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NASA NTRS1994

Low-frequency magnetic fluctuation spectra in the magnetosheath and plasma depletion layer

Recent observations have delineated several different kinds of enhanced magnetic fluctuation spectra below the proton cyclotron frequency in the terrestrial magnetosheath. A model is presented that represents the variation of plasma parameters across the plasma depletion layer and into the magnetosheath proper. Using this model, we find that many of the properties of the observed spectra follow directly from the predictions of linear Vlasov instability theory. The observed progression of spectral features is a natural progression from mirror mode to merged (in frequency range) proton and He(2+) cyclotron modes to bifurcated (in frequency range) cyclotron modes as plasma convects earthward in the magnetosheath. The necessary change in dispersion surface topology from separated proton and He(2+) cyclotron surfaces at low beta to merged surfaces at high beta is described.

Denton, Richard E.↗

NASA NTRS1994

Low-frequency oscillations of forced barotropic flow

Jin and Ghil demonstrate that for topographically resonant flow, low-frequency finite-amplitude oscillations may arise from wave -- wave interactions and topographic form drag. Their model is extended to include a zonally asymmetric vorticity source, which is shown to interact with the perturbation field to produce zonally rectified wave fluxes that dramatically alter the Hopf bifurcation from stationary solutions to low-frequency oscillations. The frequency, intensity, and general character of these oscillations are shown to depend crucially upon the phasing and relative strength of the forcings.

Nathan, Terrence R.↗

NASA NTRS1994

Theoretical models of polar-cap convection under the influence of a northward interplanetary magnetic field

The unexpected patterns of high-latitude auroral luminosity and ionospheric convection that are observed when the interplanetary magnetic field (IMF) has a northward orientation have inspired a variety of theoretical interpretations. The existing models, all referring to steady-state conditions, can be classified according to the topology of the polar magnetic field lines and of the polar-cap convection streamlines. The classes of model include: (1) a closed magnetosphere model, (2) a conventional open model with a distorted, but topologically unchanged, polar-cap boundary, (3) a conventional open model with distorted, but topologically unchanged, polar-cap convection cells, (4) a modified open model with 'lobe convection cells' contained wholly on open magnetic-field lines, and (5) a modified open model with a bifurcated polar cap. The third and fourth types require significant regions of sunward flow on open polar-cap field lines, a concept that presents serious theoretical difficulties. The other three types appear equally viable from a theoretical point of view, and the comparison against observations is an ongoing enterprise. Outstanding theoretical questions include (a) how do observed structures in the polar ionosphere map along magnetic field lines into the magnetosphere?, (b) what is the mechanism that drives the observed sunward convection at highest latitudes on the day side?, and (c) what role does time dependence play in the observed phenomena?

Hill, T. W.↗

NASA NTRS1994

Wavelets, period-doubling, and time-frequency localization with application to organization of convection over the tropical western Pacific

In this paper, preliminary results in using orthogonal and continuous wavelet transform (WT) to identify period doubling and time-frequency localization in both synthetic and real data are presented. First, the Haar WT is applied to synthetic time series derived from a simple nonlinear dynamical system- a first-order quadratic difference equation. Second, the complex Morlet WT is used to study the time-frequency localization of tropical convection based on a high-resolution Japanese Geostationary Meteorological Satellite infrared (IR) radiance dataset. The Haar WT of the synthetic time series indicates the presence and distinct separation of multiple frequencies in a period-doubling sequence. The period-doubling process generates a multiplicity of intermediate frequencies, which are manifested in the nonuniformity in time with respect to the phase of oscillations in the lower frequencies. Wavelet transform also enables the detection of extremely weak signals in high-order subharmonics resulting from the period-doubling bifurcations. These signals are either undetected or considered statistically insignificant by traditional Fourier analysis. The Morlet WT of the IR radiance dataset indicates the presence of multiple timescales, which are localized in both frequency and time. There are two regimes in the variation of IR radiance, corresponding to the wet and dry periods. Multiple timescales, ranging from semidiurnal, diurnal, synoptic, to intraseasonal with embedding structures, are active in the wet regime. In particular, synoptic variability is more prominent during the wet phase of an intensive intraseasonal cycle. These are not only consistent with, but also show more details than, previous findings by using other techniques. The phase-locking relationships among the oscillations with different time-scales suggest that both synoptic and intraseasonal variations may be mixed oscillations due to the interaction of self-excited oscillations in the tropical atmosphere and external forcings such as annual and diurnal solar radiation variations. Both examples show that WT is a powerful tool for analysis of phenomena involving multiscale interactions that exhibit localization in both frequency and time. A discussion on the caveats in the use of WT in geophysical data analysis is also presented.

Weng, Hengyi↗

NASA NTRS1993

A diffusion-limited aggregation model for the evolution of drainage networks

We propose a modified diffusion-limited aggregation (DLA) model for the evolution of fluvial drainage networks. Random walkers are introduced randomly on a grid, and each two-dimensional random walk proceeds until the walker finds a drainage network on which to accrete. This model for headward growth of drainage networks generates drainage patterns remarkably similar to actual drainages. The model also predicts statistical features which agree with actual networks, including the frequency-order (bifurcation) ratio (R(sub b) = 3.98) and the stream length-order (R(sub r) = 2.09). Using the definition of network fractal dimension D = log R(sub b)/log R(sub r), we find that our DLA model gives D = 1.87, near the observed range of D approximately equal to 1.80 - 1.85.

Masek, Jeffrey G.↗

NASA NTRS1994

A phyllosilicate-sulfide vein in Kaidun

A fragment of a carbonaceous chondrite (#53.12, maximal dimension about 2 mm) containing a phyllosilicate-sulfide vein was found during an inspection of small pieces of the Kaidun meteorite. Phyllosilicate veins are apparently rare in carbonaceous chondrites and have so far only been reported from the Y82162 CI chondrite. In hand sample the vein was visible on two perpendicular faces. The polished section prepared from one side displays a complex structure. A single vein, 150 microns in width, bifurcates, and each branch narrows toward a large rounded object (RO). The section contains abundant ROs, most of them less than or equal to 100 microns in diameter. The vein has sharp contacts to the surrounding matrix, whereas the RO contacts are diffuse. The phyllosilicate in the main vein has a massive texture along the contact, which becomes platy toward the vein center where the crystals protrude into an open space. The texture of the largest RO resembles that of a barred olivine (BO) chondrule. Some of the smaller ROs also texturally resemble chondrules. The BO chondrule contains rounded sulfide-silicate objects and small metal grains covered by oxides. Phyllosilicates of the main vein consist mainly of serpentine. The phyllosilicate near the contact with the matrix has low contents of minor elements and a high Mg/Fe ratio. The composition changes in a regular manner toward the center: Al, Na, Ca, Ni, and S increase, indicating increasing amounts of sulfates admixed. The phyllosilicate vein could only have formed after a substantial rock was formed. Mechanical stress probably opened a crack that was subsequently filled by phyllosilicate, pyrrhotite, and finally by a (Fe,Mg)-sulfate. The source of the matter mobilized to form the vein could have been within the rock itself or outside. No compositional or mineralogical zoning is apparent at the vein-rock contacts. The nature of the transporting agent (liquid H2O or vapor) must also remain an enigma. M. Zolensky has recently observed similar phyllosilicate-filled veins in dark, wet clasts in the Al Rais CR chondrite.

Ivanov, A. V.↗

NASA NTRS1994

HST observations of Cygnus A: Circumnuclear effects of a powerful jet?

We present 340 nm continuum and (O II) line images of the nuclear region of the radio galaxy Cygnus A at 0.1 sec resolution. At this high resolution the northwestern of the two nuclear components is resolved into two separate, line emitting subcomponents, and the radio jet points accurately between them. This suggests that the radio jet has blasted a path through emission-line clouds, and that the emission line clouds, having cooled after the passage of the shock, are being photoionized by a (presumably hidden) central source or by the shock itself. We confirm previous detections of a small component at a location corresponding to the radio nuclear position and discuss the evidence for a possible bifurcation of the emission region on the unseen 'counterjet' side.

Jackson, N.↗

NASA NTRS1994

Neutral cloud theory of the Jovian nebula: Anomalous ionization effect of superthermal electrons

The standard model of the Jovian nebula postulates that its particle source is the extended cloud of neutral sulfur and oxygen atoms that escape from the satellite Io and become ionized through electron impact from the corotating plasma. Its energy source is the gyroenergy acquired by newly formed pickup ions as they are swept up to corotation velocity by the planetary magnetic field. Elastic collisions between plasma ions and electrons cool the ions and heat the electrons, while inelastic collisions cool the electrons and excite the ions to radiate intense line emission, which is the primary energy-loss mechanism for the plasma. This neutral cloud theory of the Io plasma torus, as it has come to be known, has been the subject of recent critcism which asserts that the theory cannot account for the observed charge state of the plasma which features O(+) and S(2+) as the dominant ions. It is shown in this work that the inclusion of a small population of super-thermal electrons is required to achieve the correct ion partitioning among various charge states. It is also argued that the anomalous ionization effect of the superthermal electrons is responsible for the overall spatial bifurcation of the nebula into a hot multiply charged plasma region outside of 5.7 Jovian radii and a cool singly ionized plasma inside this distance.

Barbosa, D. D.↗

NASA NTRS1994

Low-latitude boundary layer near noon: An open field line model

We propose that many features of the cusp and low-latitude boundary layer (LLBL) observed near noon MLT can be explained by interpreting the LLBL as being on open lines with an inner boundary at the separatrix between open and closed magnetic field lines. This interpretation places the poleward boundary of the LLBL and equatorward boundary of the cusp along the field line that bifurcates at the cusp neutral point. The interpretation accounts for the abrupt boundary of magnetosheath particles at the inner edge of the LLBL, a feature that is inconsistent with LLBL formation by diffusion onto closed field lines, and for the distribution of magnetosheath particles appearing more as one continuous region than as two distinct regions across the noon cusp/LLBL boundary. Furthermore, we can explain the existence of energetic radiation belt electrons and protons with differing pitch angle distributions within the LLBL and their abrupt cutoff at the poleward boundary of the LLBL. By modeling the LLBL and cusp region quantitatively, we can account for a hemispherical difference in the location of the equatorial boundary of the cusp that is observed to be dependent on the dipole tilt angle but not on the interplanetary magnetic field (IMF) x component. We also find important variations and hemispherical differences in that the size of the LLBL that should depend strongly upon the x component of the IMF. This prediction is observationally testable. Finally, we find that when the IMF is strongly northward, the LLBL may include a narrow region adjacent to the magnetopause where field lines are detached (i.e., have both ends connected to the IMF).

Lyons, L. R.↗

NASA NTRS1995

Preliminary chaotic model of snapover on high voltage solar cells

High voltage power systems in space will interact with the space plasma in a variety of ways. One of these, snapover, is characterized by sudden enlargement of the current collection area across normally insulating surfaces generating enhanced electron current collection. Power drain on solar array power systems results from this enhanced current collection. Optical observations of the snapover phenomena in the laboratory indicates a functional relation between glow area and bia potential as a consequence of the fold/cusp bifurcation in chaos theory. Successful characterizations of snapover as a chaotic phenomena may provide a means of snapover prevention and control through chaotic synchronization.

Mackey, Willie R.↗

NASA NTRS1995

Durability and life prediction modeling in polyimide composites

Sudden appearance of cracks on a macroscopically smooth surface of brittle materials due to cooling or drying shrinkage is a phenomenon related to many engineering problems. Although conventional strength theories can be used to predict the necessary condition for crack appearance, they are unable to predict crack spacing and depth. On the other hand, fracture mechanics theory can only study the behavior of existing cracks. The theory of crack initiation can be summarized into three conditions, which is a combination of a strength criterion and laws of energy conservation, the average crack spacing and depth can thus be determined. The problem of crack initiation from the surface of an elastic half plane is solved and compares quite well with available experimental evidence. The theory of crack initiation is also applied to concrete pavements. The influence of cracking is modeled by the additional compliance according to Okamura's method. The theoretical prediction by this structural mechanics type of model correlates very well with the field observation. The model may serve as a theoretical foundation for future pavement joint design. The initiation of interactive cracks of quasi-brittle material is studied based on a theory of cohesive crack model. These cracks may grow simultaneously, or some of them may close during certain stages. The concept of crack unloading of cohesive crack model is proposed. The critical behavior (crack bifurcation, maximum loads) of the cohesive crack model are characterized by rate equations. The post-critical behavior of crack initiation is also studied.

Binienda, Wieslaw K.↗

NASA NTRS1996

Heat and Momentum Transfer Studies in High Reynolds Number Wavy Films at Normal and Reduced Gravity Conditions

We examined the effect of the gas flow on the liquid film when the gas flows in the countercurrent direction in a vertical pipe at normal gravity conditions. The most dramatic effect of the simultaneous flow of gas and liquid in pipes is the greatly increased transport rates of heat, mass, and momentum. In practical situations this enhancement can be a benefit or it can result in serious operational problems. For example, gas-liquid flow always results in substantially higher pressure drop and this is usually undesirable. However, much higher heat transfer coefficients can be expected and this can obviously be of benefit for purposes of design. Unfortunately, designers know so little of the behavior of such two phase systems and as a result these advantages are not utilized. Due to the complexity of the second order boundary model as well as the fact that the pressure variation across the film is small compared to the imposed gas phase pressure, the countercurrent gas flow affect was studied for the standard boundary layer model. A different stream function that can compensate the shear stress affect was developed and this stream function also can predict periodic solutions. The discretized model equations were transformed to a traveling wave coordinate system. A stability analysis of these sets of equations showed the presence of a Hopf bifurcation for certain values of the traveling wave velocity and the shear stress. The Hopf celerity was increased due to the countercurrent shear. For low flow rate the increases of celerity are more than for the high flow rate, which was also observed in experiments. Numerical integration of a traveling wave simplification of the model also predicts the existence of chaotic large amplitude, nonperiodic waves as observed in the experiments. The film thickness was increased by the shear.

Balakotaiah, V.↗

NASA NTRS1996

Classical Trajectories and Quantum Spectra

A classical model of the Schrodinger's wave packet is considered. The problem of finding the energy levels corresponds to a classical manipulation game. It leads to an approximate but non-perturbative method of finding the eigenvalues, exploring the bifurcations of classical trajectories. The role of squeezing turns out decisive in the generation of the discrete spectra.

Mielnik, Bogdan↗

NASA NTRS1996

Transonic Shock Oscillations and Wing Flutter Calculated with an Interactive Boundary Layer Coupling Method

A viscous-inviscid interactive coupling method is used for the computation of unsteady transonic flows involving separation and reattachment. A lag-entrainment integral boundary layer method is used with the transonic small disturbance potential equation in the CAP-TSDV (Computational Aeroelasticity Program - Transonic Small Disturbance) code. Efficient and robust computations of steady and unsteady separated flows, including steady separation bubbles and self-excited shock-induced oscillations are presented. The buffet onset boundary for the NACA 0012 airfoil is accurately predicted and shown computationally to be a Hopf bifurcation. Shock-induced oscillations are also presented for the 18 percent circular arc airfoil. The oscillation onset boundaries and frequencies are accurately predicted, as is the experimentally observed hysteresis of the oscillations with Mach number. This latter stability boundary is identified as a jump phenomenon. Transonic wing flutter boundaries are also shown for a thin swept wing and for a typical business jet wing, illustrating viscous effects on flutter and the effect of separation onset on the wing response at flutter. Calculations for both wings show limit cycle oscillations at transonic speeds in the vicinity of minimum flutter speed indices.

Edwards, John W.↗

NASA NTRS1996

Migrational Instabilities in Particle Suspensions

This work deals with an instability arising from the shear-induced migration of particles in dense suspensions coupled with a dependence of viscosity on particle concentration. The analysis summarized here treats the inertialess (Re = O) linear stability of homogeneous simple shear flows for a Stokesian suspension model of the type proposed by Leighton and Acrivos (1987). Depending on the importance of shear-induced migration relative to concentration-driven diffusion, this model admits short-wave instability arising from wave-vector stretching by the base flow and evolving into particle-depleted shear bands. Moreover, this instability in the time-dependent problem corresponds to loss of ellipticity in the associated static problem (Re = O, Pe = O). While the isotropic version of the Leighton-Acrivos model is found to be stable with their experimentally determined parameters for simple shear, it is known that the stable model does not give a good quantitative description of particle clustering in the core of pipe flow (Nott and Brady 1994). This leads to the conjecture that an appropriate variant on the above model could explain such clustering as a two-phase bifurcation in the base flow.

Goddard, Joe D.↗

NASA NTRS1996

Low-Dimensional Dynamical Models of Thermal Convection

A low-dimensional dynamic model for transitional buoyancy-driven flow in a differentially heated tall enclosure is presented. The full governing partial differential equations with the associated boundary conditions are solved by a spectral element method for a cavity of aspect ratio A=20. Proper orthogonal decomposition is applied to the oscillatory solution at Prandtl number Pr=P tau (omega) = 0.71 and Grashof number G tau (omega) = 3.2 x 10 (exp 4) to construct empirical eigenfunctions. Using the four most energetic empirical eigenfunctions for the velocity and temperature as basis functions and applying Galerkin's method, a reduced model consisting of eight nonlinear ordinary differential equations is obtained. Close to the 'design' conditions (P tau(omega) G tau(omega)), the low-order model (LOM) predictions are in excellent agreement with the predictions of the full model. In particular, the critical Grashof number at the onset of the first temporal flow instability (Hopf bifurcation) was well as the frequency and amplitude of oscillations at supercritical conditions are in excellent agreement with the predictions of the full model. Far from the 'design' conditions, the LOM predicts the existence of multiple stable steady solutions at large values of G tau, and a unique stable steady solution at small values of G tau, and exhibits hysteretic behavior that is qualitatively similar to that observed in direct numerical simulations based on the full model.

Liakopoulos, Anthony↗

NASA NTRS1996

The Extensional Rheology of Non-Newtonian Materials

The evolution of the transient extensional stresses in dilute and semi-dilute viscoelastic polymer solutions are measured with a filament stretching rheometer of a design similar to that first introduced by Sridhar, et al. The solutions are polystyrene-based (PS) Boger fluids that are stretched at constant strain rates ranging from 0.6 less than or equal to epsilon(0) less than or equal to 4s(exp -1) and to Hencky strains of epsilon greater than 4. The test fluids all strain harden and Trouton ratios exceeding 1000 are obtained at high strains. The experimental data strain hardens at lower strain levels than predicted by bead-spring FENE models. In addition to measuring the transient tensile stress growth, we also monitor the decay of the tensile viscoelastic stress difference in the fluid column following cessation of uniaxial elongation as a function of the total imposed Hencky strain and the strain rate. The extensional stresses initially decay very rapidly upon cessation of uniaxial elongation followed by a slower viscoelastic relaxation, and deviate significantly from FENE relaxation predictions. The relaxation at long times t is greater than or equal to 5 s, is compromised by gravitational draining leading to non-uniform filament profiles. For the most elastic fluids, partial decohension of the fluid filament from the endplates of the rheometer is observed in tests conducted at high strain rates. This elastic instability is initiated near the rigid endplate fixtures of the device and it results in the progressive breakup of the fluid column into individual threads or 'fibrils' with a regular azimuthal spacing. These fibrils elongate and bifurcate as the fluid sample is elongated further. Flow visualization experiments using a modified stretching device show that the instability develops as a consequence of an axisymmetry-breaking meniscus instability in the nonhomogeneous region of highly deformed fluid near the rigid endplate.

Spiegelberg, Stephen H.↗

NASA NTRS1996

Influence of Thermocapillary Flow on Capillary Stability: Long Float-Zones in Low Gravity

A model problem is posed to study the influence of flow on the interfacial stability of a nearly cylindrical liquid bridge for lengths near its circumference (the Plateau-Rayleigh limit). The flow is generated by a shear stress imposed on the deformable interface. The symmetry of the imposed shear stress mimics the thermocapillary stress induced on a float-zone by a ring heater (i.e. a full zone). Principal assumptions are (1) zero gravity, (2) creeping flow, and (3) that the imposed coupling at the free surface between flow and temperature fields is the only such coupling. A numerical solution, complemented by a bifurcation analysis, shows that bridges substantially longer than the Plateau-Rayleigh limit are possible. An interaction of the first two capillary instabilities through the stress-induced flow is responsible. Time-periodic standing waves are also predicted in certain parameter ranges. Motivation comes from extra-long float-zones observed in MEPHISTO space lab experiments (June 1994).

Chen, Yi-Ju↗