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NASA NTRS1984

The ethereal rings of Jupiter and Saturn

The brighter main band of the Jovian ring, which is tenuous and exhibits little substructure, lies in the equatorial plane at 1.7-1.8 Jupiter radii, R(J); this is well within the Roche limit. Since dynamical evolution times and survival lifetimes for micron grains are of the order of less than 100-1000 years, the visible Jovian ring must be continuously replenished. It is suggested that most small grains are generated by micrometeoroids colliding into unseen parent bodies residing in the main band. The halo is composed of still smaller particles and is radially localized at about 1.3-1.7 R(J). Unlike the rings of Saturn and Uranus, the Jovian rings are distinguished by the determination of their form by single-particle dynamics rather than collective effects.

Burns, J. A.↗

NASA NTRS1985

Time-dependent dusty gasdynamical flow near cometary nuclei

This paper presents time-dependent solutions to the coupled dusty hydrodynamics equations describing the spherically symmetric expansion of cometary neutral gas in the vicinity of a cometary nucleus. The sublimation process is repressented by gas outflow from a dust-covered reservoir containing stationary gas whose pressure and density values are determined by the sublimating (Ts) and surface (T0) temperatures. The model resolves earlier ambiguities in determining gas production rates and provides analytic relations between Ts, T0, and the gas parameters at the sonic point. The time evolution of a cometary outburst was modeled. It was found that, as a result of the strong gas-dust interaction in the inner coma region, a 'slow' disturbance in both the dust and gas parameters will be created in addition to the familiar gas blast-wave solution. This new 'slow' disturbance, which propagates with a velocity of about 0.2 km/s, might be responsible for some of the observed slowly expanding cometary halos, such as the one which was recently identified using 1910 Mount Wilson high-resolution comet Halley photographs.

Gombosi, T. I.↗

NASA NTRS1985

Contribution of explosion and future collision fragments to the orbital debris environment

The time evolution of the near-earth man-made orbital debris environment modeled by numerical simulation is presented in this paper. The model starts with a data base of orbital debris objects which are tracked by the NORAD ground radar system. The current untrackable small objects are assumed to result from explosions and are predicted from data collected from a ground explosion experiment. Future collisions between earth orbiting objects are handled by the Monte Carlo method to simulate the range of collision possibilities that may occur in the real world. The collision fragmentation process between debris objects is calculated using an empirical formula derived from a laboratory spacecraft impact experiment to obtain the number versus size distribution of the newly generated debris population. The evolution of the future space debris environment is compared with the natural meteoroid background for the relative spacecraft penetration hazard.

Su, S.-Y.↗

NASA NTRS1985

Transition control by periodic suction-blowing

The applicability of active control of transition by period suction-blowing is investigated via direct numerical simulations of the Navier-Stokes equations. The time-evolution of finite-amplitude disturbances in plane channel flow is compared in detail with and without control. The analysis indicates that for relatively small three-dimensional amplitudes, a two-dimensional control effectively reduces disturbance growth rates even for linearly unstable Reynolds numbers. After the flow goes through secondary instability, three-dimensional control seems necessary to stabilize the flow. An investigation of the temperature field suggests that passive temperature contamination is operative to reflect the vorticity dynamics during transition.

Biringen, S.↗

NASA NTRS1985

Robustness of continuous-time adaptive control algorithms in the presence of unmodeled dynamics

This paper examines the robustness properties of existing adaptive control algorithms to unmodeled plant high-frequency dynamics and unmeasurable output disturbances. It is demonstrated that there exist two infinite-gain operators in the nonlinear dynamic system which determines the time-evolution of output and parameter errors. The pragmatic implications of the existence of such infinite-gain operators is that: (1) sinusoidal reference inputs at specific frequencies and/or (2) sinusoidal output disturbances at any frequency (including dc), can cause the loop gain to increase without bound, thereby exciting the unmodeled high-frequency dynamics, and yielding an unstable control system. Hence, it is concluded that existing adaptive control algorithms as they are presented in the literature referenced in this paper, cannot be used with confidence in practical designs where the plant contains unmodeled dynamics because instability is likely to result. Further understanding is required to ascertain how the currently implemented adaptive systems differ from the theoretical systems studied here and how further theoretical development can improve the robustness of adaptive controllers.

Rohrs, C. E.↗

NASA NTRS1986

Uniformly high order accurate essentially non-oscillatory schemes 3

In this paper (a third in a series) the construction and the analysis of essentially non-oscillatory shock capturing methods for the approximation of hyperbolic conservation laws are presented. Also presented is a hierarchy of high order accurate schemes which generalizes Godunov's scheme and its second order accurate MUSCL extension to arbitrary order of accuracy. The design involves an essentially non-oscillatory piecewise polynomial reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell. The reconstruction algorithm is derived from a new interpolation technique that when applied to piecewise smooth data gives high-order accuracy whenever the function is smooth but avoids a Gibbs phenomenon at discontinuities. Unlike standard finite difference methods this procedure uses an adaptive stencil of grid points and consequently the resulting schemes are highly nonlinear.

Harten, A.↗

NASA NTRS1986

Nucleation experiments in a microgravity environment

A simple experimental apparatus is described in which a wide variety of vapor phase nucleation studies of refractory materials could be performed aboard NASA's KC-135 Research Aircraft. The chief advantage of a microgravity environment for these studies is the expected absence of thermally driven convective motions in the gas. The absence of convection leads to much more accurate knowledge of both the temperature distribution in the system and the time evolution of the refractory vapor concentration as a function of distance from the crucible.The evolution of the apparatus will be described as more experience is gained with the microgravity environment. Such experiments will be used to prepare for similar ones carried out aboard either the shuttle or Space Station where considerably longer duration experiments are possible.

Nuth, J. A.↗

NASA NTRS1985

Electromagnetic hot ion beam instabilities - Quasi-linear theory and simulation

This paper considers the quasi-linear theory of the right- and left-hand resonant electromagnetic instabilities driven by a hot ion beam streaming parallel to a magnetic field in a homogeneous Vlasov plasma. Using the single-mode approximation, the time evolutions of important parameters are obtained to show that for the range of parameters considered, reduction of the beam speed and formation of temperature anisotropies are the most significant factors in the quasi-linear stabilization process. Combining both instabilities in a quasi-linear study is found to produce a roughly equal mixture of both polarizations and relatively isotropic conditions for tenuous beam densities and low initial beam drift speeds. Computer simulations are used to compare with the quasi-linear results. The simulations justify the single-mode assumption, verify that quasi-linear changes are the means of saturation for the parameter range of concern, and check the nonlinear evolution of the system when both modes are present.

Rogers, B.↗

NASA NTRS1985

The Toda lattice as a forced integrable system

The analytic properties of the Jost functions for the inverse scattering transform associated with the forced Toda lattice are shown to determine the time evolution of this particular boundary value problem. It is suggested that inverse scattering methods may be used generally to analyze forced integrable systems. Thus an extension of the applicability of the inverse scattering transform is indicated.

Hansen, P. J.↗

NASA NTRS1986

Evidence for beamed electrons in a limb X-ray flare observed by Hard X-Ray Imaging Spectrometer (HXIS)

The limb flare of November 18, 1980, 14:51 UT, was investigated on the basis of X-ray images taken by the Hard X-ray Imaging Spectrometer (HXIS) and of X-ray spectra from the Hard X-Ray Burst Spectrometer (HXRBS) aboard the Solar Maximum Mission (SMM). The impulsive burst was also recorded at microwave frequencies between 2 and 20 GHz whereas no optical flare and no radio event at frequencies below 1 GHz were reported. The flare occurred directly at the SW limb of the solar disk. Taking advantage of the spatial resolution of HXIS images, the time evolution of the X-radiation originating from relatively small source regions can be studied. Using Monte Carlo computations of the energy distribution of energetic electrons traversing the solar plasma, the bremsstrahlung spectra produced by the electrons were derived.

Haug, Eberhard↗

NASA NTRS1985

Numerical solution of the unsteady Navier-Stokes equation

The construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws are discussed. These schemes share many desirable properties with total variation diminishing schemes, but TVD schemes have at most first-order accuracy, in the sense of truncation error, at extrema of the solution. In this paper a uniformly second-order approximation is constructed, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell.

Osher, Stanley J.↗

NASA NTRS1987

A numerical study of three-dimensional vortex breakdown

A numerical simulation of bubble-type vortex breakdown using a unique discrete form of the full 3-D, unsteady incompressible Navier-Stokes equations was performed. The Navier-Stokes equations were written in a vorticity-velocity form and the physical problem was not restricted to axisymmetric flow. The problem was parametized on a Rossby- Reynolds-number basis. Utilization of this parameter duo was shown to dictate the form of the free-field boundary condition specification and allowed control of axial breakdown location within the computational domain. The structure of the breakdown bubble was studied through time evolution plots of planar projected velocity vectors as well as through plots of particle traces and vortex lines. These results compared favorably with previous experimental studies. In addition, profiles of all three velocity components are presented at various axial stations and a Fourier analysis was performed to identify the dominant circumferential modes. The dynamics of the breakdown process were studied through plots of axial variation of rate of change of integrated total energy and rate of change of integrated enstrophy, as well as through contour plots of velocity, vorticity and pressure.

Spall, Robert E.↗

NASA NTRS1986

Numerical simulation of transitional flow

The applicability of active control of transition by periodic suction-blowing is investigated via direct simulations of the Navier-Stokes equations. The time-evolution of finite-amplitude disturbances in plane channel flow is compared in detail with and without control. The analysis indicates that, for relatively small three-dimensional amplitudes, a two-dimensional control effectively reduces disturbance growth rates even for linearly unstable Reynolds numbers. After the flow goes through secondary instability, three-dimensional control seems necessary to stabilize the flow. An investigation of the temperature field suggests that passive temperature contamination is operative to reflect the flow dynamics during transition.

Biringen, Sedat↗

NASA NTRS1987

Phase space simulation of collisionless stellar systems on the massively parallel processor

A numerical technique for solving the collisionless Boltzmann equation describing the time evolution of a self gravitating fluid in phase space was implemented on the Massively Parallel Processor (MPP). The code performs calculations for a two dimensional phase space grid (with one space and one velocity dimension). Some results from calculations are presented. The execution speed of the code is comparable to the speed of a single processor of a Cray-XMP. Advantages and disadvantages of the MPP architecture for this type of problem are discussed. The nearest neighbor connectivity of the MPP array does not pose a significant obstacle. Future MPP-like machines should have much more local memory and easier access to staging memory and disks in order to be effective for this type of problem.

White, Richard L.↗

NASA NTRS1987

A numerical study of transition control by periodic suction-blowing

The applicability of active control of transition by periodic suction-blowing is investigated via direct numerical simulations of the Navier-Stokes equations. The time-evolution of finite-amplitude disturbances in plane channel flow is compared in detail with and without control. The analysis indicates that, for relatively small three dimensional amplitudes, a two dimensional control effectively reduces disturbance growth rates even for linearly unstable Reynolds numbers. After the flow goes through secondary instability, three dimensional control seems necessary to stabilize the flow. An investigation of the temperature field suggests that passive temperature contamination is operative to reflect the flow dynamics during transition.

Biringen, Sedat↗

NASA NTRS1985

A comparison of the bounded derivative and the normal mode initialization methods using real data

A bounded derivative initialization method (BDI) formerly used only in theoretical studies to balance gravitational wave influences is extended to a real world data set and the results are compared with those from a normal mode initialization (NMI). BDI proceeds by defining the characteristic scales of motion of interest and then constraining the time derivatives to match motions on a slow scale. A global barotropic model which considers orographic forcing is initialized by the scaled balance equations of the BDI scheme, which uses vorticity alone to achieve an initial balanced state. An external mode projector is employed to realize the NMI scheme, and five Machenhauer iterations reduce the total balance by four orders of magnitude. The initial states generated with both schemes are essentially equivalent, including the time evolution of a height field and divergence behavior being centered around regions of high orographic elevation.

Semazzi, F. H. M.↗

NASA NTRS1986

Gravitational Landau damping for an isotropic cluster of stars

The problem of ascertaining the dynamical stability and the existence of Landau damping in static, isotropic 'collisionless' star clusters is addressed. The second-order formalism of Kandrup and Sygnet (1985) is applied to a homogeneous and isotropic plasma, demonstrating formally that the unperturbed configuration will always be stable and that the modes must be purely oscillatory. The form of these modes is explicitly examined, culminating in an analytic expression for the time evolution of the density induced by an initial perturbation. It is shown how these considerations can be adapted trivially to localized, nonradial disturbances of a self-gravitating system of stars. The possible existence of gravitational Landau damping for more generic perturbations is discussed.

Habib, Salman↗

NASA NTRS1986

On the tidal interaction between protoplanets and the protoplanetary disk. III - Orbital migration of protoplanets

The tidal interaction between a protoplanet and a gaseous protoplanetary disk is investigated, and the dynamical evolution of the disk and the orbital migration of the protoplanet in a self-consistent manner is considered. It is shown that the orbital migration of a protoplanet does not suppress the tendency for tidal truncation in the vicinity of its orbit. If the necessary condition for tidal truncation is satisfied, the protoplanet induces a tidal feedback mechanism that regulates the rate of angular momentum transfer between the protoplanet and the disk. Significant orbital migration can only occur on the viscous evolution time scale of the disk.

Lin, D. N. C.↗