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 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Nonlinear evolution of a large-amplitude circularly polarized Alfven wave: High beta

The nonlinear dynamics following saturation of the parametric instabilities of a monochromatic field-aligned large-amplitude circularly polarized Alfven wave is investigated via direct numerical simulation in the case of high plasma beta and no wave dispersion. The magnetohydrodynamic (MHD) code permits nonlinear couplings in the parallel direction to the ambient magnetic field and one perpendicular direction. Compressibility is included in the form of a polytropic equation of state. Turbulent cascades develop after saturation of two coupled oblique three-wave parametric instabilities; one of which is an oblique filamentationlike instability reported earlier. Remnants of the parametric processes, as well as of the original Alfven pump wave, persist during late nonlinear times. Nearly incompressible MHD features such as spectral anisotropies appear as well.

Ghosh, S.↗
NASA NTRS2003

The Effect of Surface Topography on the Nonlinear Dynamics of Rossby Waves

Boussinesq convection in rotating systems attracts a sustained attention of the fluid dynamics community, because it has intricate non-linear dynamics (Cross & Hohenberg 1993) and plays an important role in geophysical and astrophysical applications, such as the motion of the liquid outer core of Earth, the Red Spot in Jupiter, the giant cells in the Sun etc. (Alridge et al. 1990). A fundamental distinction between the real geo- and astrophysical problems and the idealized laboratory studies is that natural systems are inhomogeneous (Alridge et al. 1990). Heterogeneities modulate the flow and influence significantly the dynamics of convective patterns (Alridge et al. 1990; Hide 1971). The effect of modulations on pattern formation and transition to turbulence in Boussinesq convection is far from being completely understood (Cross & Hohenberg 1993; Aranson & Kramer 2002). It is generally accepted that in the liquid outer core of the Earth the transport of the angular momentum and internal heat occurs via thermal Rossby waves (Zhang et al. 2001; Kuang & Bloxham 1999). These waves been visualized in laboratory experiments in rotating liquid-filled spheres and concentric spherical shells (Zhang et al. 2001; Kuang & Bloxham 1999). The basic dynamical features of Rossby waves have been reproduced in a cylindrical annulus, a system much simpler than the spherical ones (Busse & Or 1986; Or & Busse 1987). For convection in a cylindrical annulus, the fluid motion is two-dimensional, and gravity is replaced by a centrifugal force, (Busse & Or 1986; Or & Busse 1987). Hide (1971) has suggested that the momentum and heat transport in the core might be influenced significantly by so-called bumps, which are heterogeneities on the mantle-core boundary. To model the effect of surface topography on the transport of momentum and energy in the liquid outer core of the Earth, Bell & Soward (1996), Herrmann & Busse (1998) and Westerburg & Busse (2001) have studied the nonlinear dynamics of thermal Rossby waves in a cylindrical annulus with azimuthally modulated height.

Abarzhi, S. I.↗
NASA NTRS1991

MHD shocks in coronal mass ejections

The primary objective of this research program is the study of the magnetohydrodynamic (MHD) shocks and nonlinear simple waves produced as a result of the interaction of ejected lower coronal plasma with the ambient corona. The types of shocks and nonlinear simple waves produced for representative coronal conditions and disturbance velocities were determined. The wave system and the interactions between the ejecta and ambient corona were studied using both analytic theory and numerical solutions of the time-dependent, nonlinear MHD equations. Observations from the SMM coronagraph/polarimeter provided both guidance and motivation and are used extensively in evaluating the results. As a natural consequence of the comparisons with the data, the simulations assisted in better understanding the physical interactions in coronal mass ejections (CME's).

Steinolfson, R. S.↗
NASA NTRS1974

Nonlinear acoustic propagation in rectangular ducts

The method of multiple scales is used to obtain a second-order uniformly valid expansion for nonlinear acoustic wave propagation in a rectangular duct whose walls are treated with a nonlinear acoustic material. The wave propagation in the duct is characterized by the unsteady nonlinear Euler equations. The results show that nonlinear materials attenuate sound more than linear materials except at high acoustic frequencies. The nonlinear materials produce higher and combination tones which have higher attenuation rates than the fundamentals. Moreover, the attenuation rates of the fundamentals increase with increasing amplitude.

Nayfeh, A. H.↗
NASA NTRS1981

Plasma lasers (a strong source of coherent radiation in astrophysics)

The generation of electromagnetic radiation from the free energy available in electron streams is discussed. The fundamental principles involved in a particular class of coherent plasma radiation sources, i.e., plasma lasers, are reviewed, focusing on three wave coupling, nonlinear parametric instabilities, and negative energy waves. The simplest case of plasma lasers, that of an unmagnetized plasma containing a finite level of density fluctuations and electrons streaming with respect to the ions, is dealt with. A much more complicated application of plasma lasers to the case of auroral kilometric radiation is then examined. The concept of free electron lasers, including the role of relativistic scattering, is elucidated. Important problems involving the escape of the excited radiation from its generation region, effects due to plasma shielding and nonlinear limits, are brought out.

Papadopoulos, K.↗
NASA NTRS1980

An investigation of wave sheltering by islands

The results of SAR, HF radar, wave rider buoy, and pressure sensor studies of wave behavior around San Clemente Island off the coast of California are reported. The SAR operated at a frequency of 1.2 GHz corresponding to a wavelength of 25 cm at 25 m resolution. Imagery was corrected for the slant range distortion and two-dimensional fast Fourier transforms were used to obtain two-dimensional wave number spectra. A 1 MW source was employed for the HF radar, with a receiving antenna synthesized by mounting the receiver on a van which drove along straight stretches of an oceanside highway. The measurement of 77 m waves displayed a shadow effect after the island, with an unexpected recovery which implies local wave generation. Reflected energy was determined to be too weak to account for the waves, and a nonlinear transfer of wave energy from waves moving parallel to the island was concluded to be the source of the observed inner wave energy.

Hsiao, S. V.↗
NASA NTRS1983

Microscopic Lagrangian description of warm plasmas. IV - Macroscopic approximation

The averaged-Lagrangian method is applied to linear wave propagation and nonlinear three-wave interaction in a warm magnetoplasma, in the macroscopic approximation. The microscopic Lagrangian treated by Kim and Crawford (1977) and by Galloway and Crawford (1977) is first expanded to third order in perturbation. Velocity integration is then carried out, before applying Hamilton's principle to obtain a general description of wave propagation and coupling. The results are specialized to the case of interaction between two electron plasma waves and an Alfven wave. The method is shown to be more powerful than the alternative possibility of working from the beginning with a macroscopic Lagrangian density.

Kim, H.↗
NASA NTRS1989

Group-kinetic theory and modeling of atmospheric turbulence

A group kinetic method is developed for analyzing eddy transport properties and relaxation to equilibrium. The purpose is to derive the spectral structure of turbulence in incompressible and compressible media. Of particular interest are: direct and inverse cascade, boundary layer turbulence, Rossby wave turbulence, two phase turbulence; compressible turbulence, and soliton turbulence. Soliton turbulence can be found in large scale turbulence, turbulence connected with surface gravity waves and nonlinear propagation of acoustical and optical waves. By letting the pressure gradient represent the elementary interaction among fluid elements and by raising the Navier-Stokes equation to higher dimensionality, the master equation was obtained for the description of the microdynamical state of turbulence.

Tchen, C. M.↗
NASA NTRS1988

Nonlinear interaction of near-planar TS waves and longitudinal vortices in boundary-layer transition

The nonlinear interactions that evolve between a planar or nearly planar Tollmien-Schlichting (TS) wave and the associated longitudinal vortices are considered theoretically for a boundary layer at high Reynolds number. The vortex flow is either induced by the TS nonlinear forcing or is input upstream, and similarly for the nonlinear wave development. Three major kinds of nonlinear spatial evolution, Types 1-3, are found. Each can start from secondary instability and then become nonlinear, Type 1 proving to be relatively benign but able to act as a pre-cursor to the Types 2, 3 which turn out to be very powerful nonlinear interactions. Type 2 involves faster stream-wise dependence and leads to a finite-distance blow-up in the amplitudes, which then triggers the full nonlinear 3-D triple-deck response, thus entirely altering the mean-flow profile locally. In contrast, Type 3 involves slower streamwise dependence but a faster spanwise response, with a small TS amplitude thereby causing an enhanced vortex effect which, again, is substantial enough to entirely alter the meanflow profile, on a more global scale. Streak-like formations in which there is localized concentration of streamwise vorticity and/or wave amplitude can appear, and certain of the nonlinear features also suggest by-pass processes for transition and significant changes in the flow structure downstream. The powerful nonlinear 3-D interactions 2, 3 are potentially very relevant to experimental findings in transition.

Smith, F. T.↗
NASA NTRS1986

The wave magnetic field amplitude threshold for nonlinear trapping of energetic gyroresonant and Landau resonant electrons by nonducted VLF waves in the magnetosphere

A recently developed theory is used to calculate the wave magnetic field amplitude threshold, B-tau, necessary to allow the nonlinear trapping of energetic gyroresonant and Landau resonant electrons by VLF whistler mode waves in the magnetosphere propagating at an arbitrary angle, psi, with respect to the earth's magnetic field. A detailed raytracing study is carried out to establish the variation of psi with position along each magnetic shell in the range L = 2-5 and for frequencies 5-17.8 kHz. It is found that the minimum values of B-tau along each L shell generally occur at points of second-order resonance. In general, for nonducted fixed frequency signals there is only one point of second-order resonance on each L shell, and this is located within a few degrees of the magnetic equator. However, over a narrow range of L, there are as many as three points of second-order resonance and as many as three associated minima in B-tau. At least one of these points is located more than 10 deg from the magnetic equator.

Bell, T. F.↗
NASA NTRS1988

Wavenumber selection for single-wave steady states in a nonlinear baroclinic system

The principles involved in the selection of a wavenumber for single-wave steady states are examined numerically and analytically in the framework of an Eady-type model with uneven Ekman dissipation. The process of selection involves the determination of the preferred wavenumber for a given parameter setting in the nonlinear system by testing the stability of steady single-wave states in a triad with wavenumbers n(0) - 1, n(0), and n(0) + 1, where n(0) may change successively in the selection procedure. In a given triad for a given parameter setting, the preferred wave is the wave with the nonlinear Eady angle that is last to vanish.

Weng, H.-Y.↗
NASA NTRS1995

Nonlinear interaction between a pair of oblique modes in a supersonic mixing layer: Long-wave limit

The nonlinear interaction between a pair of symmetric, oblique, and spatial instability modes is studied in the long-wave limit using asymptotic methods. The base flow is taken to be a supersonic mixing layer whose Mach number is such that the corresponding vortex sheet is marginally stable according to Miles' criterion. It is shown that the amplitude of the mode obeys a nonlinear integro-differential equation. Numerical solutions of this equation show that, when the obliqueness angle is less than pi/4, the effect of the nonlinearity is to enhance the growth rate of the instability. The solution terminates in a singularity at a finite streamwise location. This result is reminiscent of that obtained in the vicinity of the neutral point by other authors in several different types of flows. On the other hand, when the obliqueness angle is more than pi/4, the streamwise development of the amplitude is characterized by a series of modulations. This arises from the fact that the nonlinear term in the amplitude equation may be either stabilizing or destabilizing, depending on the value of the streamwise coordinate. However, even in this case the amplitude of the disturbance increases, though not as rapidly as in the case for which the angle is less than pi/4. Quite generally then, the nonlinear interaction between two oblique modes in a supersonic mixing layer enhances the growth of the disturbance.

Balsa, Thomas F.↗
NASA NTRS1993

Strongly nonlinear evolution of low-frequency wave packets in a dispersive plasma

The evolution of strongly nonlinear, strongly modulated wave packets is investigated in a dispersive plasma using a hybrid numerical code. These wave packets have amplitudes exceeding the strength of the external magnetic field, along which they propagate. Alfven (left helicity) wave packets show strong steepening for p < 1, while fast (fight heIicity) wave packets hardly steepen for any beta. Substantial regions of opposite helicity form on the leading side of steepened Alfven wave packets. This behavior differs qualitatively from that exhibited by the solutions to the derivative nonlinear Schrodinger (DNLS) equation.

Vasquez, Bernard J.↗
NASA NTRS1974

Nonlinear acoustic propagation in two-dimensional ducts

The method of multiple scales is used to obtain a second-order uniformly valid expansion for the nonlinear acoustic wave propagation in a two-dimensional duct whose walls are treated with a nonlinear acoustic material. The wave propagation in the duct is characterized by the unsteady nonlinear Euler equations. The results show that nonlinear effects tend to flatten and broaden the absorption versus frequency curve, in qualitative agreement with the experimental observations. Moreover, the effect of the gas nonlinearity increases with increasing sound frequency, whereas the effect of the material nonlinearity decreases with increasing sound frequency.

Nayfeh, A. H.↗
NASA NTRS1983

Observation of wave-wave interactions in the stratosphere

Data from the LIMS instrument for January 1979 are used to provide further evidence for the often observed vacillation between the amplitudes of waves 1 and 2 in the stratosphere. The vacillation is shown to result primarily from nonlinear wave-wave interactions within the stratosphere. Two ways of interpreting nonlinearity are discussed. In the first, the basic state is defined to include large amplitude waves as well as the mean zonal wind. A forced wave propagates with respect to this asymmetric basic state, which can lead to changes in the conventional zonal wavenumber measured at one latitude. The other view of nonlinearity, interaction of wave with the zonal flow and with other wavenumbers are considered separately. Wave-wave interactions among waves 1, 2 and 3 are calculated. The derivation and computation of wave-wave interaction terms in the potential enstrophy balance are given. The observations indicate that enstrophy transfer among waves can be substantial even when the amplitude of one of the contributing waves is small. The computed enstrophy balance also demonstrates that wave-wave interactions can have a large effect on the interaction of waves with the mean flow.

Smith, A. K.↗
NASA NTRS1990

Critical-layer nonlinearity in the resonance growth of three-dimensional waves in boundary layers

The nonlinear interactions of a triad of initially linear stability waves are addressed. The triad consisted of a single two-dimensional mode at a given frequency and two oblique modes with equal and opposite spanwise wave numbers. The oblique waves were at half the frequency and streamwise wave number of the two-dimensional mode. Attention was focused on the boundary-layer transition at low frequencies and high Reynolds numbers. A five-zoned structure and low-frequency scaling were used to derive the nonlinear-interaction equations. The initial nonlinear development of the waves was analyzed; the results indicated that the two-dimensional wave behaves according to linear theory. Nonlinear interactions caused exponential-of-an-exponential growth of the oblique modes. This resonant amplification of the subharmonic depended on the initial amplitude of the two-dimensional wave and on the initial phase angle between the two-dimensional wave and the oblique waves. The resonant growth of the oblique modes was more pronounced at lower frequencies than at higher frequencies. The results are in good agreement with experimental results and offer explanations of the observed process.

Mankbadi, Reda R.↗
NASA NTRS1986

Comparative energetics diagnosis of the observed and simulated blockings in the Northern Hemisphere

The blocking phenomena, in particular winter blocking, are stuided using energetic diagnostics. Sequences of blockings during the FGGE winter and summer in observed and simulated circulations, and energy transformations associated with blockings are examined. It is observed that the simulation of the Northern Hemisphere circulation correlates better with the observed circulation during summer than during winter. It is noted that the observed winter blockings are maintained by the supply of kinetic energy to the ultralong waves from the shorter cyclone scales through nonlinear wave-wave interaction; in the simulated winter blocking, the energy converted at the cyclone scale cascades down to the shorter wave range; and the summer blockings are supported by the baroclinic conversion of long waves in both the observed and simulated circulations.

Kung, Ernest C.↗
NASA NTRS1993

Collisionless parallel shocks

Consideration is given to a collisionless parallel shock based on solitary-type solutions of the modified derivative nonlinear Schroedinger equation (MDNLS) for parallel Alfven waves. The standard derivative nonlinear Schroedinger equation is generalized in order to include the possible anisotropy of the plasma distribution and higher-order Korteweg-de Vies-type dispersion. Stationary solutions of MDNLS are discussed. The anisotropic nature of 'adiabatic' reflections leads to the asymmetric particle distribution in the upstream as well as in the downstream regions of the shock. As a result, nonzero heat flux appears near the front of the shock. It is shown that this causes the stochastic behavior of the nonlinear waves, which can significantly contribute to the shock thermalization.

Khabibrakhmanov, I. KH.↗