Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Nonlinear waves”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1970

Lagrangian description of warm plasmas

Efforts are described to extend the averaged Lagrangian method of describing small signal wave propagation and nonlinear wave interaction, developed by earlier workers for cold plasmas, to the more general conditions of warm collisionless plasmas, and to demonstrate particularly the effectiveness of the method in analyzing wave-wave interactions. The theory is developed for both the microscopic description and the hydrodynamic approximation to plasma behavior. First, a microscopic Lagrangian is formulated rigorously, and expanded in terms of perturbations about equilibrium. Two methods are then described for deriving a hydrodynamic Lagrangian. In the first of these, the Lagrangian is obtained by velocity integration of the exact microscopic Lagrangian. In the second, the expanded hydrodynamic Lagrangian is obtained directly from the expanded microscopic Lagrangian. As applications of the microscopic Lagrangian, the small-signal dispersion relations and the coupled mode equations are derived for all possible waves in a warm infinite, weakly inhomogeneous magnetoplasma, and their interactions are examined.

Kim, H.↗
NASA NTRS2000

Winds From Luminous Late-Type Stars: The Effects of Nonlinear Alfven Waves - 1

We present the results of magnetohydrodynamic (MHD) modeling of winds from luminous late-type stars using a 2.5-dimensional, nonlinear MHD computer code. We assume that the wind is generated within an initially hydrostatic atmosphere and is driven by torsional Alfven waves generated at the stellar surface. Two cases of atmospheric topology are considered: case I has longitudinally uniform density distribution and isotropic radial magnetic field over the stellar surface, and case II has an isotropic, radial magnetic field with a transverse density gradient, which we refer to as an "atmospheric hole." We use the same set of boundary conditions for both models. The calculations are designed to model a cool luminous star, for which we assume an initial hydrostatic pressure scale height of 0.072 Stellar Radius, an Alfven wave speed of 92 km/s at the surface, and a wave period of 76 days, which roughly corresponds with the convective turnover time. For case I the calculations produce a wind with terminal velocity of about 22 km/s and a mass loss rate comparable to the expected value of 10(exp -6) Solar Mass/yr. For case II we predict a two-component wind: a fast (25 km/s) and relatively dense wind outside of the atmospheric hole and a slow (1.5 km/s), rarefied wind inside of the hole.

Airapetian, V. S.↗
NASA NTRS1989

Oxygen acoustic solitary waves in a magnetized plasma

Ion-acoustic solitary waves in a magnetized plasma containing an arbitrary mixture of H(+) and O(+) ions are studied. A nonlinear wave equation has been derived from the Poisson-Vlasov equations, including a uniform magnetic field and dissipation due to reflected electrons. When dissipation is ignored, the equation has soliton solutions associated with both oxygen and hydrogen acoustic modes, which can be either rarefactive or compressive depending on the ion concentrations and the electron/ion temperature ratio and, more weakly, on the bulk drifts of the species. If electron reflection is included, the solitary wave can be intensified. Under somewhat restrictive conditions the oxygen solitary wave is rarefactive and propagates with a velocity comparable to that observed by the Viking satellite. The three-dimensional solitons obey a relation of scales parallel to the magnetic field and in the transverse direction. Computer simulations of one-dimensional versions of the nonlinear wave equation are presented.

Qian, S.↗
NASA NTRS1985

Nonlinear astrophysical Alfven waves - Onset and outcome of the modulational instability

The nonlinear development of Alfven waves is numerically studied, with applications to Alfven waves in astrophysical plasmas. It is found that amplitude-modulated Alfven wave packets undergo a collapse instability in which the wave packets become more intense and of smaller spatial extent. The wave packet steepening is eventually halted in a process most aptly described as soliton formation. A simple analytic model based on the method of characteristics can account for many of the results of the numerical calculations. The instability probably cannot prevent particle pitch angle isotropization due to self-generated Alfven waves. Nonlinear effects of the collapse may modify the process by which energetic electrons are reaccelerated by plasma turbulence. The model calculations can semiquantitatively account for properties of shock-associated Alfven waves in the solar system.

Spangler, S. R.↗
NASA NTRS2016

On Holo-Hilbert Spectral Analysis: A Full Informational Spectral Representation for Nonlinear and Non-Stationary Data

The Holo-Hilbert spectral analysis (HHSA) method is introduced to cure the deficiencies of traditional spectral analysis and to give a full informational representation of nonlinear and non-stationary data. It uses a nested empirical mode decomposition and Hilbert-Huang transform (HHT) approach to identify intrinsic amplitude and frequency modulations often present in nonlinear systems. Comparisons are first made with traditional spectrum analysis, which usually achieved its results through convolutional integral transforms based on additive expansions of an a priori determined basis, mostly under linear and stationary assumptions. Thus, for non-stationary processes, the best one could do historically was to use the time- frequency representations, in which the amplitude (or energy density) variation is still represented in terms of time. For nonlinear processes, the data can have both amplitude and frequency modulations (intra-mode and inter-mode) generated by two different mechanisms: linear additive or nonlinear multiplicative processes. As all existing spectral analysis methods are based on additive expansions, either a priori or adaptive, none of them could possibly represent the multiplicative processes. While the earlier adaptive HHT spectral analysis approach could accommodate the intra-wave nonlinearity quite remarkably, it remained that any inter-wave nonlinear multiplicative mechanisms that include cross-scale coupling and phase-lock modulations were left untreated. To resolve the multiplicative processes issue, additional dimensions in the spectrum result are needed to account for the variations in both the amplitude and frequency modulations simultaneously. HHSA accommodates all the processes: additive and multiplicative, intra-mode and inter-mode, stationary and nonstationary, linear and nonlinear interactions. The Holo prefix in HHSA denotes a multiple dimensional representation with both additive and multiplicative capabilities.

Huang, Norden E.↗
NASA NTRS1996

Altimeter Observations of Baroclinic Oceanic Inertia-Gravity Wave Turbulence

For a wide range of nonlinear wave processes - from capillary to planetary waves - theory predicts the existence of Kolmogorov-type spectral cascades of energy and other conserved quantities occuring via nonlinear resonant wave-wave interactions. So far, observations of wave turbulence (WT) have been limited to small-scale processes such as surface gravity and capillary-gravity waves.

wave processees capillary waves planetary waves Ko↗
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 NTRS1977

Landau damping and steepening of interplanetary nonlinear hydromagnetic waves

According to collisionless shock theories, the thickness of a shock front should be of the order of the characteristic lengths of the plasmas (the Debye length, the proton and Larmor radii, etc.). Chao and Lepping (1974), found, however, that 30% of the observed interplanetary shocks at 1 AU have thicknesses much larger than these characteristic lengths. It is the objective of the present paper to investigate whether the competition between nonlinear steepening and Landau damping can result in a wave of finite width that does not steepen into a shock. A heuristic model of such a wave is developed and tested by the examples of two structures that are qualitatively shocklike, but thicker than expected from theory. It is found that both events are in the process of steepening and their limiting thicknesses due to Landau damping are greater than the corresponding proton Larmor radius for both structures as observed at Mariner 5 (nearer the sun than 1 AU) but are comparable to the proton Larmor radius for Explorer (near 1 AU) observations.

Barnes, A.↗
NASA NTRS1980

On self-consistent waves and their stability in warm plasmas. II - Instability of circularly polarized waves both in the presence and the absence of an ambient magnetic field

The stability of a self-consistent, large-amplitude, circularly polarized wave in a warm plasma is investigated. For perturbations to the system propagating normal to the plane of circular polarization, a dispersion relation is derived employing an expansion in the nonlinear wave amplitude and the momentum of the plasma particles in the plane of polarization. Instability results both in the absence and presence of a large-scale magnetic field with a growth rate of the order of the nonlinear wave amplitude.

Lee, M. A.↗
DOE OSTI2021

Collisional broadening of nonlinear resonant wave–particle interactions

A general procedure for understanding plasma behaviour when resonant wave–particle interactions are the sole destabilizing and transport mechanism or only heating and/or current drive source is highlighted without recourse to involved numerical or analytical treatments. These phenomena are characterized by transport that appears to be collisionless even though collisions play a central role in narrow collisional boundary layers. The order of magnitude estimates, which include nonlinear effects, are shown to provide expressions in agreement with the principal results of recent toroidal Alfvén eigenmode (TAE), toroidal magnetic field ripple, and heating and current drive treatments. More importantly, the retention of nonlinearities leads to new estimates of the alpha particle energy diffusivity at saturation for TAE modes, and the ripple threshold at which superbanana plateau evaluations of alpha particle transport are modified by nonlinear radial drift effects. In addition, the estimates indicate when quasilinear descriptions for heating and current drive will begin to fail. The phenomenological procedure demonstrates that in magnetic fusion relevant plasmas, narrow collisional boundary layers must be retained for resonant wave–particle interactions as they enhance the role of collisions, and make stochastic particle motion unlikely to be more important than other nonlinear processes.

Physics↗
DOE OSTI2024

Statistical mechanics and pressure of composite multimoded weakly nonlinear optical systems

Statistical mechanics can provide a versatile theoretical framework for investigating the collective dynamics of weakly nonlinear-wave settings that can be utterly complex to describe otherwise. In optics, composite systems arise due to interactions between different frequencies and polarizations. The purpose of this work is to develop a thermodynamic theory that takes into account the synergistic action of multiple components. We find that the type of the nonlinearity involved can have important implications in the thermalization process and, hence, can lead to different thermal equilibrium conditions. Importantly, we derive closed-form expressions for the actual optomechanical pressure that is exerted on the system. In particular, the total optomechanical pressure is the sum of the partial pressures due to each component. Our results can be applied to a variety of weakly nonlinear optical settings such as multimode fibers, bulk waveguides, photonic lattices, and coupled microresonators. We present two specific examples, where two colors interact in a one-waveguide array with either a cubic or quadratic nonlinearity.

Efremidis, Nikolaos K. (ORCID:0000000298300268)↗
NASA NTRS1982

Computer modeling of multiple-channel input signals and intermodulation losses caused by nonlinear traveling wave tube amplifiers

The multiple channel input signal to a soft limiter amplifier as a traveling wave tube is represented as a finite, linear sum of Gaussian functions in the frequency domain. Linear regression is used to fit the channel shapes to a least squares residual error. Distortions in output signal, namely intermodulation products, are produced by the nonlinear gain characteristic of the amplifier and constitute the principal noise analyzed in this study. The signal to noise ratios are calculated for various input powers from saturation to 10 dB below saturation for two specific distributions of channels. A criterion for the truncation of the series expansion of the nonlinear transfer characteristic is given. It is found that he signal to noise ratios are very sensitive to the coefficients used in this expansion. Improper or incorrect truncation of the series leads to ambiguous results in the signal to noise ratios.

Stankiewicz, N.↗
DOE OSTI2021

Full Vorticity Budget of the Arabian Sea from a 0.1° Ocean Model: Sverdrup Dynamics, Rossby Waves, and Nonlinear Eddy Effects

Abstract The Arabian Sea, influenced by the Indian monsoon, has many unique features, including its basin-scale seasonally reversing surface circulation and the Great Whirl, a seasonal anticyclonic system appearing during the southwest monsoon close to the western boundary. To establish a comprehensive dynamical picture of the Arabian Sea, we utilize numerical model output and design a full vorticity budget that includes a fully decomposed nonlinear term. The ocean general circulation model has 0.1° resolution and is mesoscale eddy-resolving in the region. In the western boundary current system, we highlight the role of nonlinear eddies in the life cycle of the Great Whirl. The nonlinear eddy term is of leading-order importance in this feature’s vorticity balance. Specifically, it contributes to the Great Whirl’s persistence in boreal fall after the weakening of the southwesterly winds. In the open ocean, Sverdrup dynamics and annual Rossby waves are found to dominate the vorticity balance; the latter is considered as a key factor in the formation of the Great Whirl and the seasonal reversal of the western boundary current. In addition, we discuss different forms of vertically integrated vorticity equations in the model and argue that the bottom pressure torque term can be interpreted analogously as friction in the western boundary and vortex stretching in the open ocean.

58 GEOSCIENCES↗
NASA NTRS1995

An assessment of artificial damping models for aeroacoustic calculations

We present a study of the effect of artificial dissipation models on nonlinear wave computations using a few high order schemes. Our motivation is to assess the effectiveness of artificial dissipation models for their suitability for aeroacoustic computations. We solve three model problems in one dimension using the Euler equations. Initial conditions are chosen to generate nonlinear waves in the computational domain. We examine various dissipation models in central difference schemes such as the Dispersion Relation Preserving (DRP) scheme and the standard fourth and sixth order schemes. We also make a similar study with the fourth order MacCormack scheme due to Gottieb and Turkel.

Hayder, M. Ehtesham↗
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 NTRS1991

Critical problems of computational aeroacoustics

The aeroacoustics of rigid boundaries is discussed. Lighthill gave a formulation of this problem in which he showed that the sources of the acoustic field were quadrupole in nature. We have preferred a different formulation of the problem, in which the quadrupoles are sources for a nonlinear wave equation, as opposed to the linear one used by Lighthill. This is given here in a figure which also gives further details of a solution procedure for the Euler equations appropriate for the aeroelastic problem and motivated by the analysis of Crow. In accordance with our formulation, we contend that an algorithm for accurate solutions of an inhomogeneous nonlinear wave equation is of prime importance.

Rogers, Joel C. W.↗
NASA NTRS1995

Nonlinear Landau damping and Alfven wave dissipation

Nonlinear Landau damping has been often suggested to be the cause of the dissipation of Alfven waves in the solar wind as well as the mechanism for ion heating and selective preacceleration in solar flares. We discuss the viability of these processes in light of our theoretical and numerical results. We present one-dimensional hybrid plasma simulations of the nonlinear Landau damping of parallel Alfven waves. In this scenario, two Alfven waves nonresonantly combine to create second-order magnetic field pressure gradients, which then drive density fluctuations, which in turn drive a second-order longitudinal electric field. Under certain conditions, this electric field strongly interacts with the ambient ions via the Landau resonance which leads to a rapid dissipation of the Alfven wave energy. While there is a net flux of energy from the waves to the ions, one of the Alfven waves will grow if both have the same polarization. We compare damping and growth rates from plasma simulations with those predicted by Lee and Volk (1973), and also discuss the evolution of the ambient ion distribution. We then consider this nonlinear interaction in the presence of a spectrum of Alfven waves, and discuss the spectrum's influence on the growth or damping of a single wave. We also discuss the implications for wave dissipation and ion heating in the solar wind.

Vinas, Adolfo F.↗