two characteristic forms of wave decay on magnetic inhomogeneities. Solutions for relatively long-wavelength disturbances and large values of the resistivity have the behavior of decaying normal modes. In the opposite limits, phase mixing becomes important, with the eventual build-up of large spatial gradients in which the resistive terms dominate. This composite behavior is shown to be conceptually consistent with analytic results, which predict that the complete solution consists of the sum of collective and noncollective contributions. The numerical simulations go beyond analytic theory by defining where each contribution prevails and computing wave decay when phase mixing is effective. The dispersion relation in the normal-mode regime is also determined analytically, with some approximations, and is in good agreement with the numerical solution. The decay time of the normal modes varies with Lundquist number at S1/6, while the phase-mixed decay time scales as S1/3.

Steinolfson, R. S.↗

NASA NTRS1985

Ultraviolet DIAL measurements of O3 profiles in regions of spatially inhomogeneous aerosols

The differential absorption lidar (DIAL) technique generally assumes that atmospheric optical scattering is the same at the two laser wavelengths used in the DIAL measurement of a gas concentration profile. Erros can arise in this approach when the wavelengths are significantly separated, and there is a range dependence in the aerosol scattering distribution. This paper discusses the errors introduced by large DIAL wavelength separations and spatial inhomogeneity of aerosols in the atmosphere. A Bernoulli solution for determining the relative distribution of aerosol backscattering in the UV region is presented, and scattering ratio boundary values for these solutions are discussed. The results of this approach are used to derive a backscatter correction to the standard DIAL analysis method. It is shown that for the worst cases of severe range dependence in aerosol backscattering, the residual errors in the corrected DIAL O3 measurements were less than 10 ppbv for DIAL wavelengths at 286 and 300 nm.

Browell, E. V.↗

NASA NTRS1985

A study of backscattering and emission from closely packed inhomogeneous media

The effects of close spacing between small scattering spheres were examined by keeping the distance-dependent terms in the expressions for the transverse scattered fields. The phase matrix was then derived from these fields and was used in the radiative transfer formulation to model scattering and emission from a densely populated, inhomogeneous layer. Computed results were compared with those obtained when the phase matrix was specialized to the far-field condition. It was found that the use of the far-zone condition tended to underestimate both the level of the copolarized backscattering and the cross-polarized backscattering. In emission computations, the use of the far-zone condition overestimated the level of the brightness temperature. These effects decreased with a decrease in the volume fraction or an increase in the exploring frequency, as expected. An improvement on the snow parameter (density and crystal size) estimation was shown to be possible when this new phase matrix was used.

Fung, A. K.↗

NASA NTRS1985

Resonance cone structure in a warm inhomogeneous bounded plasma with lower-hybrid resonance layers

The paper presents a theoretical study of the problem of the wave fields excited by a gap source at the edge of an inhomogeneous magnetized plasma with a pair of lower-hybrid resonance layers present and bounded by conducting walls. The approach used is that of a solution as a sum of multiply reflected extraordinary mode and ion-thermal resonance cones as an alternative to the guided-wave mode approach. A diagrammatic scheme for writing the solution is given which can be used to determine in great detail the structure and properties of the resonance cones and the way they transform across the back-to-back hybrid layers. Evanescent resonance cones are shown to exist in the high-density region between the hybrid resonance layers and to tunnel through to the other side, maintaining this general structure if the layer is relatively thin.

Grabbe, C. L.↗

NASA NTRS1986

Observations of three BL Lacertae objects - Constraints on inhomogeneous relativistically beamed jet models

Multifrequency observations are presented of three BL Lac objects, including the first UV measurements of 0912 + 297 and 1219 + 285. An eight day optical flare was measured from 0422 = 004 in which a doubling in visual flux density was noted; other sources displayed smaller daily fluctuations. The 5-15 GHz radio flux from these three objects remained constant for two months, although the 15-20 GHz emission from 0912 + 297 varied slightly over a period of a month. Constraints which are provided by these and other Bl Lac data are discussed for inhomogeneous relativistically beamed jet models. It is concluded that a tapered jet model is in good agreement with the data for each source and that additional emission regions are not required.

Worrall, D. M.↗