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NASA NTRS1993

A numerical study of wave propagation in a confined mixing layer by eigenfunction expansions

It is well known that the growth rate of instability waves of a two-dimensional free shear layer is reduced greatly at supersonic convective Mach numbers. In previous works, it has been shown that new wave modes exist when the shear layers are bounded by a channel due to the coupling effect between the acoustic wave modes and the motion of the mixing layer. The present work studies the simultaneous propagation of multiple stability waves using numerical simulation. It is shown here that the coexistence of two wave modes in the flow field can lead to an oscillatory growth of disturbance energy with each individual wave mode propagating linearly. This is particularly important when the growth rates of the unstable waves are small. It is also shown here that the propagation of two neutrally stable wave modes can lead to a stationary periodic structure of rms fluctuations. In the numerical simulations presented here the forced wave modes are propagating at same frequency, but with different phase velocities. In order to track the growth of each wave mode as it propagates downstream, a numerical method that can effectively detect and separate the contribution of the individual wave is given. It is demonstrated that by a least square fitting of the disturbance field with eigenfunctions the amplitude of each wave mode can be found. Satisfactory results as compared to linear theory are obtained.

Hu, Fang Q.↗

NASA NTRS1993

Modulational and decay instabilities of Alfven waves - Effects of streaming He(2+)

The parametric instability of a circularly polarized Alfven wave propagating along the background magnetic field are considered, with emphasis on the effects of a second ion species, He(2+), which drifts relative to the protons. Even though its abundance is small, the He(2+) modifies the dispersion relation of the 'pump' Alfven wave and introduces a new sound wave (alpha sound) in addition to the usual sound wave carried primarily by the electrons and protons. Instabilities which are close to the He(2+) gyroresonance are found. This may provide a means of directly transferring Alfven wave energy to the alpha particles, if the alphas are able to resonantly extract energy from the unstable waves without quenching the instability altogether. Instabilities which are close to the alpha particle sound speed are also found.

Hollweg, Joseph V.↗

NASA NTRS1972

Longitudinal waves in a perpendicular collisionless plasma shock. IV - Gradient B.

The consideration of elastic waves in a Vlasov plasma of unmagnetized ions and magnetized electrons undergoing E x B electron drift and gradient B drift, pursued in the earlier three parts, is brought to conclusion in this last part of the longitudinal wave study in a collisionless plasma shock. Detailed calculations of the effects of the beta sub e dimensionless parameter on the E x B electron drift instability are presented. It is shown that the range of propagation of the elastic waves about the perpendicular remains quite narrow, and that, for oblique propagation, the already narrow angular range of unstable waves is decreased by increases in the value of the beta sub e dimensionless parameter. Also, increases in wave number generally reduce the growth rate and the angular range of propagation.

Gary, S. P.↗

NASA NTRS1978

Fluctuation spectra in the NASA Lewis bumpy-torus plasma

The electrostatic potential fluctuation spectrum in the NASA Lewis bumpy-torus plasma was studied with capacitive probes in the low pressure (high impedance) mode and in the high pressure (low impedance) mode. Under different operating conditions, the plasma exhibited electrostatic potential fluctuations (1) at a set of discrete frequencies, (2) at a continuum of frequencies, and (3) as incoherent high-frequency turbulence. The frequencies and azimuthal wave numbers were determined from digitally implemented autopower and cross-power spectra. The azimuthal dispersion characteristics of the unstable waves were examined by varying the electrode voltage, the polarity of the voltage, and the neutral background density at a constant magnetic field strength.

Singh, C. M.↗

NASA NTRS1981

A Martian general circulation experiment with large topography

A three-layer general circulation model of the Martian atmosphere is described, and the assumptions governing the model are discussed. The simulated, zonally averaged circulation is found to have only limited sensitivity to differences between this model and an earlier general circulation model; this circulation compares reasonably well with observations. It is also found that the meridional mass flow produced by the seasonal condensation of CO2 in the winter polar region has a major influence on the circulation; owing to the weak influence of atmospheric heat transport, however, the mass flow is governed almost entirely by radiation. Quasi-barotropic stationary waves, which are forced kinematically by the topography and which resemble topographically forced terrestrial planetary waves, are generated by the model in the winter hemisphere region of strong eastward flow, while baroclinic stationary waves are thermally forced by topography in the tropics and summer subtropics. It is also concluded that transient baroclinically unstable waves, of somewhat lower dominant wavenumber than those found on the earth, are generated in winter midlatitudes; their amplitudes, wavenumbers, and phase speeds closely agree with what has been deduced from the Viking lander observations.

Pollack, J. B.↗

NASA NTRS1982

Dynamics of the atmosphere

Observations of and possible explanations for the dynamics of the Venus atmosphere as revelaed by Pioneer Venus and the Venera spacecraft are discussed. An important observation was that the entire atmosphere moves in the same retrograde (westward) direction at average speeds of up to about 110 m/sec, which may be explained by zonal jets arising from interactions of meridional cells, viscosity and solar heating. Atmospheric thermal tides, temperature and wind perturbations caused by solar heating were also observed which may have influences on tidal winds and warming at the poles. In addition, atmospheric waves with periods of 5.3 and 2.9 earth days have been detected between the Venus cloud tops, and calculations of baroclinically unstable waves on Venus have been made with a general circulation model.

Elson, L. S.↗

NASA NTRS1987

Roll-up of vorticity in adverse-pressure-gradient boundary layers

It is shown how the unsteady, nonlinear critical-layer equation determines the evolution of instability waves in a weak adverse-pressure-gradient boundary layer. Numerical solutions show that the nonlinearity halts the growth of these inviscidly unstable waves. The stabilizing effect of nonlinearity, in the present case, can be described as a consequence of either the increase (toward zero) of the phase jump across the critical layer or the roll-up of the critical-layer disturbance vorticity.

Goldstein, M. E.↗

NASA NTRS1997

Observational and Model Studies of Large-Scale Mixing Processes in the Stratosphere

The following is the final technical report for grant NAGW-3442, 'Observational and Model Studies of Large-Scale Mixing Processes in the Stratosphere'. Research efforts in the first year concentrated on transport and mixing processes in the polar vortices. Three papers on mixing in the Antarctic were published. The first was a numerical modeling study of wavebreaking and mixing and their relationship to the period of observed stratospheric waves (Bowman). The second paper presented evidence from TOMS for wavebreaking in the Antarctic (Bowman and Mangus 1993). The third paper used Lagrangian trajectory calculations from analyzed winds to show that there is very little transport into the Antarctic polar vortex prior to the vortex breakdown (Bowman). Mixing is significantly greater at lower levels. This research helped to confirm theoretical arguments for vortex isolation and data from the Antarctic field experiments that were interpreted as indicating isolation. A Ph.D. student, Steve Dahlberg, used the trajectory approach to investigate mixing and transport in the Arctic. While the Arctic vortex is much more disturbed than the Antarctic, there still appears to be relatively little transport across the vortex boundary at 450 K prior to the vortex breakdown. The primary reason for the absence of an ozone hole in the Arctic is the earlier warming and breakdown of the vortex compared to the Antarctic, not replenishment of ozone by greater transport. Two papers describing these results have appeared (Dahlberg and Bowman; Dahlberg and Bowman). Steve Dahlberg completed his Ph.D. thesis (Dahlberg and Bowman) and is now teaching in the Physics Department at Concordia College. We also prepared an analysis of the QBO in SBUV ozone data (Hollandsworth et al.). A numerical study in collaboration with Dr. Ping Chen investigated mixing by barotropic instability, which is the probable origin of the 4-day wave in the upper stratosphere (Bowman and Chen). The important result from this paper is that even in the presence of growing, unstable waves, the mixing barriers around

Bowman, Kenneth P.↗

NASA NTRS1979

HF-induced parametric decay in presence of field-aligned irregularities

A nonlinear theory for the saturation of the HF-induced parametric decay instability is formulated in terms of the normal modes of a field-aligned plasma wave duct. Coupling coefficients between modes are derived, and a saturation spectrum is computed numerically for a typical irregularity. The computed spectrum shows that unstable waves may propagate at larger angles to the magnetic field than would be the case in a regular medium. The relevance of this work to the experiment of Muldrew and Showen (1977), concerning the height of the HF-induced plasma line at Arecibo, is discussed. A possible explanation is also found for the 'decay line' feature in comparison with the 'broad bump' in the observed backscatter spectrum.

Rypdal, K.↗

NASA NTRS1988

Spatial stability of a compressible mixing layer

Presented are the results of a study of the inviscid spatial stability of a parallel compressible mixing layer. The parameters of this study are the Mach number of the moving stream, the ratio of the temperature of the stationary stream to that of the moving stream, the frequency and the direction of propagation of the disturbance wave. Stability characteristics of the flow as a function of these parameters are given. It is shown that if the Mach number exceeds a critical value there are always two groups of unstable waves. One of these groups is fast with phase speeds greater than 1/2, and the other is slow with speeds less than 1/2. Phase speeds for the neutral and unstable modes are given, as well as growth rates for the unstable modes. It is shown that three dimensional modes have the same general behavior as the two dimensional modes but with higher growth rates over some range of propagation direction. Finally, a group of very low frequency unstable modes was found for sufficiently large Mach numbers. These modes have very low phase speeds but large growth rates.

Jackson, T. L.↗

NASA NTRS1989

Inviscid spatial stability of a compressible mixing layer

Presented are the results of a study of the inviscid spatial stability of a parallel compressible mixing layer. The parameters of this study are the Mach number of the moving stream, the ratio of the temperature of the stationary stream to that of the moving stream, the frequency and the direction of propagation of the disturbance wave. Stability characteristics of the flow as a function of these parameters are given. It is shown that if the Mach number exceeds a critical value there are always two groups of unstable waves. One of these groups is fast with phase speeds greater than 1/2, and the other is slow with speeds less than 1/2. Phase speeds for the neutral and unstable modes are given, as well as growth rates for the unstable modes. It is shown that three-dimensional modes have the same general behavior as the two-dimensional modes but with higher growth rates over some range of propagation direction. Finally, a group of very low frequency unstable modes was found for sufficiently large Mach numbers. These modes have very low phase speeds but large growth rates.

Jackson, T. L.↗

NASA NTRS1977

Stability of higher-order Bragg interactions in active periodic media

The stability of waves in unbounded, longitudinally periodic media is studied for index and gain coupling. Time-independent periodic media are found to support both stable and absolutely unstable waves. The wave characteristics depend upon average gain or loss, coupling type, and Bragg order. The extended coupled waves equations provide explicit values of threshold, frequency, and temporal growth rate for instabilities at all Bragg resonances through the dispersion relation. Applications to multiharmonic periodicities and complex couplings are briefly discussed with particular note taken of possible reductions of the stability thresholds and removal of threshold degeneracies. Comparisons are made to the longitudinally bounded case of distributed feedback lasers.

Jaggard, D. L.↗

NASA NTRS1993

Global-scale waves in the Venus atmosphere

The nature of global-scale waves that can exist in the atmosphere of Venus is examined. A linear three-dimensional model atmosphere with spherical geometry is used to study large-scale forced and free waves. Solutions are obtained numerically with grid points in the vertical and a spherical harmonic expansion in the horizontal. Observations have shown a global-scale traveling wave with phase speed near the cloud-top wind velocity. Global-scale wave modes are found to exist in the model at this velocity. When a radiative-dynamic cloud feedback is added to the model, the most unstable wave mode is found to have the same phase speed as the observed wave. The horizontal structure of this wave is consistent with the observed horizontal structure of the 'Y' feature seen in ultraviolet images of the Venus cloud top.

Smith, Michael D.↗

NASA NTRS1988

Alfven ion-cyclotron heating of ionospheric O(+) ions

Transversely heated ionospheric ions, in particular O(+) ions, are often observed flowing upward along auroral field lines. Currents observed in association with the transversely heated ions can drive shear Alfven waves and electrostatic ion-cyclotron waves unstable which can, in turn, be resonantly absorbed by the ions to produce the heating. Particle simulations are used to examine self-consistently the excitation of these waves and the associated heating. It is shown that the growth of the electrostatic ion-cyclotron waves quickly becomes suppressed as the ions become heated and the dominant wave fields are those of the shear Alfven wave. The resultant transverse ion heating is larger and faster than that produced by solely electrostatic ion-cyclotron wave heating. Due to trapping of ions by the shear Alfven wave, the temperature of the O(+) ions remains comparable to that of the H(+) ions.

Winglee, R. M.↗

NASA NTRS1992

Effects of long-wavelength dissipation on beam-driven Langmuir turbulence

The effects of long-wavelength dissipation on beam-driven Langmuir turbulence are investigated using numerical simulations that include both weak and strong turbulence effects. Strong-turbulence wave collapses occur concurrently with weak-turbulence energy cascades if the long-wavelength damping is sufficiently small relative to the growth rate of the beam-unstable waves. Above a threshold damping level, only the weak-turbulence backscatter cascade is observed, and it becomes increasingly truncated as the damping increases, eventually consisting of only a single backscatter. A simple Lotka-Volterra model gives an excellent description of the periodic evolution observed in the weak-turbulence regime. Suppression of the usual backscatter cascade by long-wavelength damping enables intense beam-aligned density troughs to form, which trap and duct Langmuir waves.

Robinson, P. A.↗

NASA NTRS1990

Satellite formation in capillary jet breakup

Computations of finite-amplitude, spatially periodic wave growth on a cylindrical jet have been carried out using a boundary integral method. The initial wave growth is in agreement with Rayleigh's linear theory. When followed to completion these waves pinch off large drops separated by smaller satellite drops (spherules) that decrease in size with decreasing wavelength. The computed sizes of both drops and satellites agree with experiment. It is found that satellites will form for all unstable wave numbers. The small satellites that are computed at wave numbers near the critical wave number were not predicted by near-linear analysis but are observed in experimental photographs of jet breakup. Computation of the collapse of elongated satellites shows short waves propagating on their surfaces.

Mansour, Nagi N.↗

NASA NTRS1992

Current-driven plasma acceleration versus current-driven energy dissipation. III - Anomalous transport

In the present paper the linear stability description and weak turbulence theory are used to develop a second order description of wave-particle transport and anomalous dissipation. The goal is to arrive at anomalous transport coefficients that can be readily included in fluid flow codes. In particular, expressions are derived for the heating rates of ions and electrons by the unstable waves and for the electron-wave momentum exchange rate that controls the anomalous resistivity effect. Comparative calculations were undertaken assuming four different saturation models: ion trapping, electron trapping, ion resonance broadening, and thermodynamic bound. A foremost finding is the importance of the role of electron Hall parameter in scaling the level of anomalous dissipation for the parameter range of the MPD thruster plasma. Polynomial expressions of the relevant transport coefficients cast solely in terms of macroscopic parameters are also obtained for inclusion in plasma fluid codes for the self-consistent numerical simulation of real thruster flows including microturbulent effects.

Choueiri, Edgar Y.↗

NASA NTRS1988

Shock-associated MHD waves - A model for interstellar density fluctuations

The possibility that the density fluctuations responsible for radio scintillations could be due to ion-beam-generated MHD waves near interstellar shock waves is discussed. This suggestion is inspired by spacecraft observations which reveal these phenomena near shocks in the solar system. The model quite naturally accounts for the scale on which these fluctuations occur; it is dictated by the wavelength of the unstable waves.

Spangler, Steven R.↗