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NASA NTRS1984

Phase coherent effects in a collisional turbulent plasma

The presence of mode-mode coupling in turbulent fluctuations in the positive column of a glow discharge in argon is studied experimentally and analytically. The auto-power spectra, the cross power spectra, the phase spectra, the cross correlation functions and the bispectrum are determined. The results are relevant to the theoretical speculations of Grabec and Mikac (1974) and it is shown that ionization instability is the primary cause of the turbulence. The phase spectra indicate that the system is nearly linear at low frequency and the bispectrum plots show that nonlinear wave-wave interactions play a role in the development of the fluctuation components in the turbulent spectrum. Distinctions are made between the azimuthal and axial behaviors of the fluctuations and the results imply a trend toward longer azimuthal scales and shorter axial scales for characterizing fluctuation wave-packets as the density of the turbulent environment increases.

Johnson, J. A., III↗

NASA NTRS1985

Influence of damping on quantum interference - An exactly soluble model

This paper reports the result of a calculation which shows the effect of damping on the quantum interference of two Gaussian wave packets in a harmonic potential. The influence-functional method, which seems to be the most appropriate one for this kind of calculation, is used. It is shown that quantum-interference effects are severely diminished by the presence of damping even when its influence on the system is only light. The corrections to the undamped formulas are always expressible in terms of the phenomenological damping constant, the temperature (in the high-temperature limit), the cutoff frequency of the reservoir oscillators, and the mean number of quanta of energy intially present in the system. Both weakly and strongly damped systems are analyzed in the regime of low and high temperatures.

Caldeira, A. O.↗

NASA NTRS1985

Stability of finite-difference models containing two boundaries or interfaces

The stability of finite difference models of hyperbolic initial boundary value problems is connected with the propagation and reflection of parasitic waves. Wave propagation ideas are applied to models containing two boundaries or interfaces, where repeated reflection of trapped wave packets is a potential new source of instability. Various known instability phenomena are accounted for in a unified way. Results show: (1) dissipativity does not ensure stability when three or more formulas are concatenated at a boundary or internal interface; (2) algebraic GKS instabilities can be converted by a second boundary to exponential instabilities only when an infinite numerical reflection coefficient is present; and (3) GKS-stability and P-stability can be established in certain problems by showing that all numerical reflection coefficients have modulus less than 1.

Trefethen, L. N.↗

NASA NTRS1986

Magnetohydrodynamic solitons and radio knots in jets

Weakly nonlinear surface waves are examined in the context of the beam model for jetlike radio sources. By introducing a finite scale length, viz. the beam radius, geometrical dispersion can act to balance nonlinear wave growth and thereby produce solitons, localized wave packets of stable waveform. A method for obtaining a soliton equation from the MHD equations is presented and then applied to radio knots in jets.

Fiedler, R.↗

NASA NTRS1986

Upstream waves of cometary origin detected by the Giotto magnetic field experiment

Upstream waves associated with water group ions were detected by Giotto up to 5.2 million km from the nucleus of comet Halley. They show predominantly quasi-linear polarization with spectral characteristics typical of turbulent cascade processes. Spectral power densities are well above solar wind levels and at similar or lower levels than those observed near comet Giacobini-Zinner. The waveforms exhibit different characteristics from those detected by the ICE mission. Wavefront steepening and associated higher frequency wave packets are not identified.

Acuna, M. H.↗

NASA NTRS1986

Plasma waves in the shock interaction regions at Comet Giacobini-Zinner

The nature of the comet-solar wind interaction is studied by analyzing the detailed evolution of the plasma wave spectra of Comet Giacobini-Zinner across the interaction region. Electron heat fluxes and associated electron plasma waves, steepened low-frequency wave packets, and density fluctuations observed upstream of Giacobini-Zinner shocks are also found upstream of quasi-parallel bow shocks. Downstream, the pulsations in the cometary magnetic field magnitude, in addition to the large density spikes, are usually also found downstream of quasi-parallel bow shocks. Other similarities to interplanetary shocks and terrestrial bow shocks are described.

Kennel, C. F.↗

NASA NTRS1987

Developing disturbances in shear

The origin and growth to moderate amplitude of disturbances in shear flow has been traditionally ascribed to the linear modal instability of the flow. Recent work on initial value problems has suggested that nonmodal growth of perturbations may be of equal and perhaps greater importance, at least in cases of rapid development. Examples of robust growth in model problems which support no instabilities and in baroclinic flows with realistic Ekman damping for which the exponential modes have zero or negative growth rates have been shown. Such examples have focused attention on the perturbations which are configured to tap the energy of mean flows. Here a critical examination of these favorably configured perturbations is given, making use of the simple constant free shear barotropic model which allows construction of exact two-dimensional isolated wave packet solutions.

Farrell, Brian↗

NASA NTRS1987

Dynamics of dendritic sidebranching in the two-dimensional symmetric model of solidification

Within a WKB approximation, the evolution of time-dependent deformations of the needle crystal solution of the two-dimensional symmetric model of solidification is studied. It is found that perturbations with fixed small frequencies are initially amplified as they propagate from near the tip down the dendrite but ultimately decay. Localized wave packets behave rather differently; the packet continues to grow exponentially as it moves to arbitrarily large distances from the tip. The relevance of these results to sidebranching of dendrites is discussed.

Barber, Michael N.↗

NASA NTRS1987

Dendritic sidebranching in the three-dimensional symmetric model in the presence of noise

The time-dependent behavior of sidebranching deformations in the three-dimensional symmetric model of dendritic solidification is studied within a WKB approximation. Localized wave packets generated by pulses in the neighborhood of the tip are found to grow in amplitude and to spread and stretch as they move down the sides of the dendrite. This behavior is shown to imply that noise in the solidifying medium is selectively amplified in such a way as to produce a fluctuating train of sidebranches in qualitative agreement with experimental observations. A rough estimate indicates that purely thermal noise is probably not quite strong enough to fit the data.

Langer, J. S.↗

NASA NTRS1987

Numerical simulations of turbulent spots in plane Poiseuille and boundary-layer flow

Direct numerical simulations of turbulent spots in plane Poiseuille and boundary-layer flows are performed. Mature, self-similar spots are obtained. The propagation velocities and spreading angles are found to compare well with corresponding experiments. The difference in shape of the two spots is also clearly discernible: the turbulent parts are contained within arrowhead regions that point in opposite directions for the two cases. The wing-tip region of the Poiseuille spot is also found to consist of a large-amplitude semiturbulent wave packet.

Henningson, Dan↗

NASA NTRS1989

Absorbing boundary conditions for second-order hyperbolic equations

A uniform approach to construct absorbing artificial boundary conditions for second-order linear hyperbolic equations is proposed. The nonlocal boundary condition is given by a pseudodifferential operator that annihilates travelling waves. It is obtained through the dispersion relation of the differential equation by requiring that the initial-boundary value problem admits the wave solutions travelling in one direction only. Local approximation of this global boundary condition yields an nth-order differential operator. It is shown that the best approximations must be in the canonical forms which can be factorized into first-order operators. These boundary conditions are perfectly absorbing for wave packets propagating at certain group velocities. A hierarchy of absorbing boundary conditions is derived for transonic small perturbation equations of unsteady flows. These examples illustrate that the absorbing boundary conditions are easy to derive, and the effectiveness is demonstrated by the numerical experiments.

Jiang, Hong↗

NASA NTRS1988

Turbulence characteristics inside a turbulent spot in plane Poiseuille flow

In wall-bounded shear flows the transition to turbulence through localized disturbances goes through a pattern starting with a development of shear layers. The localized normal velocity fluctuations induce normal vorticity through the lift-up effect. These shear layers become unstable to secondary disturbances, and if the amplitudes of the disturbances are large enough, a turbulent spot develops. Investigations of the spot in boundary layers has shown that the turbulent part of the spot is very similar to a fully developed boundary layer. Wygnanski et al. (1976) showed that the mean profile at the center-symmetry plane has a logarithmic region and Johansson et al. (1987) showed that both the higher-order statistics and flow structures in the spot were the same as in the corresponding fully developed flow. In what respects the turbulence inside the Poiseuille spot is similar to fully developed turbulent channel flow is studied. The numerically simulated spot is used, where the characteristics inside the spot are compared to those of the wave packet in the wingtip area. A recent experimental investigation of the velocity field associated with the Poiseuille spot by Klingmann et al. is used for comparison.

Henningson, D. S.↗

NASA NTRS1989

Dissipation of Alfven waves in solar coronal arches

The physical mechanism by which mechanical energy is delivered to and absorbed by the solar corona is discussed. A set of MHD equations for analyzing the slow evolution of the magnetic field and the fast time of Alfven waves is presented. Alfven wave dissipation is treated. It is shown that the slow motion of the feet of coronal arches leads to irregular magnetic fields and that Alfven waves propagating in the irregular magnetic structure are dissipated through filamentation of the wave packet that generates short scales necessary for efficient dissipation.

Sudan, R. N.↗

NASA NTRS1988

Numerical simulation of transition in a decelerating boundary layer

Transition in a decelerating flat-plate boundary layer is numerically simulated up to the beginning of three-dimensional breakdown, and the results are compared with an experiment. The adverse pressure gradient induced by deceleration increases the growth rate of disturbances and allows transition at lower Reynolds numbers. The primary instability is characterized by a wave packet, which undergoes three-dimensional distortion. Lambda vortices are locally observed, but they are not aligned with respect to the flow direction.

Yang, Kyung Soo↗

NASA NTRS1989

Cometary environments; Proceedings of Symposium 5, Workshop IV, and Topical Meeting of the 27th COSPAR Plenary Meeting, Espoo, Finland, July 18-29, 1988

Papers on the environment of comets are presented, covering topics such as constraints on the interstellar dust model of comet dust, dust particles and comet nuclei, models of cometary nuclei, subliming gas in the near-nuclear layer of the comet coma, the nucleus and rotation of Comet Halley, the surface albedo of comet nuclei, observational studies on Comet Halley, comet simulations, comet ion composition, and chemical abundances in comets. Additional topics include the O 1D and H2O production rate from comets, collisional coma models, the gas coma of Comet Giacobini-Zinner, IR properties of rough comet grains, studies of Comet Halley by Giotto, the impact of large dust particles on the Vega spacecraft, and carbonaceous materials as components of comet dust. Also, consideration is given to comet plasma boundaries, the comet ionopause, the solar wind-comet interaction, MHD turbulence and particle acceleration in a mass-loaded solar wind, combined first and second order Fermi acceleration at comets, discrete wave packets upstream from the earth and comets, and the visual appearance of comets under varying solar wind conditions.

Gombosi, T. I.↗

NASA NTRS1990

Kinetic effects on Alfven wave nonlinearity. II - The modified nonlinear wave equation

A previously developed Vlasov theory is used here to study the role of resonant particle and other kinetic effects on Alfven wave nonlinearity. A hybrid fluid-Vlasov equation approach is used to obtain a modified version of the derivative nonlinear Schroedinger equation. The differences between a scalar model for the plasma pressure and a tensor model are discussed. The susceptibilty of the modified nonlinear wave equation to modulational instability is studied. The modulational instability normally associated with the derivative nonlinear Schroedinger equation will, under most circumstances, be restricted to left circularly polarized waves. The nonlocal term in the modified nonlinear wave equation engenders a new modulational instability that is independent of beta and the sense of circular polarization. This new instability may explain the occurrence of wave packet steepening for all values of the plasma beta in the vicinity of the earth's bow shock.

Spangler, Steven R.↗

NASA NTRS1990

Absorbing boundary conditions for second-order hyperbolic equations

Jiang, Hong↗

NASA NTRS1990

Two-component model of strong Langmuir turbulence - Scalings, spectra, and statistics of Langmuir waves

A simple two-component model of strong turbulence that makes clear predictions for the scalings, spectra, and statistics of Langmuir waves is developed. Scalings of quantities such as energy density, power input, dissipation power wave collapse, and number density of collapsing objects are investigated in detail and found to agree well with model predictions. The nucleation model of wave-packet formation is strongly supported by the results. Nucleation proceeds with energy flowing from background to localized states even in the absence of a driver. Modulational instabilities play little or no role in maintaining the turbulent state when significant density nonuniformities are present.

Robinson, P. A.↗