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NASA NTRS1989

The electron beam instability revisited: Growth above and below f sub p

The growth of electrostatic waves near the plasma frequency (fp) due to an unstable electron beam is investigated by solving the unmagnetized electrostatic dispersion equation numerically. The numerical solutions are compared with analytic theories for reactive (or fluid-type) and kinetic versions of the beam instability, and for the O'Neil/Malmberg connection of the beam and Langmuir modes. Conditions for growth significantly above or below fp are given. Three general results are found: (1) The unstable waves do not grow on a mode with Langmuir dispersion except in the limit of a very dilute beam with growth on O'Neil/Malmberg's connected mode; (2) The properties of the unstable mode depend strongly on beam parameters such as beam density, speed and temperature; and (3) The frequency of maximum growth frequently lies significantly above or below fp, and differs significantly from that predicted by the Langmuir dispersion relation. Results imply important consequences for theories of strong turbulence and nonlinear wave-wave processes, and observational identification of fp from observed wave frequencies.

Cairns, I. H.↗

NASA NTRS1989

Multiwave Interactions in Turbulent Jets

Nonlinear wave-wave interactions in turbulent jets were investigated based on the integrated energy of each scale of motion in a cross section of the jet. The analysis indicates that two frequency components in the axisymmetric mode can interact with other background frequencies in the axisymmetric mode, thereby amplifying an enormous number of other frequencies. Two frequency components in a single helical mode cannot, by themselves, amplify other frequency components. But combinations of frequency components of helical and axisymmetric modes can amplify other frequencies in other helical modes. The present computations produce several features consistent with experimental observations such as: (1) dependency of the interactions on the initial phase differences, (2) enhancement of the momentum thickness under multifrequency forcing, and (3) the increase in background turbulence under forcing. In a multifrequency-excited jet, mixing enhancement was found to be a result of the turbulence enhancement rather than simply the amplification of forced wave components. The excitation waves pump energy from the mean flow to the turbulence, thus enhancing the latter. The high frequency waves enhance the turbulence close to the jet exit, but, the low frequency waves are most effective further downstream.

Mankbadi, Reda R.↗

NASA NTRS1988

Modes of variability in a low-order two-level model

A low-order two-level mode in a beta-plane channel is integrated over long periods of time to investigate low-frequency midlatitude variability. The model takes into account nonlinear wave-wave and wave-mean flow interactions as well as zonally asymmetric forcing by topography. The following properties of the model are examined: model scaling and response to variation of parameters, extra damping at the shortest scale, time-mean model flow, and variance.

O'Brien, Enda↗

NASA NTRS1989

Nonlinear evolution of high frequency R-mode waves excited by water group ions near comets - Computer experiments

An ion beam resonates with R-mode waves at a high-frequency RH mode and a low-frequency RL mode. The nonlinear evolution of ion beam-generated RH waves is studied here by one-dimensional hybrid computer experiments. Both wave-particle and subsequent wave-wave interactions are examined. The competing process among coexisting RH and RL mode beam instabilities and repeated decay instabilities triggered by the beam-excited RH mode waves is clarified. It is found that the quenching of the RH instability is not caused by a thermal spreading of the ion beam, but by the nonlinear wave-wave coupling process. The growing RH waves become unstable against the decay instability. This instability involves a backward-traveling RH electromagnetic wave and a forward-traveling longitudinal sound wave. The inverse cascading process is found to occur faster than the growth of the RL mode. Wave spectra decaying from the RH waves weaken as time elapses and the RL mode waves become dominant at the end of the computer experiment.

Kojima, H.↗

NASA NTRS1989

Time evolution from linear to nonlinear stages in magnetohydrodynamic parametric instabilities

The nonlinear evolution of the magnetohydrodynamic (MHD) parametric instability of wave fluctuations propagating along an unperturbed magnetic field is investigated. Both a magnetohydrodynamic perturbation-theoretical approach and a nonlinear MHD simulation are used. It is shown that high harmonic waves are rapidly excited by wave-wave coupling, and that the wave spectrum evolves from a state containing a small number of degrees of freedom in k space to one which contains a large number of degrees of freedom. It is found that the spectral evolution prior to nonlinear saturation is well described by the prturbation theory. During this stage, the ratio of the growth rate of the nth harmonic wave to the linear growth rate of the fundamental wave is n. The nonlinear saturation stage is characterized by a frequency shift of the fundamental wave that destroys the wave-wave resonance condition which, in turn, causes the wave amplitude to cease its growth.

Hoshino, M.↗

NASA NTRS1989

Dynamics of baroclinic wave systems

The research carried out in the past year dealt with nonlinear baroclinic wave dynamics. The model consisted of an Eady baroclinic basic state and uneven Elkman dissipation at the top and bottom boundaries with/without slopes. The method of solution used a truncated spectral expansion with three zonal waves and one or two meridional modes. Numerical experiments were performed on synoptic scale waves or planetary scale waves with/without wave-wave interaction.

Barcilon, Albert↗

NASA NTRS1989

Laboratory and theoretical studies of baroclinic processes

An understanding is being developed for processes which may be important in the atmosphere, and the definition and analysis of baroclinic experiments utilizing the geophysical fluid flow cells (GFFC) apparatus in microgravity space flights. Included are studies using numerical codes, theoretical models, and terrestrial laboratory experiments. The numerical modeling is performed in three stages: calculation of steady axisymmetric flow, calculation of fastest-growing linear eigenmodes, and nonlinear effects (first, wave-mean flow interactions, then wave-wave interactions). The code can accommodate cylindrical, spherical, or channel geometry. It uses finite differences in the vertical and meridional directions, and is spectral in the azimuthal. The theoretical work was mostly in the area of effects of topography upon the baroclinic instability problem. The laboratory experiments are performed in a cylindrical annulus which has a temperture gradient imposed upon the lower surface and an approximately isothermal outer wall, with the upper and inner surfaces being nominally thermally insulating.

Miller, Timothy↗

NASA NTRS1990

Multiwave nonlinear interactions in the axisymmetric mode

Mankbadi, Reda R.↗

NASA NTRS1989

Discrete electromagnetic emissions in planetary magnetospheres

The present state of knowledge and observations of discrete electromagnetic emissions detected in the magnetospheres of earth and the outer planets are reviewed. The history of ground observations and satellite observations is included. Active experiments studying wave propagation, wave-wave and wave-particle interactions, and the generation and triggering of discrete emissions are addressed. The various theories proposed to explain the phenomena are examined, and computer simulations of wave-particle interactions and the generation and triggering of discrete emissions are reviewed. Related phenomena observed at frequencies above both the electron cyclotron frequency and the plasma frequency are considered. Areas of future investigation are discussed.

Anderson, Roger R.↗

NASA NTRS1990

Wave-interactions in supersonic and hypersonic flows

Work completed under the current grant comprises the start of a theoretical and computational attack on the subharmonic route to secondary instabilities in compressible flows. The total flow field in this problem is made up of the following components: (1) a steady streamwise mean boundary layer flow which depends only on the normal space component y; (2) a two-dimensional time dependent T-S wave which moves with wavespeed c and has no spanwise dependence; and (3) a fully three-dimensional, time dependent T-S wave whose streamwise wavenumber is half of the streamwise wavenumber associated with the two-dimensional T-S wave in b. If a frame of reference is adopted which moves with the wavespeed c of the 2-D T-S wave, the time dependence of this portion of the flow can be eliminated. The effective steady mean flow in this problem is now the sum of the original parallel steady mean flow and the initial 2-D T-S instability. Dependence on the streamwise coordinate x in this mean flow can be extracted by assuming normal mode expansions involving complex exponentials and the streamwise wavenumber a. However, it is important to note that, because this is a wave-wave interaction problem, unlike the usual linear instability case, both the complex exponential, and its complex conjugate, must be retained in describing the 2-D T-S wave. The role of the perturbation to the steady mean flow is now played by the 3-D time dependent T-S wave. In treating this wave, normal modes in the streamwise and spanwise directions and time may be used. Consistent with the subharmonic nature of this transition route, the streamwise wavenumber is a/2, and complex conjugates of the complex exponential must be employed. This is not the case with the modes giving z and t dependence with wavespeed o and spanwise wavenumber B as the effective mean flow quantities are independent of z and their time dependence is accounted for by the moving frame of reference. Consequently, the wave-wave interaction which will produce mean flow modification occurs only through the streamwise exponentials.

Lakin, William D.↗

NASA NTRS1990

The effects of oppositely sloping boundaries with Ekman dissipation in a nonlinear baroclinic system

The present analytical and numerical examination of the effect of the slope Delta with dissipation delta on baroclinic flows in linear and nonlinear systems uses a modified Eady channel model with oppositely sloping top and bottom Ekman layers, and truncates the spectral wave solution up to six components. Comparisons are made wherever possible with results from beta-plane dissipative systems. In the linear system, the combined effect of Delta and delta strongly stabilizes long waves. In a nonlinear system without wave-wave interaction, Delta stabilizes the flow even for small delta and reduces the domain of vacillation while enlarging the domain of single-wave steady state.

Weng, H.-Y.↗

NASA NTRS1990

The effects of large-scale topography on the circulation in low-order models

This paper investigates the effect of topography on circulation produced by low-order quasi-geostrophic models that are capable of reproducing many basic features of midlatitude general circulation in the absence of topography. Using a simple two-level spectral model, time-mean stationary waves and low-frequency phenomena were examined for three different topographic configurations, of which two consisted of a sinusoidal mountain-valley structure, and the third was the Fourier representation of an isolated mountain peak. In the experiment with an isolated mountain, it was found that the time-mean wave in the model was highly dependent on the operation of wave-wave interactions, which had a significant impact on stationary waves through modifications in the mean zonal flow.

O'Brien, Enda↗

NASA NTRS1990

Intraseasonal oscillations in the extratropics - Hopf bifurcation and topographic instabilities

A potential vorticity model in a beta-channel is used to analyze the resonant response of equivalent-barotropic flow to topography in the presence of a forced zonal jet with arbitrary meridional structure. The nonlinear dynamics near different resonances is studied considering both wave-wave and wave-zonal flow interactions. It is shown that Hopf bifurcations from stationary to periodic flows are possible due to the nonlinear instability of nonzonal, topographically forced flow. Low-frequency, finite-amplitude oscillations arise due to a combination of two factors: (1) nonlinear wave-wave interactions, which tend to reduce the Rossby wave frequency; and (2) wave-zonal flow interactions, which reflect the importance of wave momentum transport in shifting the westerly jet and of the topographic form drag. The physical mechanism of atmospherically realistic Hopf bifurcations depends crucially on the meridional profile of the mean zonal flow giving rise to a dipole-shaped resonance.

Jin, F.-F.↗

NASA NTRS1991

Multifrequency excited jets

An analysis of nonlinear wave-wave interactions in turbulent jets based on the integrated energy of each scale of motion in a cross section of the jet shows that two frequency components in the axisymmetric mode can interact with other mackground frequencies in that mode, thereby amplifying many other frequencies. The present computations produce several features consistent with experimental observations on two-frequency excitation, such as the dependence of the interaction on the initial phase differences between the waves, the enhancement of the momentum thickness under multifrequency forcing, and the increase in background turbulence under forcing. Mixing enhancement is found to be due to turbulence enhancement, rather than the simple amplification of forced-wave components.

Mankbadi, Reda R.↗

NASA NTRS1990

Wave-particle interactions on the FAST satellite

NASA's Fast Auroral Snapshot, or 'FAST' satellite, scheduled for launch in 1993, will investigate the plasma physics of the low altitude auroral zone from a 3500-km apogee polar orbit. FAST will give attention to wave, double-layer, and soliton production processes due to electrons and ions, as well as to wave-wave interactions, and the acceleration of electrons and ions by waves and electric fields. FAST will employ an intelligent data-handling system capacle of data acquisition at rates of up to 1 Mb/sec, in addition to a 1-Gbit solid-state memory. The data need be gathered for only a few minutes during passes through the auroral zone, since the most interesting auroral phenomena occur in such narrow regions as auroral arcs, electrostatic shocks, and superthermal electron bursts.

Temerin, M. A.↗

NASA NTRS1991

Nonlinear wave scattering and electron beam relaxation

The role played by nonlinear scattering during the relaxation of a warm electron beam is investigated through a numerical code based on kinetic equations. The code encompasses the quasi-linear wave-electron interaction and wave-wave scattering off ion clouds. Ions with velocities 2 nu sub i (nu sub i being the ion thermal velocity) are found to be the most efficient for scattering the Langmuir waves off their polarization clouds. The transfer rate of the spectrum out of resonance with the beam is larger by a factor 3 compared to usual estimates. The changes produced in the dispersion relation by the presence of the beam electrons dramatically alter the characteristics of the secondary spectrum. In a late phase the classic condensate K of about 0 is depleted, with the formation of a new condensate in resonance with the flat-topped beam distribution, which follows from the fact that the mere presence of the beam electrons creates a minimum in the frequency-wave-number relation. For strong and slow beams, the predictions of the code are found to be in excellent agreement with the results of the particle simulation if a dispersion relation that includes the beam is used.

Muschietti, L.↗

NASA NTRS1991

Simulation of the nonlinear evolution of electron plasma waves

Electrostatic waves driven by an electron beam in an ambient magnetized plasma were studied using a quasi-1D PIC simulation of electron plasma waves (i.e., Langmuir waves). The results disclose the presence of a process for moving wave energy from frequencies and wavenumbers predicted by linear theory to the Langmuir-like frequencies during saturation of the instability. A decay process for producing backward propagating Langmuir-like waves, along with low-frequency waves, is observed. The simulation results, however, indicate that the backscattering process is not the conventional Langmuir wave decay. Electrostatic waves near multiples of the electron plasma frequency are generated by wave-wave coupling during the nonlinear stage of the simulations, confirming the suggestion of Klimas (1983).

Nishikawa, K.-I.↗

NASA NTRS1992

Inhibition of electron thermal conduction by electromagnetic instabilities

Heat flux inhibition by electromagnetic instabilities in a hot magnetized plasma is investigated. Low-frequency electromagnetic waves become unstable due to anisotropy of the electron distribution function. The chaotic magnetic field thus generated scatters the electrons with a specific effective mean free path. Saturation of the instability due to wave-wave interaction, nonlinear scattering, wave propagation, and collisional damping is considered. The effective mean free path is found self-consistently, using a simple model to estimate saturation level and scattering, and is shown to decrease with the temperature gradient length. The results, limited to the assumptions of the model, are applied to astrophysical systems. For some interstellar clouds the instability is found to be important. Collisional damping stabilizes the plasma, and the heat conduction can be dominated by superthermal electrons.

Levinson, Amir↗