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All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Nonlinear dynamic analysis of quasi-symmetric anisotropic structures

An efficient computational method for the nonlinear dynamic analysis of quasi-symmetric anisotropic structures is proposed. The application of mixed models simplifies the analytical development and improves the accuracy of the response predictions, and operator splitting allows the reduction of the analysis model of the quasi-symmetric structure to that of the corresponding symmetric structure. The preconditoned conjugate gradient provides a stable and effective technique for generating the unsymmetric response of the structure as the sum of a symmetrized response plus correction modes. The effectiveness of the strategy is demonstrated with the example of a laminated anisotropic shallow shell of quadrilateral planform subjected to uniform normal loading.

Noor, Ahmed K.↗
NASA NTRS2016

Influence of Stationary Crossflow Modulation on Secondary Instability

A likely scenario for swept wing transition on subsonic aircraft with natural laminar flow involves the breakdown of stationary crossflow vortices via high frequency secondary instability. A majority of the prior research on this secondary instability has focused on crossflow vortices with a single dominant spanwise wavelength. This paper investigates the effects of the spanwise modulation of stationary crossflow vortices at a specified wavelength by a subharmonic stationary mode. Secondary instability of the modulated crossflow pattern is studied using planar, partial-differential-equation based eigenvalue analysis. Computations reveal that weak modulation by the first subharmonic of the input stationary mode leads to mode splitting that is particularly obvious for Y-type secondary modes that are driven by the wall-normal shear of the basic state. Thus, for each Y mode corresponding to the fundamental wavelength of results in unmodulated train of crossflow vortices, the modulated flow supports a pair of secondary modes with somewhat different amplification rates. The mode splitting phenomenon suggests that a more complex stationary modulation such as that induced by natural surface roughness would yield a considerably richer spectrum of secondary instability modes. Even modest levels of subharmonic modulation are shown to have a strong effect on the overall amplification of secondary disturbances, particularly the Z-modes driven by the spanwise shear of the basic state. Preliminary computations related to the nonlinear breakdown of these secondary disturbances provide interesting insights into the process of crossflow transition in the presence of the first subharmonic of the dominant stationary vortex.

Vortex structure↗
NASA NTRS2021

Direct Multipoint Observations Capturing the Reformation of a Supercritical Fast Magnetosonic Shock

Using multipoint Magnetospheric Multiscale (MMS) observations in an unusual string-of-pearls configuration, we examine in detail observations of the reformation of a fast magnetosonic shock observed on the upstream edge of a foreshock transient structure upstream of Earth’s bow shock. The four MMS spacecraft were separated by several hundred km, comparable to suprathermal ion gyro-radius scales or several ion inertial lengths. At least half of the shock reformation cycle was observed, with a new shock ramp rising up out of the “foot” region of the original shock ramp. Using the multipoint observations, we convert the observed time-series data into distance along the shock normal in the shock’s rest frame. That conversion allows for a unique study of the relative spatial scales of the shock’s various features, including the shock’s growth rate, and how they evolve during the reformation cycle. Analysis indicates that: the growth rate increases during reformation, electron-scale physics play an important role in the shock reformation, and energy conversion processes also undergo the same cyclical periodicity as reformation. Strong, thin electron-kinetic-scale current sheets and large-amplitude electrostatic and electromagnetic waves are reported. Evidence is also presented of nonlinear wave decay from electromagnetic whistler-mode “lion roars” to electrostatic solitary waves in the downstream plasma regime. Results highlight the critical cross-scale coupling between electron-kinetic-and ion-kinetic-scale processes and details of the nature of nonstationarity, shock-front reformation at collisionless, fast magnetosonic shocks.

D L Turner↗
NASA NTRS2011

Current Sheets in the Heliosheath: Voyager 1, 2009

We identified all of the current sheets for which we have relatively complete and accurate magnetic field (B) data from Voyager 1 (V1) from days of year (DOYs) 1 to 331, 2009, which were obtained deep in the heliosheath between 108.5 and 111.8 AU. Three types of current sheets were found: (1) 15 proton boundary layers (PBLs), (2) 10 and 3 magnetic holes and magnetic humps, respectively, and (3) 3 sector boundaries. The magnetic field strength changes across PBL, and the profile B(t) is linearly related to the hyperbolic tangent function, but the direction of B does not change. For each of the three sector boundaries, B rotated in a plane normal to the minimum variance direction, and the component of B along the minimum variance direction was zero within the uncertainties, indicating that the sector boundaries were tangential discontinuities. The structure of the sector boundaries was not as simple as that for PBLs. The average thickness of magnetic holes and humps (approx.30 RL) was twice that of the PBLs (approx.15 RL). The average thickness of the current sheets associated with sector boundaries was close to the thickness of the PBLs. Our observations are consistent with the hypothesis that magnetic holes and humps are solitons, which are initiated by the mirror mode instability, and evolve by nonlinear kinetic plasma processes to pressure balanced structures maintained by magnetization currents and proton drift currents in the gradients of B.

Burlaga, L. F.↗
NASA NTRS1983

Electrostatic Kelvin-Helmholtz instability in a radially injected plasma cloud

An elecrostatic finite-sized particle simulation model is used to study the early time-scale phenomena asociated with an impulsively injected plasma, expanding radially, normal to a strong ambient magnetic field. Results of the simulation show the early formation of a radial polarization electric field due to ion-electron charge separation which causes electrons to drift in the azimuthal direction. Velocity shear within this motion gives rise to a Kelvin-Helmholtz (dioxotron) instability, creating a radial fluted pattern as the plasma expands. In the nonlinear stage of instability, azimuthal variations in the electric field are observed which cause electrons to drift across the magnetic field, thereby reducing the space charge created by energetic ion expansion. The results of a linear stability analysis reveal that for a decreasing amount of charge separation in the plasma, the number of unstable azimuthal modes at maximum growth rate increases. Also, as the thickness of the electron ring increases, a fewer number of unstable modes develops for a given amount of charge separation. It is concluded that electrons become unstable at the very early time scale, within an ion gyroperiod, and that unstable electrons lead to modification of the ion dynamics.

Sydora, R. D.↗
NASA NTRS1991

Drift wave instability in the Io plasma torus

A linear normal mode analysis of the drift wave instability in the Io plasma torus was carried out on the basis of the Richmond (1973) and Huang et al. (1990) analyses of drift waves in the vicinity of the earth's plasmapause. Results indicate that the outer torus boundary is linearly unstable to the growth of electrostatic drift waves. It is shown that the linear growth rate is proportional to the ion drift frequency and to the ratio of the flux tube charge content to the Jovian ionospheric Pedersen conductance. It is also shown that various theoretical models of global radial transport in Jupiter's atmosphere (including corotating convection, interchange diffusion, and transient flux tube convection) can be understood as plausible nonlinear evolutions of electrostatic drift waves.

Huang, T. S.↗
NASA NTRS1992

Multiple switch-off slow shock solutions

A new electromagnetic quasi-neutral time-dependent implicit hybrid model for simulating the slow-mode switch-off shock is developed, in which the electrons are treated as a finite-mass adiabatic fluid (gamma sub e = 5/3), whose motion along the shock normal provides local charge neutrality. The model is used to examine the effects of various boundary conditions applied during shock formation. It is shown that, for each upstream condition, two distinctly different slow-shock structures can be obtained: a low-shock structure with a trailing magnetic wave (TMW) and a slow-shock structure without a TMW, depending strongly on the boundary conditions for the electric and magnetic fields at the physical piston which generates the shock. The results indicate that the slow-shock structure with a TMW is nonlinearly unstable with respect to changes in the upstream magnetic field, suggesting that the downstream structure of slow shocks need not be associated with a TMW.

Vu, H. X.↗
NASA NTRS1983

Coupling of radiation into thin film modes by means of localized plasma resonances

The interaction between the surface plasmon mode that propagates at a metal dielectric interface and the localized plasma resonances (LPR) is investigated experimentally in Ag-island films. A stair-stepped sample geometry comprising a glass substrate, a continuous 50-nm Ag film, an LiF spacer film of thickness d = 5-60 nm, and an Ag-island film of mass thickness 3 nm is used in near-normal-reflectivity and plasmon-propagation-constant (k) determinations. The results are presented graphically and discussed. The overall shape of the reflectivity curves is found to be characteristic of Ag films, but with a dip at about 400 nm (corresponding to the absorption resonance of the island film) which is most pronounced with d = 25 nm. It is inferred that the island resonances are strongly coupled to a continuous-film dissipative mechanism at this d value. This inference is supported by the fact that the variation in k, correctd for LiF effects and plotted as a function of d, is greatest at around d = 25 nm. The implications of this finding for broad-band coupling into a thin-film mode, LPR enhancement of waveguide nonlinear effects, and new surface-enhanced-Raman-scattering geometries are indicated.

Holland, W. R.↗
NASA NTRS2002

A Thermodynamic Theory Of Solid Viscoelasticity. Part 1: Linear Viscoelasticity.

The present series of three consecutive papers develops a general theory for linear and finite solid viscoelasticity. Because the most important object for nonlinear studies are rubber-like materials, the general approach is specified in a form convenient for solving problems important for many industries that involve rubber-like materials. General linear and nonlinear theories for non-isothermal deformations of viscoelastic solids are developed based on the quasi-linear approach of non-equilibrium thermodynamics. In this, the first paper of the series, we analyze non-isothermal linear viscoelasticity, which is applicable in a range of small strains not only to all synthetic polymers and bio-polymers but also to some non-polymeric materials. Although the linear case seems to be well developed, there still are some reasons to implement a thermodynamic derivation of constitutive equations for solid-like, non-isothermal, linear viscoelasticity. The most important is the thermodynamic modeling of thermo-rheological complexity , i.e. different temperature dependences of relaxation parameters in various parts of relaxation spectrum. A special structure of interaction matrices is established for different physical mechanisms contributed to the normal relaxation modes. This structure seems to be in accord with observations, and creates a simple mathematical framework for both continuum and molecular theories of the thermo-rheological complex relaxation phenomena. Finally, a unified approach is briefly discussed that, in principle, allows combining both the long time (discrete) and short time (continuous) descriptions of relaxation behaviors for polymers in the rubbery and glassy regions.

Freed, Alan D.↗
NASA NTRS1989

A seven-month solar cycle observed with the Langmuir probe on Pioneer Venus Orbiter

Data collected by the Langmuir probe aboard the Pioneer Venus orbiter (PVO) over the years 1979 though 1987 were normalized to remove the long-period 11-year solar maximum to minimum trend and were analyzed for periodicity. Results yield evidence for the existence of an approximately 7-month solar cycle, which was also observed from SME Lyman alpha and 2800-MHz radio flux measurements carried out from an earth-based platform. This coincidence suggests that the cycle is an intrinsic periodicity in the solar output. The cycle has a frequency independent of the orbital frequency of the PVO and is distinct from a 'rotating beacon' cycle whose period depends on the orbital motion of the PVO about the sun. The second most dominant cycle discovered was a 5-month period. Results of an oscillation model of solar periodicity indicate that the 7-month and 5-month cycles are caused by long-lived flux enhancements from nonlinear interactions of global oscillation modes in the sun's convective envelope (r modes) and radiative interior (g modes).

Hoegy, W. R.↗
NASA NTRS1990

Resonant decay of global MHD modes at 'thick' interfaces

A global surface mode can exist on a 'surface' which is not a true discontinuity, but without sufficient dissipation it is not a normal mode and it decays in time via resonance absorption. The decay rate can be calculated analytically when the 'surface' is thin. The goal of this paper is to numerically estimate the decay rate when the surface is not thin. A cold plasma in a uniform magnetic field is considered in which density varies linearly across the 'surface'. In this linearized calculation, the global surface mode is driven in steady state by an antenna located in one of the uniform regions external to the surface. The frequency is a free parameter, and resonance curves are computed numerically without approximations. The widths of the resonance curves are used to estimate the free decay times of undriven surface modes, via the uncertainty principle. When applied to the active solar corona, the decay rates are large enough to account for the coronal heating, but it should be kept in mind that the role of nonlinearity in resonance absorption is still undetermined.

Hollweg, Joseph V.↗
NASA NTRS1986

The nonlinear development of Gortler vortices in growing boundary layers

The development of Gortler vortices in boundary layers over curved walls in the nonlinear regime is investigated. The growth of the boundary layer makes a parallel flow analysis impossible except in the high wavenumber regime so in general the instability equations must be integrated numerically. Here the spanwise dependence of the basic flow is described using Fourier series expansion whilst the normal and streamwise variations are taken into account using finite differences. The calculations suggest that a given disturbance imposed at some position along the wall will eventually reach a local equilibrium state essentially independent of the initial conditions. In fact, the equilibrium state reached is qualitatively similar to the large amplitude high wave-number solution described asymptotically by Hall (1982). In general, it is found that the nonlinear interactions are dominated by a mean field type of interaction between the mean flow and the fundamental. Thus, even though higher harmonics of the fundamental are necessarily generated, most of the disturbance energy is confined to the mean flow correction and the fundamental. A major result of the calculations is finding that the downstream velocity field develops a strongly inflection character as the flow moves downstream. The latter result suggests that the major effect of Gortler vortices on boundary layers of practical importance might be to make them highly receptive to rapidly growing Rayleigh modes of instability.

Hall, Philip↗
NASA NTRS1988

The nonlinear development of Goertler vortices in growing boundary layers

The development of Goertler vortices in boundary layers over curved walls in the nonlinear regime is investigated. The growth of the boundary layer makes a parallel flow analysis impossible except in the high wavenumber regime so in general the instability equations must be integrated numerically. Here the spanwise dependence of the basic flow is described using Fourier series expansion while the normal and streamwise variations are taken into account using finite differences. The calculations suggest that a given disturbance imposed at some position along the wall will eventually reach a local equilibrium state essentially independent of the initial conditions. In fact, the equilibrium state reached is qualitatively similar to the large amplitude high wave-number solution described asymptotically by Hall (1982). In general, it is found that the nonlinear interactions are dominated by a mean field type of interaction between the mean flow and the fundamental. Thus, even though higher harmonics of the fundamental are necessarily generated, most of the disturbance energy is confined to the mean flow correction and the fundamental. A major result of the calculations is finding that the downstream velocity field develops a strongly inflectional character as the flow moves downstream. The latter result suggests that the major effect of Goertler vortices on boundary layers of practical importance might be to make them highly receptive to rapidly growing Rayleigh modes of instability.

Hall, Philip↗
NASA NTRS2003

Preliminary Planar Formation: Flight Dynamics Near Sun-Earth L2 Point

NASA's Goddard Space Flight Center is planning a series of missions in the vicinity of the Sun-Earth L2 libration point. Some of these projects will involve a distributed space system of telescope spacecraft acting together as a single telescope for high-resolution. The individual telescopes will be configured in a plane, surrounding a hub, where the telescope plane can be aimed toward various astronomical targets of interest. In preparation for these missions, it is necessary to develop an improved understanding of the dynamical behavior of objects in a planar configuration near L2. The classical circular restricted three body problem is taken as the basis for the analysis. At first order, the motion of such a telescope relative to the hub is described by a system of linear second order differential equations. These equations are identical to the circular restricted problem's linear equations describing the hub motion about L2. Therefore, the fundamental frequencies, both parallel to and normal to the ecliptic plane, are the same for the relative telescope motion as for the hub motion. To maintain the telescope plane for the duration necessary for the planned observations, a halo-type orbit of the telescopes about the hub is investigated. By using a halo orbit, the individual telescopes remain in approximately the same plane over the observation duration. For such an orbit, the fundamental periods parallel to and normal to the ecliptic plane are forced to be the same by careful selection of the initial conditions in order to adjust the higher order forces. The relative amplitudes of the resulting oscillations are associated with the orientation of the telescope plane relative to the ecliptic. As in the circular restricted problem, initial conditions for the linearized equations must be selected so as not to excite the convergent or divergent linear modes. In a higher order analysis, the telescope relative motion equations include the effects of the position of the hub relative to L2. In this paper, the differential equations are developed through second order in the distance of the hub from the libration point. A modified Lindstedt-Poincad perturbation method is employed to construct the solution of these differential equations through that same order of magnitude. In the course of the solution process, relationships are determined between the initial conditions of the telescopes, selected in order to avoid resonance excitation. As the differential equations include the hub position, it is necessary to simultaneously develop the solution for the hub. As has been done in past analyses of the circular restricted problem, the hub position is written in a power series formulation in terms of its distance from L2. Then, in order to be included in the telescope equations, the hub solution is cast in terms of the nonlinear frequency of the relative telescope motion. In the course of the analysis, it is determined that the hub should also maintain a halo orbit - about L2. Additionally, relationships are formed between the initial conditions of the telescopes and the hub. These relationships may be used to associate sets of initial conditions with particular orientations of the telescope plane. The accuracy of the analytical solution is verified through various simulations and comparison to numerical integration of the differential equations. The results of the simulations are presented, along with a graphical representation of the relationships between the initial conditions of the telescopes and hub.

Segerman, Alan M.↗
NASA NTRS2019

Transitioning the NASA SLR Network to Event Timing Mode for Reduced Systematics, Improved Stability and Data Precision

NASA's legacy Satellite Laser Ranging (SLR) network produces about one-third of the global SLR data to support spacegeodesy. This network of globally distributed stations has been using Time Interval Units (TIU) for range measurements for thelast 25 + years. To improve the reliability of the SLR network and satisfy the need for stable millimeter precision data, a phasedreplacement of the TIUs in the network with picosecond-precise Event Timer Modules was initiated in 2015. This schemeallowed the time of flight and laser transmit epoch measurement to one picosecond resolution. For a network with globalscientific impact, transitioning to a new data generation metrological scheme requires significant data scrutiny and long-termscience data validation. Any long-term testing/measurement has the potential to interrupt the station's daily operational dataflow to the International Laser Ranging Service (ILRS) as the station under test will have to put its test data into quarantine.We have demonstrated a very effective way to test and implement the new device without removing the old hardware andwithout the need for the orbit analysis. This operationally noninvasive scheme performed concurrent test measurements enablinguninterrupted operational data flow to the users, while allowing simultaneous test data capture for short- and long-termsystematics and stability analysis. Extensive analysis of the test data was performed by the NASA SLR engineering team andthe ILRS Analysis Standing Committee, to uncover biases and any dependencies on the satellite ranges (for nonlinear scaleissues). Multi-ETM comparison was also performed at two of the SLR stations through the interchange of hardware to establishthe inter-device range biases and stability. Such benchmarked hardware was subsequently sent to the remaining stationsto allow traceability and normalize the network performance. The range bias intercomparison performed using the multiyearSLR data analysis agreed well with the engineering changes, thus validating the approach to flush out station-specific rangingsystematics affecting precise orbit determination. Such an improvement and rebalancing of the current network will allowan orderly transition of the current NASA SLR network operating at a maximum rate of 10 Hz to the NASA next generationSpace Geodesy Satellite Laser Ranging (SGSLR) network operating at 2 kHz (McGarry et al. in J Geod, 2018. https ://doi.org/10.1007/s0019 0-018-1191-6; Merkowitz et al. in J Geod, 2018. https ://doi.org/10.1007/s0019 0-018-1204-5).

Varghese, Thomas↗
NASA NTRS1999

Swept-Wing Receptivity Studies Using Distributed Roughness

Transition to turbulence in swept-wing flows has resisted correlation with linear theory because of its sensitivity to freestream conditions and 3-D roughness and because one of the principal instability modes quickly 'becomes nonlinear. In the face of such a formidable problem, two rather long-term fundamental efforts have been underway at DLR Gottinberg and Arizona State University that address swept-wing transition. These efforts have been recently reviewed by Bippes (1997) and Reibert and Saric (1997). Thus, the present work is a continuation of a series of studies on swept-wing boundary layers which have led to a better understanding of the transition process. In particular, we have taken advantage of the sensitivity to 3-D roughness and the modal nature of the instability in order to propose a particular control strategy. Complementing the two aforementioned reviews, general reviews of the swept-wing transition problem are found in Arnal (1997) and Kachanov (1996). Other recent reviews include Reshotko (t997), Crouch (1997), and Herbert (1997a,b). The failure of linear theory is discussed in Reed et al. (1996). The historical work is found in Reed and Sar-ic (1989). The basic idea is that the combination of sweep and chordwise pressure gradient within the boundary layer creates a velocity component perpendicular to the inviscid streamline. This crossflow profile is inflectional and exhibits both traveling and stationary unstable waves called crossflow vortices that are (approximately) aligned along the inviscid streamlines. Under conditions of low freestream turbulence levels, the dominant crossflow wave is stationary (Reibert and Saric t997) while moderate to high turbulence levels initiate dominant traveling waves (Dehle and Bippes 1996; Bippes 1997). 'Me mechanism is relatively insensitive to sound and 2-D surface roughness (Radeztsky et al. 1993) but very sensitive to 3-D roughness near the attachment line. We concentrate our work on low-turbulence freestream flows and stationary crossflow waves. Although the v' and w' components of the disturbances are very small, by convecting streamwise momentum in the wall-normal direction, they produce 0(l) changes inu'.Thus the mean flow is highly distorted with localized inflection points. Transition is then triggered by a high-frequency secondary instability of the distorted mean profile.

Saric, William S.↗
NASA NTRS1994

Raman-shifting an ArF excimer laser to generate new lines for obtaining optical diagnostic based information in flow fields

The application of tunable excimer lasers in combustion and flow diagnostics is almost routine nowadays. The properties of this laser system that enable density and temperature measurements in supersonic and hypersonic flow fields to be conducted are its high power, high repetition rate, and high spectral brightness. The limitation imposed by this system on these measurements is the paucity of lines in the wavelength region, the vacuum-ultraviolet, where species of interest, such as OH, N2, O2, H2, H2O, CO, NO, etc., are susceptible to electronic excitation to high-lying states. To circumvent this problem one normally resorts to nonlinear optical techniques such as frequency conversion via stimulated Raman scattering (SRS), more commonly known as Raman shifting or Raman mixing, to extend these nonintrusive and nonperturbing techniques to the shorter wavelengths in the VUV region and, for that matter, to longer wavelengths in the infrared region, if the need arises. The theoretical basis of SRS and its application are well documented in the literature. In essence, the Raman shift is a consequence of the inelastic scattering of the incident radiation by the sample. Most of the scattered radiation from the molecules of the sample is unchanged in frequency. However, a small fraction of the incident radiation is changed in frequency. This shift is a result of the fact that some of the incident photons on colliding with the molecules of the sample give up some of their energy and emerge with a lower energy resulting in the lower-frequency Stokes radiation. Other incident photons may increase their energy by colliding with the vibrationally excited molecules of the medium and emerge as higher-frequency antistokes radiation. The generation of the latter is the main objective of this project. The process, however, depends on several factors, including the beam quality of the pump laser, the cross-section of the gaseous medium, the gas pressure, and the ambient temperature of the gas near the focal region. Furthermore, since the Raman shifting process is polarization sensitive, it is necessary to have all of the laser energy in a single polarization. These factors were taken into consideration in the execution of the project. The implementation of the Raman shift was accomplished by focusing the 193 nm output of an ArF excimer laser (Lamda-Physik LPX 150) into a 1-meter long high pressure recirculating Raman cell filled with H2 gas. The laser system was modified in order to improve the mode quality of the pump beam to enhance the Raman shifting. To accomplish this feat, a prism beam expander and grating on the oscillator discharge provided wavelength tuning over the excimer gain profile. Furthermore, a triple-pass configuration, as opposed to unstable resonator optics, was employed in the operation of the amplifier cavity so that when the oscillator output radiation, focused by a 51-cm focal length fused silica lens through a 50 micron pinhole (serving as a spatial filter) and recollimated with a 25-cm focal length lens, was fed into the amplifier, it was injection locked, thereby providing tunable radiation with relatively low divergence. The forward scattered radiation emanating from the impingement of the modified pump beam on the Raman cell was detected using an energy meter after the latter had been separated from it using a dispersing prism.

Koker, Edmond B.↗