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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Group velocity and nonlinear dispersive wave propagation.

By the use of a Hamiltonian formulation, a basic group velocity is defined as the derivative of frequency with respect to wavenumber keeping action density constant, and is shown to represent an incremental action velocity in the general nonlinear case. The stability treatment of Whitham and Lighthill is extended to several dimensions. The water-wave analysis of Whitham (1967) is extended to two space dimensions, and is shown to predict oblique-mode instabilities for kh smaller than 1.36. A treatment of Lighthill's (1965) solution in the one-dimensional elliptic case resolves the problem of the energy distribution in the solution past the critical time.

Hayes, W. D.↗
NASA NTRSDate not supplied

Modelling Sonic Boom Propagation through Planetary Boundary Layer Turbulence near the Lateral Extent of the Carpet

Nonlinear acoustic propagation of sonic booms in the atmospheric boundary layer is considered in the context of a one-way solution to a third order wave equation. A split-step approach is utilized to compute different physical effects efficiently. Unlike previous approaches, the diffraction effects are computed exactly in the forward direction with no restriction on the angle of propagation. This results in more accurate modelling of sonic boom near the carpet edge. Heterogenous flow effects are incorporated with a wide-angle parabolic approximation. Nonlinear propagation is computed with a Burgers-Hayes method. Turbulence in the medium is constructed by the method of random Fourier modes. The turbulence spectra are constructed using an altitude dependent 3-dimensional von Karman spectrum. The turbulence field is considered frozen, as the eddy turnover time in the atmospheric boundary layer is generally much larger than the propagation time of the acoustic wave. Comparisons with benchmark predictions from the PCBoom software are conducted. The benchmark cases provide insight into the accuracy of the current prediction code for non-turbulent atmospheres. Future work is discussed regarding the prediction of shaped booms, boundary conditions, and predictions near the lateral extent of the boom carpet where previous approaches fail to capture the diffraction effects.

sonic boom↗
NASA NTRS1974

Combustion instability with partial length acoustic liners

The development of analytical techniques and numerical methods for the prediction of the stability behavior of liquid propellant rocket combustors is discussed. The studies involved nonlinear wave propagation effects and nonlinear combustion zone, liner, and nozzle responses. A second primary extension of the basic theory was directed at the inclusion of the effects of injector face baffles. Attention was restricted to the linear (small amplitude) problem, finite Mach numbers, three dimensional oscillations, and distributed combustion effects.

Mitchell, C. E.↗
NASA NTRS1985

Nonlinear acoustic wave propagation in atmosphere. Absorbing boundary conditions for exterior problems

Elliptic and hyperbolic problems in unbounded regions are considered. These problems, when one wants to solve them numerically, have the difficulty of prescribing boundary conditions at infinity. Computationally, one needs a finite region in which to solve these problems. The corresponding conditions at infinity imposed on the finite distance boundaries should dictate the boundary conditions at infinity and be accurate with respect to the interior numerical scheme. The treatment of these boundary conditions for wave-like equations is discussed.

Hariharan, S. I.↗
NASA NTRS1979

Nonlinear effects on sound propagation through high subsonic Mach number flows in variable area ducts

A nonlinear theory for sound propagation in variable area ducts carrying a nearly sonic flow is presented. Linear acoustic theory is shown to be singular and the detailed nature of the singularity is used to develop the correct nonlinear theory. The theory is based on a quasi-one dimensional model. It is derived by the method of matched asymptotic expansions. In a nearly chocked flow, the theory indicates the following processes to be acting: a transonic trapping of upstream propagating sound causing an intensification of this sound in the throat region of the duct; generation of superharmonics and an acoustic streaming effect; development of shocks in the acoustic quantities near the throat. Several specific problems are solved analytically and numerical parameter studies are carried out. Results indicate that appreciable acoustic power is shifted to higher harmonics as shocked conditions are approached. The effect of the throat Mach number on the attenuation of upstream propagating sound excited by a fixed source is also determined.

Callegari, A. J.↗
DOE OSTI2024

Space–time structure of weak magnetohydrodynamic turbulence

The two-time energy spectrum of weak magnetohydrodynamic turbulence is found by applying a wave-turbulence closure to the cumulant hierarchy constructed from the dynamical equations. Solutions are facilitated via asymptotic expansions in terms of the small parameter $\varepsilon$ , describing the ratio of time scales corresponding to Alfvénic propagation and nonlinear interactions between counter-propagating Alfvén waves. The strength of nonlinearity at a given spatial scale is further quantified by an integration over all possible delta-correlated modes compliant in a given set of three-wave interactions that are associated with energy flux through the said scale. The wave-turbulence closure for the two-time spectrum uncovers a secularity occurring on a time scale of order $\varepsilon ^{-2}$ , and the asymptotic expansion for the spectrum is reordered in a manner comparable to the one-time case. It is shown that for the regime of stationary turbulence, the two-time energy spectrum exponentially decays on a lagged time scale $(\varepsilon ^2 \gamma _k^s)^{-1}$ in proportion to the strength of the associated three-wave interactions, characterized by nonlinear decorrelation frequency $\gamma _k^s$ . The scaling of the form $k_{\perp } v_0 \chi _0$ exhibited by this frequency is reminiscent of random sweeping by the outer scale with characteristic fluctuation velocity $v_0$ that is modified due to competition with Alfvénic propagation (characterized by $\chi _0$ ) at the said scale. A brief calculation of frequency broadening of the power spectrum due to nonlinear interactions is also presented.

Physics↗
NASA NTRS1995

Particle interactions with obliquely propagating magnetosonic waves

Four cases of nonlinear obliquely propagating magnetosonic (MS) waves are considered using a test particle approach for particles interaction with (1) monochromatic waves propagating both sunward and antisunward, (2) monochromatic waves propagating unidirectionally toward the Sun, (3) a broad band spectrum, propagating both sunward and antisunward, and (4) a broadband spectrum, propagating sunward only. As the solar wind decelerates rapidly inside the bow shock, the interplanetary magnetic field (IMF) increases. Calculations have been performed taking into account such a spatially dependent IMF (based on observations). We find that significant particle acceleration is achieved for both the monochromatic wave and the 'turbulent' MS waves, for oblique propagation (angles between the interplanetary magnetic field and the propagation vector larger than 30 deg). This is due to the fact that at oblique angles resonance width increases. We have compared the relative acceleration of particles for the four cases. Pitch angle scattering and acceleration of particles are found to be much larger in the case of sunward and antisunward propagating waves than those for the sunward waves only. This is due to larger relative phase velocities in the two cases. Also, acceleration of particles is less in the case of a uniform magnetic field than that in the case of spatially increasing magnetic field. The particles get more pitch angle scattered and accelerated in the latter case.

Srivastava, Krishna M.↗
DOE OSTI2020

Generation of few-cycle pulses in media with alternating sign of effective cubic nonlinearity

An original technique is developed for spectral broadening of femtosecond pulses with compensation for the nonlinear spatial phase during the propagation through nonlinear media with effective cubic nonlinearity of different signs. It was shown that in the region of 1.5 μm, the proposed scheme with BBO crystals at the first stage and NaCl at the second stage allows, using chirped mirrors, the formation of few-cycle pulses of about 7 fs duration with a small B-integral. The possibility of focusing of pulses compressed in the proposed scheme with a large Strehl ratio is demonstrated. (paper)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1973

Investigation of scaling characteristics for defining design environments due to transient ground winds and near-field, nonlinear acoustic fields

In order to establish a foundation of scaling laws for the highly nonlinear waves associated with the launch vehicle, the basic knowledge of the relationships among the paramaters pertinent to the energy dissipation process associated with the propagation of nonlinear pressure waves in thermoviscous media is required. The problem of interest is to experimentally investigate the temporal and spacial velocity profiles of fluid flow in a 3-inch open-end pipe of various lengths, produced by the propagation of nonlinear pressure waves for various diaphragm burst pressures of a pressure wave generator. As a result, temporal and spacial characteristics of wave propagation for a parametric set of nonlinear pressure waves in the pipe containing air under atmospheric conditions were determined. Velocity measurements at five sections along the pipes of up to 210 ft. in length were made with hot-film anemometers for five pressure waves produced by a piston. The piston was derived with diaphragm burst pressures at 20, 40, 60, 80 and 100 psi in the driver chamber of the pressure wave generator.

Shih, C. C.↗
NASA NTRS1992

Direct time integration of Maxwell's equations in nonlinear dispersive media for propagation and scattering of femtosecond electromagnetic solitons

The initial results for femtosecond electromagnetic soliton propagation and collision obtained from first principles, i.e., by a direct time integration of Maxwell's equations are reported. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization and can take into account such quantum effects as Kerr and Raman interactions. The present approach is robust and should permit the modeling of 2D and 3D optical soliton propagation, scattering, and switching from the full-vector Maxwell's equations.

Goorjian, Peter M.↗
NASA NTRS1993

Particle Interactions With Obliquely Propagating Magnetosonic Waves: Energization and/or Trapping

Four cases of nonlinear obliquely propagating MS waves are considered using a test particle approach: i) monochromatic waves propagating both sunward and anti-sunward, ii) monochromatic waves propagating unidirectionally towards the Sun, iii) a broad band spectrum, propagating both sunward and anti-sunward, iv) a broad band spectrum, propagating sunward only.

Comets particle scattering Magnetosonic waves↗
DOE OSTI2025

High gas-pressure apparatus for nonlinear X-ray propagation and reshaping via stimulated X-ray Raman scattering

Abstract We describe an experimental setup for non-linear interaction and propagation of ultrashort and intense x-ray free-electron laser (XFEL) pulses in a dense gas. It allows one to provide high, but adjustable, target-gas pressures of up to 6 bar within a vacuum environment of 3∙10 − 3 mbar or better. The setup enables investigation of intense x-ray propagation in an optically thick medium with minimal absorption loss of the unfocused beam outside of the target. As an application, we demonstrate the amplification of spectrally-resolved stimulated x-ray Raman scattering (SXRS) in dense neon gas, where the most intense inner part of the beam is almost completely absorbed. As a result, in the inner part of the beam, the SXRS signal exceeds the residual XFEL pulse by a factor of around two. In principle, this reshaping effect allows for a spatial separation of the two spectral components, i.e., the driving pulse and the SXRS signal.

Magunia, Alexander↗
NASA NTRS1991

Finite difference time domain calculation of transients in antennas with nonlinear loads

In this paper transient fields for antennas with more general geometries are calculated directly using Finite Difference Time Domain methods. In each FDTD cell which contains a nonlinear load, a nonlinear equation is solved at each time step. As a test case the transient current in a long dipole antenna with a nonlinear load excited by a pulsed plane wave is computed using this approach. The results agree well with both calculated and measured results previously published. The approach given here extends the applicability of the FDTD method to problems involving scattering from targets including nonlinear loads and materials, and to coupling between antennas containing nonlinear loads. It may also be extended to propagation through nonlinear materials.

Luebbers, Raymond J.↗
NASA NTRS1991

Finite difference time domain calculation of transients in antennas with nonlinear loads

Determining transient electromagnetic fields in antennas with nonlinear loads is a challenging problem. Typical methods used involve calculating frequency domain parameters at a large number of different frequencies, then applying Fourier transform methods plus nonlinear equation solution techniques. If the antenna is simple enough so that the open circuit time domain voltage can be determined independently of the effects of the nonlinear load on the antennas current, time stepping methods can be applied in a straightforward way. Here, transient fields for antennas with more general geometries are calculated directly using Finite Difference Time Domain (FDTD) methods. In each FDTD cell which contains a nonlinear load, a nonlinear equation is solved at each time step. As a test case, the transient current in a long dipole antenna with a nonlinear load excited by a pulsed plane wave is computed using this approach. The results agree well with both calculated and measured results previously published. The approach given here extends the applicability of the FDTD method to problems involving scattering from targets, including nonlinear loads and materials, and to coupling between antennas containing nonlinear loads. It may also be extended to propagation through nonlinear materials.

Luebbers, Raymond J.↗
NASA NTRS1974

Limit pulses in passive nonlinear absorbers

The propagation of coherent pulses in absorbers with nonlinear refractive index is investigated. It is shown that a term neglected by previous authors places an upper limit on the attainable field strength in steady-state pulses. In ruby with a Cr(3+) doping density of 10 to the 17th power per cu cm, for example, this limit is less than 2,000,000 V/cm.

Lee, C. T.↗
NASA NTRSDate not supplied

Turbulence Effects on Shaped Booms: Finite Impulse Response Filter Development

Numerical simulations of propagation through turbulent atmospheres can quantify effects on ground waveforms, but such simulations are computationally expensive. To enable quick turnaround analyses as required by NASA’s Quesst Mission, updating the N-wave filtering approach developed by researchers at The Pennsylvania State University to include shaped booms is proposed as an alternative method for estimating turbulence effects on acoustic metrics more quickly. Beginning with a nearfield pressure cylinder modeled after the on-design X-59 configuration, a database of propagation results at 45 turbulence conditions was compiled using nonlinear turbulence propagation modeling code (KZKFourier) and used as input to a process for generating finite impulse response (FIR) filters. Ground waveforms distorted by turbulence were selected to represent mean and mean±standard deviation levels for six metrics, and corresponding FIR filters were generated through a matrix deconvolution process. In order to evaluate how well the FIR filters perform, additional KZKFourier verification cases were devised with different input conditions, and results used as a benchmark. Convolution of shaped boom waveforms modeled using nonturbulent propagation simulations with the new FIR filters showed better agreement on average with KZKFourier statistical results than the N-wave-based FIR filters.

turbulence↗
NASA NTRS2019

Efficient method for approximating nonlinear dynamics: applications to uncertainty propagation and estimation

High-order Taylor series expansions can be used to model nonlinear dynamics at the cost of integrating a large set of variational equations to obtain high-order state-transition tensors (STTs). This paper presents an innovative technique for approximating the high-order STTs that reduces significantly the computational cost by retaining only the dominant secular terms. We propagate the low-order partial derivatives of Kepler’s equation, which only requires the integration of six additional equations to extend an n-th order approximation to order (n + 1). The approximation stems from the Lindstedt-Poincare procedure and exploits the stability properties of orbital motion. Since the method makes no dynamical assumptions, it can accommodate any source of orbital perturbations. We show how the approximation of the second-order STT significantly increases the accuracy of the linear method for uncertainty propagation with only a small computational overhead. Finally, we derive a high-order approximate extended Kalman filter that implements the proposed approximation of the STT and improves the performance of linear filters. Examples of application with different perturbation sources include the heliocentric orbit of an asteroid, an orbiter around Europa, and an Earth-orbiting satellite.

Park, Ryan S↗