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NASA NTRS1985

Multiple Equilibria of the Barotropic Vorticity Equation on a Sphere

Multiple states of the barotropic vorticity equation in which the balance is between the first and third terms on the r.h.s. of (1) are given. Solutions of this type were also considered by Charney and Devore (1979) in their discussion of thermally, rather than topographically, forced waves. Whereas in the case of topographic forcing the multiplicity arises from what they called form-drag instability in the wave-zonal flow interaction, in the thermal forcing case the associated instability appears to be the Rossby-wave instability discussed by Lorenz (1972), and the multiple states of the highly truncated model proved to be unstable when more degrees of freedom were added. The multiple statistically steady solutions described are thus novel in that they do not involve form-drag instability, they have stable statistics in calculations with a large number of degrees of freedoms, and they occur on the sphere, with no artificial confinement in a resonant cavity. Furthermore, the solutions are obtained with no external forcing of the zonal flow. The full non-linear equations for two-dimensional non-divergent motion between smooth, rigid boundaries on a sphere were used.

Suarez, M. J.↗

NASA NTRS1988

Nonlinear stability of the dayside cometary ionopause

The MHD stability of the cometary ionopause is investigated by nonlinear analysis, describing that stability in terms of the finite perturbation amplitude of both Kelvin-Helmholtz and Rayleigh-Taylor modes. The evolution of the unstable modes is examined, determining the conditions under which finite amplitude effects are expected to stabilize a growing wave disturbance. The analysis is applied to the ionopause at Comet Halley and Comet Giacobini-Zinner, showing that the theoretical prediction concerning the stability of this interface based on an earlier linear analysis remains valid in both cases despite the nonlinear stabilization effects.

Ershkovich, A. I.↗

NASA NTRS1988

International workshop on Time-Variable Phenomena in the Jovian System

Many of the scientifically interesting phenomena that occur in the Jovian system are strongly time variable. Some are episodic (e.g., Io volcanism); some are periodic (wave transport in Jupiters atmosphere); and some are exceedingly complex (magnetosphere - Io - Torus-Auroral interactions) and possibly unstable. To investigate this class of phenomena utilizing Voyager data and, in the future, Galileo results, a coherent program of ground based and earth-orbital observations, and of theory that spans the time between the missions, is required. To stimulate and help define the basis of such a scientific program researchers organized an International Workshop on the subject with the intent of publishing the proceedings which would represent the state of knowledge in 1987.

Belton, Michael J. S.↗

NASA NTRS1996

Mixing and Transition Control Studied

Considerable progress in understanding nonlinear phenomena in both unbounded and wallbounded shear flow transition has been made through the use of a combination of high- Reynolds-number asymptotic and numerical methods. The objective of this continuing work is to fully understand the nonlinear dynamics so that ultimately (1) an effective means of mixing and transition control can be developed and (2) the source terms in the aeroacoustic noise problem can be modeled more accurately. Two important aspects of the work are that (1) the disturbances evolve from strictly linear instability waves on weakly nonparallel mean flows so that the proper upstream conditions are applied in the nonlinear or wave-interaction streamwise region and (2) the asymptotic formulations lead to parabolic problems so that the question of proper out-flow boundary conditions--still a research issue for direct numerical simulations of convectively unstable shear flows--does not arise. Composite expansion techniques are used to obtain solutions that account for both mean-flow-evolution and nonlinear effects. A previously derived theory for the amplitude evolution of a two-dimensional instability wave in an incompressible mixing layer (which is in quantitative agreement with available experimental data for the first nonlinear saturation stage for a plane-jet shear layer, a circular-jet shear layer, and a mixing layer behind a splitter plate) have been extended to include a wave-interaction stage with a three-dimensional subharmonic. The ultimate wave interaction effects can either give rise to explosive growth or an equilibrium solution, both of which are intimately associated with the nonlinear self-interaction of the three dimensional component. The extended theory is being evaluated numerically. In contrast to the mixing-layer situation, earlier comparisons of theoretical predictions based on asymptotic methods and experiments in wall-bounded shear-flow transition have been somewhat lacking in one aspect or another. The current work strongly suggests that the main weakness is the underlying asymptotic representation of the linear "part" of the problem and not the explicit modeling of the nonlinear/wave-interaction effects. Consequently, the long-wave-length/high-Reynolds-number asymptotic limit for the Blasius boundary-layer stability problem was reexamined, and a new dispersion relationship for the instability waves that is uniformly valid for both the upper- and lower branch regions to the required order of approximation was obtained. A comparison with numerical results, obtained by solving the Orr-Sommerfeld stability problem, shows that the asymptotic formula provides surprisingly good results, even for values of the frequency parameter usually encountered in experimental investigations. This is particularly evident in the dynamically important upper-branch region, where much of the nonlinear interactions in transition experiments are believed to take place. The result is important in that it can be used to greatly improve the accuracy of weakly nonlinear critical-layer-based theories, and a consistent nonlinear theory is currently under evaluation.

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NASA NTRS1994

Two-layer viscous instability in a rotating couette device

A novel experiment to study the interfacial shear instability between two liquids is described. Density-matched immiscible liquids are confined between concentric cylinders such that the interface is parallel to the cylinder walls. Interfacial waves that develop because of viscosity differences between the shearing fluids are studied as a function of rotation rate and depth ratio using optical techniques. Conditions neutral stability and the most unstable wavenumber agree reasonably well with predictions from linear stability analysis of the Navier-Stokes equations. Illumination using laser sheets allows precise measurement of the interface shape. Future experiments will verify the correctness of weakly nonlinear theories that describe energy transfer and saturation of wave growth by nonlinear effects. Measurements of solitary wave shapes, that occur far above neutral stability, will be compared to similar measurements for systems that have gravity as an important force to determine how gravity effects large disturbances. These results will be used to interpret slug and annular flow data that have been obtained in other mu g studies.

Gallagher, Christopher↗

NASA NTRS2001

Arctic Sea Ice Export Through Fram Strait and Atmospheric Planetary Waves

A link is found between the variability of Arctic sea ice export through Ram Strait and the phase of the longest atmospheric planetary wave (zonal wave 1) in SLP for the period 1958-1997. Previous studies have identified a link between From Strait ice export and the North Atlantic Oscillation (NAO), but this link has been described as unstable because of a lack of consistency over time scales longer than the last two decades. Inconsistent and low correlations are also found between From Strait ice export and the Arctic Oscillation (AD) index. This paper shows that the phase of zonal wave 1 explains 60% - 70% of the simulated From Strait ice export variance over the Goodyear period 1958 - 1997. Unlike the NAB and AD links, these high variances are consistent for both the first and second halves of the Goodyear period. This consistency is attributed to the sensitivity of the wave I phase at high latitudes to the presence of secondary low pressure systems in the Barents Sea that serve to drive sea ice southward through From Strait. These results provide further evidence that the phase of zonal wave 1 in SLP at high latitudes drives regional as well as hemispheric low frequency Arctic Ocean and sea ice variability.

Cavalieri, Donald J.↗

NASA NTRS1994

Growing 'Alfvenic' modes in the upstream region of Saturn

Recent studies of low-frequency electromagnetic waves upstream of the Saturn bow shock have shown that these waves, in contrast to those at Earth, are observed not in one, but in at least two, distinct frequency bands. The results of wave mode identification based on the Hall-magnetohydrodynamic (MHD) model of plasma and observed wave polarization suggested that these waves propagate in the high beta intermediate mode. However, the underlying instability was not unambiguously determined. In the present paper we use the full electromagnetic dispersion relation derived from linear Vlasov theory in order to examine which of the plasma modes, with observed properties, are unstable in an isotropic Maxwellian plasma in the presence of backstreaming proton beams consistent with Voyager 2 observations at Saturn. As a result we find that the unstable 'Alfvenic' beam mode, as well as resonant and non-resonant fast magnetosonic modes have properties consistent with the data. Moreover, we find that in contrast to the Earth's upstream waves, at Saturn no 'kinetic' normal mode can account for the observed magnetic polarization.

Orlowski, D. S.↗

NASA NTRS1992

The behavior of a liquid drop levitated and drastically flattened by an intense sound field

The deformation and break-up are studied of a liquid drop in levitation through the radiation pressure. Using high-speed photography ripples are observed on the central membrane of the drop, atomization of the membrane by emission of satellite drops from its unstable ripples, and shattering of the drop after upward buckling like an umbrella, or after horizontal expansion like a sheet. These effects are captured on video. The ripples are theorized to be capillary waves generated by the Faraday instability excited by the sound vibration. Atomization occurs whenever the membrane becomes so thin that the vibration is sufficiently intense. The vibration leads to a destabilizing Bernoulli correction in the static pressure. Buckling occurs when an existent equilibrium is unstable to a radial (i.e., tangential) motion of the membrane because of the Bernoulli effect. Besides, the radiation stress at the rim of the drop is a suction stress which can make equilibrium impossible, leading to the horizontal expansion and the subsequent break-up.

Lee, C. P.↗

NASA NTRS1987

On the nonlinear interaction of Gortler vortices and Tollmien-Schlichting waves in curved channel flows at finite Reynolds numbers

The flow in a two-dimensional curved channel driven by an azimuthal pressure gradient can become linearly unstable due to axisymmetric perturbations and/or nonaxisymmetric perturbations depending on the curvature of the channel and the Reynolds number. For a particular small value of curvature, the critical neighborhood of this curvature value and critical Reynolds number, nonlinear interactions occur between these perturbations. The Stuart-Watson approach is used to derive two coupled Landau equations for the amplitudes of these perturbations. The stability of the various possible states of these perturbations is shown through bifurcation diagrams. Emphasis is given to those cases which have relevance to external flows.

Daudpota, Q. Isa↗

NASA NTRS1988

On the nonlinear interaction of Goertler vortices and Tollmien-Schlichting waves in curved channel flows at finite Reynolds numbers

Daudpota, Q. Isa↗

NASA NTRS1987

Resonant interactions between cometary ions and low frequency electromagnetic waves

The conditions for resonant wave amplification in a plasma with a ring-beam distribution which is intended to model pick-up ions in a cometary environment are investigated. The inclination between the interplanetary field and the solar wind is found to play a crucial role in governing both the resonant frequency and the growth rate of any unstable mode. It is suggested that the low-frequency MHD mode should experience the most rapid amplification for intermediate inclination. In the frame of the solar wind, such waves should propagate along the field in the direction upstream toward the sun with a phase speed lower than the beaming velocity of the pick-up ions. This mechanism may account for the presence of the interior MHD waves noted by satellites over a region surrounding comets Giacobini-Zinner and Halley.

Thorne, Richard M.↗

NASA NTRS1981

The role of zonally asymmetric heating in the vertical and temporal structure of the global scale flow fields during FGGE SOP-1

The global scale structure of atmospheric flow is best documented on time scales longer than a few days. Theoretical and observational studies of ultralong waves have emphasized forcing due to global scale variations of topography and surface heat flux, possibly interacting with baroclinically unstable or vertically refracting basic flows. Analyses of SOP-1 data in terms of global scale spherical harmonics is documented with emphasis upon weekly transitions.

Paegle, J.↗

NASA NTRS1983

Absolute barotropic instability and monsoon depressions

Monsoon depressions over the Bay of Bengal develop almost entirely in July and August. After studies conducted by Lindzen et al. (1980) and Stevens and Lindzen (1978), only barotropic instability remains as a mechanism for the development of the wave disturbances associated with monsoon depressions. The present investigation has the objective to show that barotropic instability is able to explain the wave aspects of monsoon depressions, but that normal mode analysis is inadequate. It is found that the local barotropically unstable response to regional perturbations in the Bay of Bengal during July and August will be dominated by the lower troposphere. The analysis clearly identifies the features of the mean flow which lead to monsoon depressions in July. The features include the development of an easterly jet as opposed to semijet structure in the mean flow, and the development of a modest easterly flow at the jet center as opposed to westerly flow.

Lindzen, R. S.↗

NASA NTRS1984

Strong electron heat flux modes in Jupiter's foreshock

Analysis of Voyager plasma wave data from the Jovian foreshock has revealed the existence of a new oscillation with center frequency below fp and typically lying above the upper limit Doppler shift frequency for ion acoustic waves. The properties of these waves are consistent with modes generated by a strong electron heat flux in an unmagnetized plasma. Such modes become unstable when the effective drift velocity exceeds n(cold)/(hot) exp 1/2 times the thermal speed of the hot component. The occasional simultaneous appearance of more than one frequency band is a possible indication of multiple magnetic connection with the shock.

Moses, S. L.↗

NASA NTRS1992

Instabilities in astrophysical jets. II - Numerical simulations of slab jets

Numerical simulations of an unstable supersonic slab-symmetric jet are described. The instabilities within the jet are characterized by growing internal body waves and their coupled surface waves that are also predicted in linear perturbation theory. The characteristic theory of fluid dynamics is used to help interpret the wave morphologies. It is demonstrated that these waves can be excited by imposing an arbitrary disturbance. From the numerical simulations, it is found that the sound waves propagating against the flow slow down as they propagate outward, and they grow in amplitude. These waves eventually disrupt the jet at a certain length. This disruption length is related to the jet Mach number and the perturbation intensity. Thus, the Mach number of a jet observed with a radio telescope can be estimated by measuring the disruption length and estimating the perturbation intensity. The jet Mach numbers in radio tailed sources determined in this way agree quite well with estimates from ram pressure bending arguments. The wiggles and flares observed in many extragalactic jets, especially in tailed radio sources, appear to be intimately related to instabilities and the jet disruption process.

Zhao, Jun-Hui↗

NASA NTRS1986

Particle propagation, wave growth and energy dissipation in a flaring flux tube

Wave amplification by downgoing particles in a common flare model is investigated. The flare is assumed to occur at the top of a coronal magnetic flux loop, and results in the heating of plasma in the flaring region. The hot electrons propagate down the legs of the flux tube towards increasing magnetic field. It is simple to demonstrate that the velocity distributions which result in this model are unstable to both beam instabilities and cyclotron maser action. An explanation is presented for the propagation effects on the distribution, and the properties of the resulting amplified waves are explored, concentrating on cyclotron maser action, which has properties (emission in the z mode below the local gyrofrequency) quite different from maser action by other distributions considered in the context of solar flares. The z mode waves will be damped in the coronal plasma surrounding the flaring flux tube and lead to heating there. This process may be important in the overall energy budget of the flare. The downgoing maser is compared with the loss cone maser, which is more likely to produce observable bursts.

White, S. M.↗

NASA NTRS1982

Dynamics Explorer observations of equatorial spread F - Evidence for drift waves

Recent DE-2 data from the Langmuir probe, vector electric field, and ion drift meter instruments are employed to study equatorial spread F in the frequency regime of the low frequency drift and the lower hybrid drift instabilities. Strong electron density gradients topside equatorial F region correspond to regions of high electric field waves and large ion drift velocities. The electric field waves are seen in two distinct wavelength ranges which correspond to the parameter regimes of the low frequency drift and the lower hybrid drift instabilities. In the smaller of the two wavelength ranges the lower hybrid drift instability is found to be unstable, based on the ion drift velocity and the other plasma parameters measured on DE-2, and using published theory. Thus there is experimental evidence that the lower hybrid drift instability may produce the observed short wavelength waves without invoking a cascading mechanism.

Hoegy, W. R.↗

NASA NTRS1993

Ion acceleration and abundance enhancements by electron beam instabilities in impulsive solar flares

We show that a nonrelativistic electron beam in a hydrogen-helium solar flare plasma will excite H(+) electromagnetic ion cyclotron, shear Alfven, and R-X waves, in addition to waves resulting from the two-stream instability. The H(+) electromagnetic ion cyclotron and shear Alfven waves are able to selectively accelerate ambient He-3 and Fe, respectively, to MeV energies through first harmonic gyroresonance, and thereby account for the large (He-3)/(He-4) and Fe/C ratios seen in the energetic particles from impulsive solar flares. In this model, separate heating and acceleration mechanisms for either He-3 or Fe are not required, and Fe acceleration is quite efficient since it does not need to occur by second harmonic gyroresonance. The combination of the other two unstable modes is able to accelerate ions to hundreds of MeV if the particles become trapped in an electrostatic potential well of a two-stream wave.

Miller, James A.↗