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At least 919 records · Page 51
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NASA NTRS2018

Collisionless Relaxation of the Ion Ring Distribution in Space Plasma

Energetic processes often produce transversely-heated angular distributions of the magnetized core (lowest energy) plasma. This characteristic is found in solar wind ion pickup, resulting from cometary or interstellar gas ionization, in Earths' ionosphere, and with hot ions formed around the Space Transportation System during gas releases. We investigate the thermalization of O+ ion pickup using the 2.5D hybrid simulation method (with fluid electrons and kinetic ions) of the ion pickup (ring) distributions, formed in the auroral ionosphere, with a range of ring velocities and thermal to magnetic pressure ratios. We find that in the unstable collisonless regime the anisotropy of the non-thermal distribution produces the ion-cyclotron instability, and the nonlinear relaxation is accompanied by wave-particle scattering that results in an emitted power of EMIC waves. We conclude that ionospheric pickup thermalization is slow due to the small ring speed compared to the thermal and Alfven speeds, while in the solar wind and other space plasmas regions with larger ion-ring velocity the collisionless relaxation and thermalization is rapid in terms of O+ ion gyro-period.

Ofman, Leon↗
NASA NTRS2008

Nondestructive Evaluation of Metal Fatigue Using Nonlinear Acoustics

Safe-life and damage-tolerant design philosophies of high performance structures have driven the development of various methods to evaluate nondestructively the accumulation of damage in such structures resulting from cyclic loading. Although many techniques have proven useful, none has been able to provide an unambiguous, quantitative assessment of damage accumulation at each stage of fatigue from the virgin state to fracture. A method based on nonlinear acoustics is shown to provide such a means to assess the state of metal fatigue. The salient features of an analytical model are presented of the microelastic-plastic nonlinearities resulting from the interaction of an acoustic wave with fatigue-generated dislocation substructures and cracks that predictably evolve during the metal fatigue process. The interaction is quantified by the material (acoustic) nonlinearity parameter extracted from acoustic harmonic generation measurements. The parameters typically increase monotonically by several hundred percent over the fatigue life of the metal, thus providing a unique measure of the state of fatigue. Application of the model to aluminum alloy 2024-T4, 410Cb stainless steel, and IN100 nickel-base superalloy specimens fatigued using different loading conditions yields good agreement between theory and experiment. Application of the model and measurement technique to the on-site inspection of steam turbine blades is discussed.

Cantrell, John H., Jr.↗
NASA NTRS1975

Effect of Nozzle Nonlinearities upon Nonlinear Stability of Liquid Propellant Rocket Motors

A three dimensional, nonlinear nozzle admittance relation is developed by solving the wave equation describing finite amplitude oscillatory flow inside the subsonic portion of a choked, slowly convergent axisymmetric nozzle. This nonlinear nozzle admittance relation is then used as a boundary condition in the analysis of nonlinear combustion instability in a cylindrical liquid rocket combustor. In both nozzle and chamber analyses solutions are obtained using the Galerkin method with a series expansion consisting of the first tangential, second tangential, and first radial modes. Using Crocco's time lag model to describe the distributed unsteady combustion process, combustion instability calculations are presented for different values of the following parameters: (1) time lag, (2) interaction index, (3) steady-state Mach number at the nozzle entrance, and (4) chamber length-to-diameter ratio. In each case, limit cycle pressure amplitudes and waveforms are shown for both linear and nonlinear nozzle admittance conditions. These results show that when the amplitudes of the second tangential and first radial modes are considerably smaller than the amplitude of the first tangential mode the inclusion of nozzle nonlinearities has no significant effect on the limiting amplitude and pressure waveforms.

Padmanabhan, M. S.↗
NASA NTRS2017

Instability Wave-Streak Interactions in a Supersonic Boundary Layer

Optimal initial conditions for transient growth in a two-dimensional boundary layer flow correspond to stationary, counter-rotating vortices that subsequently develop into streamwise elongated streaks, which are characterized by an alternating pattern of low and high streamwise velocity. For incompressible flows, previous studies have shown that boundary layer modulation due to streaks below a threshold amplitude level can stabilize the Tollmien-Schlichting instability waves, resulting in a delay in the onset of laminar-turbulent transition. In the supersonic regime, the linearly, most-amplified waves become three-dimensional, corresponding to oblique, first-mode waves. This change in the character of dominant instabilities leads to an important change in the transition process, which is now dominated by oblique breakdown via nonlinear interactions between pairs of first-mode waves that propagate at equal but opposite angles with respect to the free stream. Because the oblique breakdown process is characterized by a rapid amplification of stationary streamwise streaks, artificial excitation of such streaks may be expected to promote transition in a supersonic boundary layer. Indeed, suppression of those streaks has been shown to delay the onset of transition in prior literature. Consistent with those findings, the present study shows that optimally growing stationary streaks indeed destabilize the first-mode waves, but only when the spanwise wavelength of the instability waves is equal to or smaller than twice the streak spacing. Transition in a benign disturbance environment typically involves first-mode waves with significantly longer spanwise wavelengths, and hence, these waves are stabilized by the optimal growth streaks. Thus, as long as the amplification factors for the destabilized, short wavelength instability waves remain below the threshold level for transition, a significant net stabilization is achieved, yielding a transition delay that is comparable to the length of the laminar region in the uncontrolled case.

Boundary layer transition↗
NASA NTRS1992

Nonlinear vibration and radiation from a panel with transition to chaos

The dynamic response of an aircraft panel forced at resonance and off-resonance by plane acoustic waves at normal incidence is investigated experimentally and numerically. Linear, nonlinear (period doubling), and chaotic responses are obtained by increasing the sound pressure level of the excitation. The response time history is sensitive to the input level and to the frequency of excitation. The change in response behavior is due to a change in input conditions, triggered either naturally or by modulation of the bandwidth of the incident waves. Off-resonance bifurcation is diffused and difficult to maintain; thus the panel response drifts into a linear behavior. The acoustic pressure emanated by the panel is either linear or nonlinear as is the vibration response. The nonlinear effects accumulate during the propagation with distance. Results are also obtained on the control of the panel response using damping tape on an aluminum panel and a graphite epoxy panel having the same size and weight. Good agreement is obtained betwen the experimental and numerical results.

Maestrello, Lucio↗
NASA NTRS1976

Nonlinear interaction between two electrostatic harmonics in a plasma

The problem of harmonic and subharmonic generation of electrostatic waves in a general collisionless plasma is treated using coupled-mode theory based on two time scales. A novel feature is that one of the two interacting waves may be a negative-energy wave. Since the model describing the medium need not be specified, only a general linear and nonlinear conductivity or an equivalent description is required. Just by invoking wave-energy conservation, the coupled-mode equations are obtained in such a way that unequivocal conclusions can be drawn. When both waves have positive energy, they exchange part of it in a periodic fashion, provided that both have some energy initially. If initially all the energy is in the fundamental, all of it will eventually end up (irreversibly) in the second harmonic. If all the energy is in the harmonic initially, no generation of the fundamental (or subharmonic) will take place. If one of the two waves is a negative-energy wave, an explosive instability develops, regardless of initial values. For comparable conditions, the instability time depends on whether the negative-energy wave is in the fundamental or in the upper harmonic.

Verheest, F.↗
NASA NTRS1990

Radiation from accelerated Alfven solitons in inhomogeneous plasmas

In a weakly inhomogeneous plasma, the large-amplitude Alfven waves propagating parallel to the ambient magnetic field are shown to evolve into accelerated Alfven solitons. Nonlinear interaction of the accelerated Alfven solitons with the Langmuir waves results in the emission of coherent radiations. Analytical expression for the power radiated per unit solid angle from a soliton is derived for two inhomogeneity profiles, namely the linear profile and the parabolic profile. For the case of uniform plasmas, the emission occurs via a decay-type process or resonant modes. In the presence of inhomogeneity, nonresonant modes provide a new channel for the emission of radiation. The power radiated per unit solid angle is computed for the parameters relevant to Comet Halley's plasma environment. For the nonresonant modes it is found to be several orders of magnitude higher than that for the case of resonant modes.

Lakhina, G. S.↗
NASA NTRS1997

The Stability of Radiatively Cooling Jets I. Linear Analysis

The results of a spatial stability analysis of a two-dimensional slab jet, in which optically thin radiative cooling is dynamically important, are presented. We study both magnetized and unmagnetized jets at external Mach numbers of 5 and 20. We model the cooling rate by using two different cooling curves: one appropriate to interstellar gas, and the other to photoionized gas of reduced metallicity. Thus, our results will be applicable to both protostellar (Herbig-Haro) jets and optical jets from active galactic nuclei. We present analytical solutions to the dispersion relations in useful limits and solve the dispersion relations numerically over a broad range of perturbation frequencies. We find that the growth rates and wavelengths of the unstable Kelvin-Helmholtz (K-H) modes are significantly different from the adiabatic limit, and that the form of the cooling function strongly affects the results. In particular, if the cooling curve is a steep function of temperature in the neighborhood of the equilibrium state, then the growth of K-H modes is reduced relative to the adiabatic jet. On the other hand, if the cooling curve is a shallow function of temperature, then the growth of K-H modes can be enhanced relative to the adiabatic jet by the increase in cooling relative to heating in overdense regions. Inclusion of a dynamically important magnetic field does not strongly modify the important differences between an adiabatic jet and a cooling jet, provided the jet is highly supermagnetosonic and not magnetic pressure-dominated. In the latter case, the unstable modes behave more like the transmagnetosonic magnetic pressure-dominated adiabatic limit. We also plot fluid displacement surfaces associated with the various waves in a cooling jet in order to predict the structures that might arise in the nonlinear regime. This analysis predicts that low-frequency surface waves and the lowest order body modes will be the most effective at producing observable features in the jet.

Hardee, Philip E.↗
NASA NTRS1989

Waves in low-beta plasmas - Slow shocks

Results from wave theory and numerical simulation of the nonlinear MHD equations are used to study the response of a conducting fluid containing an embedded magnetic field with beta less than 1 to the sudden injection of material along the field lines. It is shown that the injection produces slow shocks with configurations which are concave toward the ejecta driver. Fast-mode waves which have not steepened into the shock precede the slow shock and alter the ambient medium. When beta equals 0.1, the fast mode becomes a transverse wave for parallel propagation, while the slow wave approaches a longitudinal, or sound, wave.

Steinolfson, R. S.↗
NASA NTRS1993

Controlled experiments in cosmological gravitational clustering

A systematic study is conducted of gravitational instability in 3D on the basis of power-law initial spectra with and without spectral cutoff, emphasizing nonlinear effects and measures of nonlinearity; effects due to short and long waves in the initial conditions are separated. The existence of second-general pancakes is confirmed, and it is noted that while these are inhomogeneous, they generate a visually strong signal of filamentarity. An explicit comparison of smoothed initial conditions with smoothed envelope models also reconfirms the need to smooth over a scale larger than any nonlinearity, in order to extrapolate directly by linear theory from Gaussian initial conditions.

Melott, Adrian L.↗
NASA NTRS1988

On the generation of mean flows by the interaction of Goertler vortices and Tollmien-Schlichting waves in curved channel flows

There are many fluid flows where the onset of transition can be caused by different instability mechanisms which compete in the nonlinear regime. The interaction of a centrifugal instability mechanism with the viscous mechanism which causes Tollmein-Schlichting waves is discussed. The interaction between these modes can be strong enough to drive the mean state; the interaction is investigated in the context of curved channel flows so as to avoid difficulties associated with boundary layer growth. Essentially it was found that the mean state adjusts itself so that any modes present are neutrally stable even at finite amplitude. In the first instance, the mean state driven by a vortex of short wavelength in the absence of Tollmein-Schlichting waves is considered. It is shown that for a given channel curvature and vortex wavelength, there is an upper limit to the mass flow rate which the channel can support as the pressure gradient is increased. When the Tollmein-Schlichting waves are present, then the nonlinear differential equation to determine the mean state is modified.

Bassom, Andrew P.↗
NASA NTRS1975

Wave theory of turbulence in compressible media

An acoustical theory of turbulence was developed to aid in the study of the generation of sound in turbulent flows. The statistical framework adopted is a quantum-like wave dynamical formulation in terms of complex distribution functions. This formulation results in nonlinear diffusion-type transport equations for the probability densities of the five modes of wave propagation: two vorticity modes, one entropy mode, and two acoustic modes. This system of nonlinear equations is closed and complete. The technique of analysis was chosen such that direct applications to practical problems can be obtained with relative ease.

Kentzer, C. P.↗
NASA NTRS1999

Strong Evidence for Stochastic Growth of Langmuir-Like Waves in Earth's Foreshock

Bursty Langmuir-like waves driven by electron beams in Earth's foreshock have properties which are inconsistent with the standard plasma physics paradigm of uniform exponential growth saturated by nonlinear processes. Here it is demonstrated for a specific period that stochastic growth theory (SGT) quantitatively describes these waves throughout a large fraction of the foreshock. The statistical wave properties are inconsistent with nonlinear processes or self-organized criticality being important. SGT's success in explaining the foreshock waves and type III solar bursts suggests that SGT is widely applicable to wave growth in space, astrophysical, and laboratory plasmas.

Cairns, Iver H.↗
NASA NTRS2004

Ring Current Electrodynamic Coupling

In this talk we will address the two primary issues of ring current (RC) electrodynamic coupling: 1. RC self-consistent coupling with electromagnetic ion cyclotron (EMIC) waves (small scale electrodynamic coupling); and 2. RC self-consistent magnetosphere-ionosphere coupling that includes calculation of the magnetospheric electric field (large scale electrodynamic coupling). Our study will be based on two RC models that we have recently developed in our group. The first model by Khazanov et al. [2002, 20031 couples the system of two kinetic equations: one equation which describes the RC ion dynamics and another equation which describes the energy density evolution of EMIC waves. The second model by Khazanov et al. [2003] deals with large scale electrodynamic coupling processes and provides a self-consistent simulation of RC ions, electrons and the magnetospheric electric field. There is presently no model that addresses both of these issues simultaneously in a self-consistent calculation. However, the need exists for such a model, because these two processes directly influence each other, with the mesoscale coupling changing the drift paths of the thermal and energetic particle populations in the inner magnetosphere, thereby changing the wave interactions, and the microscale coupling altering the pitch angle distributions and ionospheric conductivities (through increased precipitation), thus changing the field-aligned currents and electric potential structure. The initial thrust of the work will be the development of a combined kinetic model of micro- and meso-scale RC electrodynamic coupling processes and to examine their interactions with each other on a global scale. We also discuss the nonlinear coupling of EMIC and lower hybrid waves in the RC region during the May 2-7, 1998 storm period.

Khazanov, G. V.↗
NASA NTRS2016

Cluster Observations of Non-Time Continuous Magnetosonic Waves

Equatorial magnetosonic waves are normally observed as temporally continuous sets of emissions lasting from minutes to hours. Recent observations, however, have shown that this is not always the case. Using Cluster data, this study identifies two distinct forms of these non temporally continuous use missions. The first, referred to as rising tone emissions, are characterized by the systematic onset of wave activity at increasing proton gyroharmonic frequencies. Sets of harmonic emissions (emission elements)are observed to occur periodically in the region +/- 10 off the geomagnetic equator. The sweep rate of these emissions maximizes at the geomagnetic equator. In addition, the ellipticity and propagation direction also change systematically as Cluster crosses the geomagnetic equator. It is shown that the observed frequency sweep rate is unlikely to result from the sideband instability related to nonlinear trapping of suprathermal protons in the wave field. The second form of emissions is characterized by the simultaneous onset of activity across a range of harmonic frequencies. These waves are observed at irregular intervals. Their occurrence correlates with changes in the spacecraft potential, a measurement that is used as a proxy for electron density. Thus, these waves appear to be trapped within regions of localized enhancement of the electron density.

Walker, Simon N.↗
NASA NTRS1988

Wave interactions in a three-dimensional attachment line boundary layer

The 3-D boundary layer on a swept wing can support different types of hydrodynamic instability. Attention is focused on the so-called spanwise contamination problem, which occurs when the attachment line boundary layer on the leading edge becomes unstable to Tollmien-Schlichting waves. In order to gain insight into the interactions important in that problem, a simplified basic state is considered. This simplified flow corresponds to the swept attachment line boundary layer on an infinite flat plate. The basic flow here is an exact solution of the Navier-Stokes equations and its stability to 2-D waves propagating along the attachment can be considered exactly at finite Reynolds number. This has been done in the linear and weakly nonlinear regimes. The corresponding problem is studied for oblique waves and their interaction with 2-D waves is investigated. In fact, oblique modes cannot be described exactly at finite Reynolds number so it is necessary to make a high Reynolds number approximation and use triple deck theory. It is shown that there are two types of oblique wave which, if excited, cause the destabilization of the 2-D mode and the breakdown of the disturbed flow at a finite distance from the leading edge. First, a low frequency mode related to the viscous stationary crossflow mode is a possible cause of breakdown. Second, a class of oblique wave with frequency comparable with that of the 2-D mode is another cause of breakdown. It is shown that the relative importance of the modes depends on the distance from the attachment line.

Hall, Philip↗