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NASA NTRS1976

Thermal-chemical instabilities in CO clouds

The stability of interstellar clouds containing CO is analyzed taking account of formation processes for CO. Two such processes are examined: O(+) charge exchange and C(+) radiative association. It is found that the C(+) radiative-association chemistry leads to low-temperature instabilities which influence the evolution of clouds. It is also found that instability may set in if CO production increases sufficiently with density, that the O(+) charge-exchange chemistry leads to instability associated with attenuation of the interstellar radiation field by grains, and that thermal instabilities will also result if grain formation, rather than ion-molecule chemistry, dominates CO production. It is suggested that such instabilities play a role in the fragmentation of interstellar clouds and in the formation of protostellar objects.

Glassgold, A. E.↗

NASA NTRS1979

Simulation of liquid propellant rocket engine combustion instabilities

A simulation technique for studying the high frequency combustion instabilities of liquid propellant rocket engines has been developed and used to investigate various aspects of instability phenomena. Of importance was investigation of the significance of the method of coupling the combustion and the gas dynamics of the system. Two coupling processes were studied: linear response of the combustion process to pressure fluctuations, and the nature of the resulting instabilities; and nonlinear response of the combustion process to velocity fluctuations, and the nature of the resulting instabilities. For the combustion model studied, nonlinear (velocity) coupling was found to more closely characterize liquid propellant instabilities.

Ventrice, M. B.↗

NASA NTRS1979

Secondary instability in boundary-layer flows

The stability of a secondary Tollmien-Schlichting wave, whose wavenumber and frequency are nearly one half those of a fundamental Tollmien-Schlichting instability wave is analyzed using the method of multiple scales. Under these conditions, the fundamental wave acts as a parametric exciter for the secondary wave. The results show that the amplitude of the fundamental wave must exceed a critical value to trigger this parametric instability. This value is proportional to a detuning parameter which is the real part of k - 2K, where k and K are the wavenumbers of the fundamental and its subharmonic, respectively. For Blasius flow, the critical amplitude is approximately 29% of the mean flow, and hence many other secondary instabilities take place before this parametric instability becomes significant. For other flows where the detuning parameter is small, such as free-shear layer flows, the critical amplitude can be small, thus the parametric instability might play a greater role.

Nayfeh, A. H.↗

NASA NTRS1979

Generalized lower-hybrid-drift instability

The theory of lower-hybrid-drift instability is extended to include a finite value of the component of wave vector parallel to the ambient magnetic field so that the analysis bridges the usual lower-hybrid-drift instability of flute modes and the modified-two-stream instability. The present theory also includes electromagnetic and ambient magnetic field-gradient effects. It is found that in the cold-electron limit the density and magnetic gradients can qualitatively modify the conclusion obtained in the early theory of the modified-two-stream instability. For example, even if the relative drift far exceeds the Alfven speed of the plasma, the instability may still persist. This result is in contrast to that established in the literature. When the electron temperature is finite, the problem is complicated. Numerical solutions are obtained for a number of cases.

Hsia, J. B.↗

NASA NTRS1980

Form-drag instability, multiple equilibria and propagating planetary waves in baroclinic, orographically forced, planetary wave systems

A two-layer baroclinic model is used to study the planetary-scale motions of a thermally driven atmosphere in the presence of topography, and in doing so to extend previous results obtained with a barotropic model. Highly truncated spectral equations are used to obtain multiple wavelike stationary equilibrium states, to examine the instabilities that produce them, and to study the instabilities that feed on them and give rise to traveling planetary waves. Although the equilibria cannot exist without orography, their energy comes from the potential energy of the mean flow, not from kinetic energy transfer via the mountain torque. Low-index (blocking) equilibria as well as high-index equilibria require a large thermal driving and are associated with both orographic and baroclinic instability of the Hadley circulation. It is suggested that blocking in nature is a quasi-stable circulation arising from orographic instability with strong thermal driving; and that observed low-frequency, propagating planetary waves are due to instabilities of the quasi-stationary, topographically forced equilibria.

Charney, J. G.↗

NASA NTRS1979

Perturbation solutions of combustion instability problems

A method involving approximate modal analysis using the Galerkin method followed by an approximate solution of the resulting modal-amplitude equations by the two-variable perturbation method (method of multiple scales) is applied to two problems of pressure-sensitive nonlinear combustion instability in liquid-fuel rocket motors. One problem exhibits self-coupled instability while the other exhibits mode-coupled instability. In both cases it is possible to carry out the entire linear stability analysis and significant portions of the nonlinear stability analysis in closed form. In the problem of self-coupled instability the nonlinear stability boundary and approximate forms of the limit-cycle amplitudes and growth and decay rates are determined in closed form while the exact limit-cycle amplitudes and growth and decay rates are found numerically. In the problem of mode-coupled instability the limit-cycle amplitudes are found in closed form while the growth and decay rates are found numerically. The behavior of the solutions found by the perturbation method are in agreement with solutions obtained using complex numerical methods.

Googerdy, A.↗

NASA NTRS1981

Simulation of the current-driven electrostatic ion cyclotron instability

Results are presented of a self-consistent particle simulation of the growth and saturation of electrostatic ion cyclotron (EIC) waves along auroral field lines. The driving mechanism for the waves is an initial drifting Maxwellian distribution for the electrons. The magnetic field is taken to lie in the simulation plane, so that modes such as the ion acoustic instability and the EIC instability can be excited, thus making it possible to study the behavior of EIC waves in the presence of ion acoustic turbulence. A dc electric field, which tends to keep the current constant along the field lines, is included. It is shown that the EIC instability grows to a moderate level before saturating due to plateau formation. The perpendicular ion temperature increases by typically 40%, with an increase arising from bulk heating only. The anomalous resistivity, associated with the EIC instability is determined and compared with previous calculations and with that due to the ion acoustic instability. Implications of the results for observation of ion cyclotron waves on auroral field lines are discussed.

Pritchett, P. L.↗

NASA NTRS1982

Generation of instability waves at a leading edge

This paper describes the generation of instability waves downstream of a leading edge by an imposed upstream disturbance. Two cases are considered. The first is concerned with mean flows of the Blasius type wherein the instabilities are represented by Tollmien-Schlichting waves. It is shown that the latter are generated fairly far downstream of the edge and are the result of a wave length reduction process that tunes the free stream disturbances to the Tollmien-Schlichting wave length. The other case is concerned with inflectional, uni-directional, transversely sheared mean flows. Such idealized flows provide a fairly good local representation to the nearly parallel flows in jets. They can support inviscid instabilities of the Kelvin-Helmholtz type. The various mathematically permissible mechanisms that can couple these instabilities to the upstream disturbances are discussed. The results are compared to some acoustic measurements and conclusions are drawn about the generation of the instabilities in these flows.

Goldstein, M. E.↗

NASA NTRS1982

Collisionless electrostatic interchange instabilities

The linear Vlasov dispersion equation for electrostatic plasma instabilities driven by gravity and weak density gradients perpendicular to a uniform magnetic field is derived and solved numerically. Two interchange instabilities emerge: the well-known fluid mode at long wavelengths and a kinetic model at wavelengths short compared with the ion gyroradius. The properties of both instabilities are studied, as well as the effects of gravity on the universal and lower-hybrid density drift instabilities. The results show that the kinetic interchange generally has a larger growth rate than the fluid interchange instability, indicating that, whenever the latter is present in a collisionless plasma, the former may also be found.

Gray, S. P.↗

NASA NTRS1983

Density drift instabilities and weak collisions

A model is developed which describes the effects of weak collisions on the linear kinetic theory of electrostatic density drift instabilities. A dispersion equation valid at all frequencies and wave numbers is derived using the assumptions of a weak, uniform density gradient; a uniform magnetic field; and the BGK collision operator with a modification of the local approximation. The properties of the universal and collisional density drift instabilities at maximum growth rates are examined in detail. The thresholds of the instabilities are examined for an ionospheric model which includes ion-neutral, electron-neutral, and electron-ion collisions, and are compared with the threshold of the lower hybrid density drift instability. It is concluded that the k to the -5th short wavelength density power spectra observed above 280 km in the PLUMEX experiment are due to the effects of the universal density drift instability.

Gary, S. P.↗

NASA NTRS1984

Anomalous transport by magnetohydrodynamic Kelvin-Helmholtz instabilities in the solar wind-magnetosphere interaction

The high latitude, or downstream flank, and dayside low latitude magnetospheric boundaries are modeled in an MHD simulation of Kelvin-Helmholtz instablities in a compressible plasma for parallel and transverse configurations. Detailed attention is given to the nonlinear consequences of the instabilities for several different Alfven and sound Mach numbers in both configurations. Emphasis is given to the anomalous transport of momentum and energy by the Kelvin-Helmholtz instabilities across the magnetospheric boundary, which is crucial in evaluating the instabilities' contribution to magnetospheric convection. It is concluded that the anomalous tangential stress at the magnetospheric boundary caused by the instability may be of the order of 1 percent of the magnetosheath flow momentum adjacent to the boundary, and gives a contribution to the convection potential drop over the polar cap of 10-30 kV.

Miura, A.↗

NASA NTRS1985

Effect of Scattering on Instabilities in Line-driven Stellar Winds

Line driven O-B stellar winds are unstable to perturbations of short spatial wavelength and the growth rates for such instabilities are very rapid. The nature of the nonlinear development of this instability is unknown, but might possibly be one of blobs of gas driven through ambient gas or a quasiregular train of outward moving shocks. In either case the resulting dissipation of mechanical energy might explain the observed anomalous heating n O-B stars as evidenced by their X-ray emission and high ionization state. It also might explain the observed fine structure of the absorption lines and their time variability. The driving due to the absorption of the stellar continuum flux was considered and the effects of the diffuse, scattered radiation field were neglected. It was shown that under certain special conditions the effect of scattering could reduce the instability growth rate to zero. A stability analysis that includes scattering, but that uses the more physically realistic assumption of complete redistribution instead of coherent scattering, and that includes the effects of transverse velocity gradients, which become important as the flow moves away from the stellar surface is presented. It is found that the instability is eliminated right at the base of the wind, but that as the flow moves outward the instability rate rapidly becomes equal to a substantial fraction of the calculated value, the fraction asymptotically reaching 80% at large radii. Since this still implies many e folds in a characteristic outflow time, the primary conclusion that these winds are highly unstable is unchanged.

Owocki, S. P.↗

NASA NTRS1985

New Instabilities in Line Driven Winds

The physical mechanisms which potentially lead to instabilities in line driven winds, the drift instability and the line shape instability, are discussed. A general three dimensional treatment of the stability problem of line driven winds which leads to the general dispersion equation is proposed. From this dispersion equation automatically a third physical mechanism driving instability in stellar winds is deduced; the thermal drift instability which is related to changes in absorption of radiation caused by temperature perturbations. This mechanism results in growing inwardly propagating sound waves.

Martens, P. C. H.↗

NASA NTRS1985

The HEAO-2 Guest Investigator Program: Non-linear growth of instabilities in line-driven stellar winds

The linear instability of line-driven stellar winds to take proper account of the dynamical effect of scattered radiation were analyzed. It is found that: (1) the drag effect of the mean scattered radiation does greatly reduce the contribution of scattering lines to the instability at the very base of the wind, but the instability growth rate associated with such lines rapidly increases as the flow moves outward from the base, reaching more than 50% of the growth rate for pure absorption lines within a stellar radius of the surface, and eventually reaching 80% of that rate at large radii; (2) perturbations in the scattered radiation field may be important for the propagation of wind disturbances, but they have little effect on the wind instability; and (3) the contribution of strongly shadowed lines to the wind instability is often reduced compared to that of unshadowed lines, but their overall effect is not one of damping in the outer parts of the wind. It is concluded that, even when all scattering effects are taken into account, the bulk of the flow in a line-driven stellar wind is still highly unstable.

Rybicki, G. B.↗

NASA NTRS1985

Electrostatic instabilities in plasmas with two electron components

This paper considers the linear theory of electrostatic Vlasov instabilities driven by the relative drift between two Maxwellian electron components in an unmagnetized, homogeneous plasma bearing zero current. The dispersion properties, threshold drift speeds and growth rates of the electron beam instability, the conventional ion acoustic instability, and the ion acoustic beam instability are compared in detailed parametric studies. A new way of illustrating the parameter regimes in whih each of these three instabilities has the lowest threshold drift speed is demonstrated. This leads to clearly illustrated criteria for determining when enhanced electrostatic fluctuations between the ion and the electron plasma frequencies may be observed in plasmas with two electron components. In the case of a hot beam this criterion is a beam density n(b) which satisfies n(b)/n(e) is between 0.05 and 0.30 where n(e) is the total electron density.

Gary, S. P.↗

NASA NTRS1984

Investigation of a nozzle instability on an F100 engine equipped with a digital electronic engine control

An instability in the nozzle of the F100 engine, equipped with a digital electronic engine control (DEEC), was observed during a flight evaluation on an F-15 aircraft. The instability occurred in the upper left hand corner (ULMC) of the flight envelope during augmentation. The instability was not predicted by stability analysis, closed-loop simulations of the the engine, or altitude testing of the engine. The instability caused stalls and augmentor blowouts. The nozzle instability and the altitude testing are described. Linear analysis and nonlinear digital simulation test results are presented. Software modifications on further flight test are discussed.

Burcham, F. W., Jr.↗

NASA NTRS1985

Electromagnetic electron beam instabilities - Hot, isotropic beams

This paper considers the linear theory of electromagnetic instabilities driven by an electron beam in a homogeneous, nonrelativistic, Vlasov plasma. The beam is relatively hot, isotropic in its own frame, and streams parallel or antiparallel to a magnetic field B. Numerical solutions of the full dispersion equation for propagation parallel or antiparallel to B are presented, and the linear properties of the whistler heat flux and electron beam firehose instabilities are exhibited and compared. Under a broad range of parmameters the former mode has the lower beam speed threshold, and the larger maximum growth rate. In addition, it is demonstrated that, for a sufficiently large relative beam density, relative beam temperature, and plasma beta the whistler heat flux instability has a much lower beam speed threshold than the electrostatic electron beam instability. The application of these instabilities to first-order Fermi acceleration of electrons at space plasma shocks is discussed.

Gary, S. P.↗

NASA NTRS1985

Instabilities in line-driven stellar winds. II - Effect of scattering

An earlier analysis (Owocki and Rybicki) of the linear instability of line-driven stellar winds is extended to take proper account of the dynamical effect of scattered radiation. The principal findings are as follows: (1) the drag effect of the mean scattered radiation does indeed greatly reduce the contribution of scattering lines to the instability at the very base of the wind, but the instability growth rate associated with such lines rapidly increases as the flow moves outward from the base, reaching more than 50 percent of the growth rate for pure absorption lines within a stellar radius of the surface, and eventually reaching 80 percent of that rate at large radii; (2) perturbations in the scattered radiation field may be important for the propagation of wind disturbances, but they have little effect on the wind instability; (3) the contribution of a strongly shadowed line to the wind instability is often reduced compared to that of an unshadowed line, but its effect is not one of damping in the outer parts of the wind. The primary conclusion derived from these results is thus that, even when all scattering effects are taken into account, the bulk of the flow in a line-driven stellar wind is still highly unstable.

Owocki, S. P.↗