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NASA NTRS1974

Radiative-dynamical equilibrium states for Jupiter

In order to obtain accurate estimates of the radiative heating that drives motions in Jupiter's atmosphere, previous radiative equilibrium calculations are improved by including the NH3 opacities and updated results for the pressure-induced opacities. These additions increase the radiative lapse rate near the top of the statically unstable region and lead to a fairly constant radiative lapse rate below the tropopause. The radiative-convective equilibrium temperature structure consistent with these changes is calculated, but it differs only slightly from earlier calculations. The radiative equilibrium calculations are used to calculate whether equilibrium states can occur on Jupiter which are similar to the baroclinic instability regimes on the earth and Mars. The results show that Jupiter's dynamical regime cannot be of this kind, except possibly at very high latitudes, and that its regime must be a basically less stable one than this kind.

Trafton, L. M.↗

NASA NTRS1974

Linear viscous stability analysis of the stratified Bickley jet

The stability of the stably stratified Bickley jet to small disturbances in a viscous, heat conducting fluid is explored by numerical integration of the governing differential equation. Curves of neutral stability are presented in the alpha-R plane and the parametric dependence of these curves upon Richardson number and Prandtl number is examined. The results show a curious bimodal behavior of the curve of neutral stability for small Richardson numbers. In addition, closed neutral curves are found for Richardson numbers in excess of the critical value for the inviscid flow. The unstable regions in the interior of these curves increase with decreasing Prandtl number. Energy balances are computed which show the relative magnitude of the Reynolds stress production, buoyancy dissipation, and viscous dissipation terms across the flow. As the thermal diffusivity becomes large compared with the kinematic viscosity, the buoyancy term is suppressed and the thermal stratification becomes irrelevant.

Gage, K. S.↗

NASA NTRS1979

The wave structures of the Eady model of baroclinic instability

By solving the linear quasi-geostrophic set of equations pertinent to the Eady model, the complex eigenvalues and the eigenfunctions are obtained. The propagation speed and the growth rate are computed. Quantitative information is provided about the wave structures for several unstable models, a marginally stable mode, and a stable mode. The peculiarities concerning the amplitude and the phase variations of the waves are noted as the wavenumber varies from the unstable region to the stable region. Physical interpretations of the interrelationships among the dynamical variables are given, with a view toward revealing important aspects of the energy transfer from the basic state to the growing waves.

Hyun, J. M.↗

NASA NTRS1984

Dynamics of dendritic pattern formation

This paper is a brief review of recent and ongoing developments in the theory of dendritic pattern formation. A marginal stability hypothesis has achieved some success in predicting dendritic growth rates, but a fully nonlinear dynamic theory of the dendritic growth mechanism has yet to be developed. A possible clue for the construction of such a theory is the existence of a class of one-dimensional models in which a pattern is found to spread into an unstable region by propagating at the slowest stable speed. This mathematical realization of the marginal stability mechanism has led to the development of a boundary layer model which describes localized dynamics of fully two- or three-dimensional solidification fronts and which retains some of the mathematical features of the propagating systems. Preliminary results of numerical calculations using the boundary layer model indicate that it is capable of probing fully nonlinear features of dendritic pattern formation.

Langer, J. S.↗

NASA NTRS1987

Thermal instabilities in diffuse molecular clouds - Formation of molecular cloud cores

The stability of diffuse clouds to thermal instabilities is examined using the semiempirical cooling function derived by Tarafdar et al. (1985) for these clouds. It is found that diffuse clouds which obey such a cooling function are susceptible to thermal instability at densities n of less than about 70-80/cu cm. The growth rate for instability is large and the mass contained in unstable regions ranges from about 0.001 to 1 solar mass. It is suggested that such instabilities may trigger formation of molecular cloud cores of the type found in low-mass molecular clouds (e.g., TMC-2). Criteria for thermal instability in self-gravitating systems are also derived.

Graziani, Frank R.↗

NASA NTRS1987

Combustion stability analysis of preburners in liquid propellant rocket engines during shutdown

A linearized one-dimensional lumped-parameter model capable of predicting the occurrence of the low frequency combustion instability (chugging) experienced during preburner shutdown in the Space Shuttle Main Engines is discussed, and predictions are compared with NASA experimental results. Results from a parametric study of parameters including chamber pressure, fuel and oxygen temperatures, and the effective bulk modulus of the liquid oxidizer suggest that chugging is probably affected by conditions at shutdown through the fuel and oxidizer temperatures. It is suggested that chugging is initiated when the fuel, oxidizer, and helium temperature and flow rates pass into an unstable region, and that chugging may be terminated by decaying pressures.

Lim, Kair-Chuan↗

NASA NTRS1990

On the fragmentation of protogalactic clouds

After its initial collapse, a protogalactic cloud is expected to be shock heated to its virial temperature of about 1 million K. This temperature lies near a very unstable region of the cooling curve, so that density enhancements will be expected to grow rapidly as the protogalaxy cools to lower temperatures. In this contribution, the dynamical effects on the growth of perturbations are examined. It is shown that perturbations with large initial amplitudes lead to the formation of H2, which results in rapid cooling to 100 K, and the formation of population III stars. Perturbations with small initial amplitudes, however, do not cool significantly ahead of the background, do not develop strong contrasts with the background, and so cannot induce the formtion of H2. They thus remain near 10,000 K, forming a population of protoclusters with masses of about 10 to the 7th solar masses, somewhat larger than typical globular cluster masses. Contamination by metals from a primordial generation of stars may lead to cooling and a significant reduction of the Jeans mass. Photodissociation induced by a background source of hard photons can also prevent cooling below 10,000 K, enhancing the formation of protoclusters relative to stars.

Murray, Stephen D.↗

NASA NTRS1991

Spanwise-nonuniform excitation of a plane shear layer

The receptivity of a plane mixing layer to spanwise-nonuniform phase excitation Phi(z,t) has been studied in a closed-return water facility. When the peak amplitude of Phi(z) equals pi the primary vortices undergo spanwise-periodic (localized) pairing. Distortion in transverse distributions of the streamwise velocity component and the appearance of inflection points indicate the formation of locally-unstable regions of large shear in which broadband perturbations may undergo rapid amplification followed by breakdown to turbulence. Schlieren visualization and detailed measurements of the streamwise velocity component shed light on the nature of 'vortex dislocations' previously observed by other investigators.

Nygaard, Kris J.↗

NASA NTRS1991

Evolution of streamwise vortices and generation of small-scale motion in a plane mixing layer

The present study investigates the evolution of streamwise vortices in a plane mixing layer and their role in the generation of small-scale 3D motion in a closed-return water facility. Spanwise-periodic streamwise vortices are excited by a time-harmonic wavetrain with spanwise-periodic amplitude variations synthesized by a mosaic of 32 surface film heaters flush-mounted on the low partition. The onset of streamwise vortices is accompanied by significant distortion in the transverse distribution of the streamwise velocity component. The presence of inflexion points, absent in corresponding velocity distributions of the unforced flow, suggests the formation of locally unstable regions of large shear in which broadband perturbations already present in the base flow undergo rapid amplification, followed by breakdown to small-scale motion. The cores of the primary vortices are significantly altered as a result of spanwise nonuniform excitation. The 3D features of the streamwise vortices and their interaction with the base flow are inferred from surfaces or rms velocity fluctuations and an approximation to cross-stream vorticity using 3D single component velocity data.

Nygaard, K. J.↗

NASA NTRS1992

Viscous and inviscid instabilities of a trailing vortex

The linear stability of the trailing line vortex model of Batchelor (1964) is studied using a spectral collocation and matrix eigenvalue method. The entire unstable region in the swirl/axial wavenumber parameter space is mapped out for various azimuthal wavenumbers for both the inviscid and viscous stability problem. The results of the study provide a direct numerical validation of the large-azimuthal-wavenumber asymptotic analysis of Leibovich and Stewartson (1983). It is shown that accurate results are obtained up to azimuthal wavenumbers of 10,000 and greater, and the agreement with the asymptotic theory is excellent.

Mayer, Ernst W.↗

NASA NTRS1993

The stratopause semiannual oscillation in the NCAR Community Climate Model

The middle atmospheric version of the NCAR Community Climate Model (CCM2) has been used to study the development of the equatorial semiannual oscillation (SAO) in the stratosphere. The model domain extends from the ground to about 80 km, with a vertical resolution of 1 km. Transport of nitrous oxide (N2O) with simplified photochemistry is included in the calculation to illustrate the influence of tropical circulations on the distribution of trace species. Diagnosis of model output reveals two distinct phases in the evolution of the zonal mean state on the equator. In early December, a strong and broad easterly jet appears near the stratopause in connection with a midlatitude wave event (sudden stratospheric warming) that reverses the winter westerlies of the Northern Hemisphere throughout the upper stratosphere. When the wave forcing dies out, the radiative drive allows the westerlies to recover at midlatitudes, while easterlies persist in the tropics. The resulting strong meridional gradient of the zonal mean wind provides favorable conditions for the development of inertial instability at lower latitudes. The meridional circulation associated with the instability shapes the 'nose' of the easterly jet, reducing the extension of the unstable region. In equinoctial conditions, a jet of westerlies appears in the lower equatorial mesosphere and descends to lower altitudes; positive accelerations associated with the descending westerlies are due primarily to Kelvin waves. The descent of the westerly jet does not reproduce well the observed behavior of the SAO westerly phase, either in amplitude or in the extent of downward propagation. As a consequence, the model does not simulate the 'double peak' observed in the tropical distribution of N2O. Comparison of wave amplitudes in the model with those derived from satellite observations shows that the calculated amplitudes are larger than observed in the upper stratosphere. It follows that inadequate Kelvin wave forcing is not the cause of the weak westerly phase in the model, and that some other mechanism must be responsible for the generation of the strong westerly phase observed.

Sassi, Fabrizio↗

NASA NTRS1999

Whistler Solitons in Plasma with Anisotropic Hot Electron Admixture

The longitudinal and transverse modulation instability of whistler waves in plasma, with a small admixture of hot anisotropic electrons, is discussed. If the hot particles temperature anisotropy is positive, it is found that, in such plasma, longitudinal perturbations can lead to soliton formation for frequencies forbidden in cold plasma. The soliton is enriched by hot particles. The frequency region unstable to transverse modulation in cold plasma in the presence of hot electrons is divided by stable domains. For both cases the role of hot electrons is more significant for whistlers with smaller frequencies.

Khazanov, G. V.↗

NASA NTRS1999

Whistler Solitons in Plasma with Anisotropic Hot Electron Admixture

Khazanov, G. V.↗

NASA NTRS1994

The FU Orionis Outburst as a Thermal Disk Accretion Event: Detailed Calculations and Comparison to Observations

FU Orionis outbursts are temporary large increases in luminosity: x (40 - 250) thought to occur repeatedly in all low mass young stellar systems. We discuss detailed calculations of viscous accretion disks suggesting that FU Ori events signify the existence of a protostellar disk transporting mass at a rate of (1 - 10) x 10(exp 6) solar mass / yr, in agreement with theoretical and observational estimates of molecular cloud core collapse rates. Accretion through the inner edge of disks subject to outburst is self-regulated through the thermal ionization instability such that long periods (approx. 1000 yrs) of low mass flux: (1 - 10) x 10(exp -5) solar mass / yr, are punctuated by short periods (approx. 100 yrs) of high mass flux: (1-10) x 10(exp -5) solar mass / yr. The unstable region of the disk extends radially only to a distance of approx. = 1/4 AU. Beyond this region matter is transported stably at the infall rate. In systems for which M(sum *) = 1 solar mass with an inner disk edge of 3 solar radius, the critical rate for outbursts is 5 x 10(exp -7) solar mass / yr independent of the magnitude of the viscous ce parameter consistent with estimates of boundary layer mass flux in T Tauri stars. We use timescales of observed outbursts to constrain the magnitude of the alpha parameter to be 10(exp -4) where hydrogen is neutral and 10(exp -3) where ionized. Light curves of V1515 Cyg, FU Ori, and V1057 Cya are reproduced; the latter two require application of a small perturbation in surface density to produce observed rapid rise times. Detailed reply is made to objections to the accretion disk model for outbursts. Comparison to observations are made of time dependent spectral energy distributions, colors, and line-width velocity evolution.

Bell, K. R.↗

NASA NTRS1994

The FU Orionis Outburst as a Thermal Disk Accretion Event: Detailed Calculations and Comparison to Observations

FU Orionis outbursts are temporary large increases in luminosity: x(40-250) thought to occur repeatedly in all low mass young stellar systems. We discuss detailed calculations of viscous accretion disks suggesting that FU Ori events signify the existence of a protostellar disk transporting mass at a rate of (1-10) x 10(exp -6) Solar Mass/yr, in agreement with theoretical and observational estimates of molecular cloud core collapse rates. Accretion through the inner edge of disks subject to outburst is self-regulated through the thermal ionization instability such that long periods (approximately 1000 yrs) of low mass flux: (1-10) x 10(exp -8) Solar Mass/yr, are punctuated by short periods (approximately 100 yrs) of high mass flux: (1-10) x 10(exp -5) Solar Mass/yr. The unstable region of the disk extends radially only to a distance of approximately 1/4 AU. Beyond this region matter is transported stably at the infall rate. In systems for which M = 1 Solar Mass, with an inner disk edge of 3 Solar Radius, the critical rate for outbursts is 5 x 10(exp -7) Solar Mass/yr independent of the magnitude of the viscous alpha parameter consistent with estimates of boundary layer mass flux in T Tauri stars. We use timescales of observed outbursts to constrain the magnitude of the alpha parameter to be 10(exp -4) where hydrogen is neutral and 10(exp -3) where ionized. Light curves of V1515 Cyg, FU Ori, and V1057 Cyg are reproduced; the latter two require application of a small perturbation in surface density to produce observed rapid rise times. Detailed reply is made to objections to the accretion disk model for outbursts. Comparison to observations are made of time dependent spectral energy distributions, colors, and line-width velocity evolution.

Bell, K. R.↗

NASA NTRS2002

Servicing and Deployment of National Resources in Sun-Earth Libration Point Orbits

Spacecraft travel between the Sun-Earth system, the Earth-Moon system, and beyond has received extensive attention recently. The existence of a connection between unstable regions enables mission designers to envision scenarios of multiple spacecraft traveling cheaply from system to system, rendezvousing, servicing, and refueling along the way. This paper presents examples of transfers between the Sun-Earth and Earth-Moon systems using a true ephemeris and perturbation model. It shows the (Delta)V costs associated with these transfers, including the costs to reach the staging region from the Earth. It explores both impulsive and low thrust transfer trajectories. Additionally, analysis that looks specifically at the use of nuclear power in libration point orbits and the issues associated with them such as inadvertent Earth return is addressed. Statistical analysis of Earth returns and the design of biased orbits to prevent any possible return are discussed. Lastly, the idea of rendezvous between spacecraft in libration point orbits using impulsive maneuvers is addressed.

Folta, David C.↗

NASA NTRS2005

Buoyancy Suppression in Gases at High Temperatures

The computational fluid dynamics code FLUENT was used to study Rayleigh instability at large temperature differences in a sealed gas-filled enclosure with a cold top surface and a heated bottom wall (Benard problem). Both steady state and transient calculations were performed. The results define the boundaries of instability in a system depending on the geometry, temperature and pressure. It is shown that regardless of how fast the bottom-wall temperature can be ramped up to minimize the time spent in the unstable region of fluid motion, the eventual stability of the system depends on the prevailing final pressure after steady state has been reached. Calculations also show that the final state of the system can be different depending on whether the result is obtained via a steady-state solution or is reached by transient calculations. Changes in the slope of the pressure-versus-time curve are found to be a very good indicator of changes in the flow patterns in the system.

Kuczmarski, Maria A.↗

NASA NTRS2005

TRIO: Turbulent Response in Oxygen

This project was designed to build on the results from the successful launch of the Turbulent Oxygen Mixing Experiment (TOMEX) mother-daughter (instrumented and chemical-release) payload (21.126) that was launched in October 2000 from the White Sands Missile Range. The overall science objective was to investigate the evolution of the atmospheric response. at altitudes between 80 and 120 km, to the presence of unstable regions with vertical scales of the order of 1 to 10 km. TRIO was designed to use Na lidar measurements from the MAUUMALT observation on MAUI with a launch of a payload from Pacific Missile Range Facility (PMRF), located on Kauai. During this project, Aerospace participated in a Mission Initiation Conference. put together a science requirements document. performed a site visit to PMRF. prepared a CDR document. and developed a production and calibration procedure for one of the payload instruments. the 3-channel photometer. Unfortunately. NASA decided to terminate the program because of unforeseen (by NASA) range costs. This CDR document represents our view of this project at termination and provides a roadmap to perform this experiment should it be proposed again.

Hecht, J. H.↗