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NASA NTRS1984

Generation of instability waves in flows separating from smooth surfaces

This paper analyses the coupling between an imposed disturbance and an instability wave that propagates downstream on a shear layer which emanates from a separation point on a smooth surface. Since the wavelengths of the most-amplified instability waves will generally be small compared with the streamwise body dimensions, the analysis is restricted to this 'high-frequency' limit and the solution is obtained by using matched asymptotic expansions. An 'inner' solution, valid near the separation point, is matched onto an outer solution, which represents an instability wave on a slowly diverging mean flow. The analysis relates the amplitude of this instability to that of the imposed disturbance.

Goldstein, M. E.↗

NASA NTRS1984

Sound generation and upstream influence due to instability waves interacting with non-uniform mean flows

Attention is given to the sound produced by artificially excited, spatially growing instability waves on subsonic shear layers. Real flows that always diverge in the downstream direction allow sound to be produced by the interaction of the instability waves with the resulting streamwise variations of the flow. The upstream influence, or feedback, can interact with the splitter plate lip to produce a downstream-propagating instability wave that may under certain conditions be the same instability wave that originally generated the upstream influence. The present treatment is restricted to very low Mach number flows, so that compressibility effects can only become important over large distances.

Goldstein, M. E.↗

NASA NTRS1984

A numerical simulation of barotropic instability. II Wave-wave interaction

A fully nonlinear numerical model of the point jet barotropic instability is used to test and confirm the hypothesis that the magnitude of the wave vorticity does not exceed the magnitude of the initial shear. This result arises directly from the local conservation of vorticity following a parcel and the fact that unstable waves are principally confined to the region where the zonal mean vorticity can be smoothed by the wave so as to eliminate the instability. Comparisons are made between fully nonlinear and quasi-linear models of the point jet instability and their tracer transport properties. Differences become particularly evident after wave saturation. The most important effect neglected by the wave-mean flow model appears to be the advection of wave vorticity by the most unstable mode. However, as equilibration of the instability proceeds, the globally averaged properties of both models are found to be similar.

Nielsen, J. E.↗

NASA NTRS1985

Instability in hydraulic machines demonstration rig

In fluid flow machines, the working fluid involved in rotative motion due to shaft rotation significantly modifies the rotor synchronous response. This can result in the rotor maintaining the high vibration amplitude that occurs at resonance over an extended rotative speed range. The phase changes in this range are typically very small. The fluid may also create rotor instability, i.e., subsynchronous self-excited vibrations, when the rotative speed is sufficiently high. This rotor instability is often related and increases with higher rotor unbalance (Opposite to other types of instability such as oil whirl/whip, internal friction, etc.). The rotor rig demonstrates typical dynamic behavior of hydraulic machines. At lower speeds the effect of amplitude/phase mentioned above is noticeable; at higher speeds the subsynchronous instability occurs.

Muszynska, A.↗

NASA NTRS1986

Electromagnetic instabilities and gyrophase-bunched particles

The linear theory of electromagnetic instabilities at propagation parallel or antiparallel to a uniform magnetic field B(0) is used to calculate the relative phase angle between the fluctuating velocity vector of the jth component and the fluctuating magnetic field. A criterion that determines when this phase relationship leads to observable gyrophase bunching during the linear growth phase of an instability is also derived. The theory is applied to bunching of ion components by ion beam instabilities. Among the electromagnetic cool ion beam instabilities, it is found that the right-hand resonant mode is most likely to cause observable gyrophase bunching of an ion beam during linear growth.

Gary, S. P.↗

NASA NTRS1986

Electrostatic instabilities of velocity-space-shell distributions in magnetized plasmas

Electron instabilities of magnetized spherical shell distributions in velocity space with a colder Maxwellian background are investigated analytically with simulations using electrostatic particle codes. The resonant and nonresonant instabilities observed in the particle simulations are in agreement with zeros of the dielectric function, as found from the resonant approximations for waves with an electric field component along the magnetic field or by computation with a root solver code in the case of perpendicular propagation. Saturation of the instabilities is by nonlinear cyclotron resonance with the cold background in the resonant case or by nonstochastic cyclotron harmonic damping by the cold background in the nonresonant case. Instabilities invariably lead to perpendicular acceleration and heating of the cold background to velocities sometimes exceeding the shell velocity.

Sentman, D. D.↗

NASA NTRS1986

Taylor-Goertler instabilities of Tollmien-Schlichting waves and other flows governed by the interactive boundary-layer equations

The Taylor-Goertler vortex instability equations are formulated for steady and unsteady interacting boundary-layer flows. The effective Goertler number is shown to be a function of the wall shape in the boundary layer and the possibility of both steady and unsteady Taylor-Goertler modes exists. As an example the steady flow in a symmetrically constricted channel is considered and it is shown that unstable Goertler vortices exist before the boundary layers at the wall develop the Goldstein singularity discussed by Smith and Daniels (1981). As an example of an unsteady spatially varying basic state, it is considered the instability of high-frequency large-amplitude two- and three-dimensional Tollmien-Schlichting waves in a curved channel. It is shown that they are unstable in the first 'Stokes-layer stage' of the hierarchy of nonlinear states discussed by Smith and Burggraf (1985). This instability of Tollmien-Schlichting waves in an internal flow can occur in the presence of either convex or concave curvature. Some discussion of this instability in external flows is given.

Hall, Philip↗

NASA NTRS1986

Electrostatic beam instabilities in a positive/negative ion plasma

This paper examines the linear theory of electrostatic waves and instabilities in an unmagnetized, homogeneous Vlasov plasma. The first configuration considered is that of a stable plasma with three Maxwellian components: electrons, positive ions, and negative ions. The dispersion properties of the lightly damped ion modes are studied as a function of relative electron density and relative component temperatures. The second configuration considered is that of a tenuous electron-ion beam with drift speed streaming through a negative/positive ion plasma. If the beam is very tenuous, an electron beam instability is excited; if the beam is more dense, the instability becomes Buneman-like with parabolic dispersion. The thresholds and maximum growth rates of these instabilities are described as functions of the beam density and drift speed.

Galvez, Miguel↗

NASA NTRS1987

Electromagnetic ion beam instabilities - Growth at cyclotron harmonic wave numbers

The linear theory of electromagnetic ion beam instabilities for arbitrary angles of propagation is studied, with an emphasis on the conditions necessary to generate unstable modes at low harmonics of the ion cyclotron resonance condition. The present results extend the analysis of Smith et al. (1985). That paper considered only the plasma parameters at a time during which harmonic wave modes were observed in the earth's foreshock. The parameters of that paper are used as the basis of parametric variations here to establish the range of beam properties which may give rise to observable harmonic spectra. It is shown that the growth rates of both left-hand and right-hand cyclotron harmonic instabilities are enhanced by an increase in the beam temperature anisotropy and/or the beam speed. Decreases in the beam density and/or the core-ion beta reduce the overall growth of the cyclotron harmonic instabilities but favor the growth of these modes over the growth of the nonresonant instability and thereby enhance the observability of the harmonics.

Smith, Charles W.↗

NASA NTRS1987

On the spatial instability of piecewise linear free shear layers

The main goal of this paper is to clarify the spatial instability of a piecewise linear free shear flow. This is done by obtaining numerical solutions to the Orr-Sommerfeld equation of high Reynolds numbers. The velocity profile chosen is very much like a piecewise linear one, with the exception that the corners have been rounded so that the entire profile is infinitely differentiable. It is found that the (viscous) spatial instability of this modified profile is virtually identical to the inviscid spatial instability of the piecewise linear profile and agrees qwalitatively with the inviscid results for the tanh profile when the shear layers are convectively unstable. The unphysical features, previously identified for the piecewise linear velocity profile, arise only when the flow is absolutely unstable. It is concluded that there is nothing wrong with the inviscid spatial instability of piecewise linear shear flows.

Balsa, T. F.↗

NASA NTRS1987

Waves and instabilities

The U.S research activities during the mid-1982 to mid-1986 period in the area of plasma waves and instabilities are described. The principal results obtained by satellite observations and theoretical research can be divided into the following six categories: (1) whistler-mode wave-electron interactions, (2) wave-induced particle precipitation, (3) ULF wave phenomena, (4) ion-mode waves and instabilities, (5) auroral kilometric radiation, and (6) ionospheric irregularities and instabilities. In addition, waves and instabilities found in the outer magnetosphere, including the geomagnetic tail, magnetopause, and bow shock regions, are briefly discussed.

Inan, Umran S.↗

NASA NTRS1987

Mirror instability in the magnetosphere of Comet Halley

High resolution Vega 1 and 2 magnetic measurements in the cometary magnetosphere and magnetosheath of Halley reveal the presence of fluctuations with the signature expected for the mirror instability. This instability is a mechanism by which homogeneously produced cometary ions with a large perpendicular temperature anisotropy can be concentrated into discrete linear features. Thus, the mirror instability may provide a new mechanism for the generation of cometary rays. To our knowledge the presence of this instability in the cometary plasma was not predicted.

Russell, C. T.↗

NASA NTRS1987

A linear MHD instability analysis of solar mass ejections with gravitation

The linear MHD instability of a cylindrical plasma is used to investigate the origin of solar mass ejections, and the dispersion relation is solved numerically. The initial plasma-flow velocity is found to have a significant effect on the instability criteria and growth rate, and the instability growth-rate is shown to be larger in cases where plasma flow exists, relative to the static case. Results suggest that the plasma column may break into small pieces. Assuming a thin-tube approximation, gravity is found to have little effect on the instability of quasi-horizontal ejection, but to have considerable effect on the vertical ejection. In considering the gravitational force, an exact analytical solution is found for the vertical case, while asymptotic solutions are given for the horizontal and oblique cases.

Song, M. T.↗

NASA NTRS1987

Electron/ion whistler instabilities and magnetic noise bursts

Two whistler instabilities are investigated by means of the linear Vlasov dispersion equation. They are called the electron/ion parallel and oblique whistler instabilities, and are driven by electron/ion relative drifts along the magnetic field. It is demonstrated that the enhanced fluctuations from these instabilities can explain several properties of magnetic noise bursts in and near the plasma sheet in the presence of ion beams and/or field-aligned currents. At sufficiently high plasma beta, these instabilities may affect the current system in the magnetotail.

Akimoto, K.↗

NASA NTRS1988

Nonlinear evolution of the Kelvin-Helmholtz instability in the high-latitude ionosphere

The first numerical simulations of the nonlinear evolution of the electrostatic Kelvin-Helmholtz (K-H) instability with ionospheric Perderson conductivity coupling are presented. It is found that the K-H instability develops in a distinctly different manner in the nonlinear regime with Pedersen coupling than without it. Pedersen coupling effects, in conjunction with a neutral wind and density gradient, are shown to result in an increased time scale for K-H instability wave growth, to inhibit K-H vortex formation, to lead to nonlinear structures which can be described as 'breaking waves', and to generate, in the nonlinear regime, small-scale turbulence by means of secondary instabilities growing on primary waves. The spatial power spectra of the electrostatic potential and density fluctuations are computed, and differences with and without Pedersen effects are reported.

Keskinen, M. J.↗

NASA NTRS1988

On thermal instability and hydrostatic equilibrium in cooling flows

The nature of thermal instability in cluster cooling flows is investigated. The radial modes of a spherical static system are discussed, and it is shown that only the acoustical modes are present at short wavelengths and that there are no isobaric thermal instabilities. The analysis is expanded to include nonradial modes, and it is demonstrated that there are azimuthal high wavenumber thermal modes which can indeed become unstable according to the classical Field (1965) criterion. A new convective instability criterion is derived, and thermal instability and its limitations are briefly discussed.

Balbus, Steven A.↗

NASA NTRS1988

Current driven instabilities of an electromagnetically accelerated plasma

A plasma instability that strongly influences the efficiency and lifetime of electromagnetic plasma accelerators was quantitatively measured. Experimental measurements of dispersion relations (wave phase velocities), spatial growth rates, and stability boundaries are reported. The measured critical wave parameters are in excellent agreement with theoretical instability boundary predictions. The instability is current driven and affects a wide spectrum of longitudinal (electrostatic) oscillations. Current driven instabilities, which are intrinsic to the high-current-carrying magnetized plasma of the magnetoplasmadynmic (MPD) accelerator, were investigated with a kinetic theoretical model based on first principles. Analytical limits of the appropriate dispersion relation yield unstable ion acoustic waves for T(i)/T(e) much less than 1 and electron acoustic waves for T(i)/T(e) much greater than 1. The resulting set of nonlinear equations for the case of T(i)/T(e) = 1, of most interest to the MPD thruster Plasma Wave Experiment, was numerically solved to yield a multiparameter set of stability boundaries. Under certain conditions, marginally stable waves traveling almost perpendicular to the magnetic field would travel at a velocity equal to that of the electron current. Such waves were termed current waves. Unstable current waves near the upper stability boundary were observed experimentally and are in accordance with theoretical predictions. This provides unambiguous proof of the existence of such instabilites in electromagnetic plasma accelerators.

Chouetri, E. Y.↗

NASA NTRS1988

A mirror instability associated with newly created ions in a moving plasma

Using a plasma model in which the ambient magnetic field is parallel to the z axis and the wave vector, an instability that resembles the usual hydromagnetic mirror instability is demonstrated. The instability is caused by freshly created ions in a moving plasma; the source of its free energy is associated with the ring distribution of the newly created ions, resulting in a high ion kinetic temperature in the direction transverse to the ambient magnetic field. The results of a stability analysis indicate that this instability can lead to the amplification of magnetosonic waves.

Wu, C. S.↗