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.

SourceResearch connectionFrom yearThrough year

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

At least 505 records · Page 28

All sources NASA NTRS DOE OSTI

NASA NTRS1987

Selection principles and pattern formation in fluid mechanics and nonlinear shell theory

Wave theories of vortex breakdown were studied. A setting which involved dynamical systems and bifurcations of homoclinic and heteroclinic orbits in infinite-dimensional spaces was investigated. The determination of axisymmetric inviscid flows bifurcating from the primary flow lead to the study of a system of ordinary differential equations. The problem of rotating plane Couette flow was solved by means of the structure parameter approach.

Sather, Duane P.↗

NASA NTRS2023

Breaking Wave Field Statistics With A Multi-Layer Model

The statistics of breaking wave fields are characterised within a novel multi-layer framework, which generalises the single-layer Saint-Venant system into a multi-layer and non-hydrostatic formulation of the Navier–Stokes equations. We simulate an ensemble of phase-resolved surface wave fields in physical space, where strong nonlinearities, including directional wave breaking and the subsequent highly rotational flow motion, are modelled, without surface overturning. We extract the kinematics of wave breaking by identifying breaking fronts and their speed, for freely evolving wave fields initialised with typical wind wave spectra. The Λ(c) distribution, defined as the length of breaking fronts (per unit area) moving with speed c to c + dc following Phillips (J. Fluid Mech., vol. 156, 1985, pp. 505–531), is reported for a broad range of conditions. We recover the Λ(c) ∝ c−6 scaling without wind forcing for sufficiently steep wave fields. A scaling of Λ(c) based solely on the root-mean-square slope and peak wave phase speed is shown to describe the modelled breaking distributions well. The modelled breaking distributions are in good agreement with field measurements and the proposed scaling can be applied successfully to the observational data sets. The present work paves the way for simulations of the turbulent upper ocean directly coupled to a realistic breaking wave dynamics, including Langmuir turbulence, and other sub-mesoscale processes.

Jiarong Wu↗

NASA NTRS1978

Nonlinear Landau damping in the ionosphere

A model is presented to explain the non-resonant waves which give rise to the diffuse resonance observed near 3/2 f sub H by the Alouette and ISIS topside sounders, where f sub H is the ambient electron cyclotron frequency. In a strictly linear analysis, these instability driven waves will decay due to Landau damping on a time scale much shorter than the observed time duration of the diffuse resonance. Calculations of the nonlinear wave particle coupling coefficients, however, indicate that the diffuse resonance wave can be maintained by the nonlinear Landau damping of the sounder stimulated 2f sub H wave. The time duration of the diffuse resonance is determined by the transit time of the instability generated and nonlinearly maintained diffuse resonance wave from the remote short lived hot region back to the antenna. The model is consistent with the Alouette/ISIS observations, and clearly demonstrates the existence of nonlinear wave-particle interactions in the ionosphere.

Kiwamoto, Y.↗

NASA NTRS1994

Electrotastic Solitary Waves (ESW) in the magnetotail: BEN wave forms observed by GEOTAIL

Wave forms of BEN (Broadband Electrostatic Noise) in the geomagnetic tail were first detected by the Wave Form Capture reciever on the GEOTAIL spacecraft. The results show that most of the BEN in the plasma sheet boundary layer (PSBL) are not continuous broadband noise but are composed of a series of solitary pulses having a special form which we term 'Electrostatic Solitary Waves (ESW)'. A nonlinear BGK potential model is proposed as the generation mechanism for the ESW based upon a simple particle simulation which considers the highly nonlinear evolution of the electron beam instability. The wave forms produced by this simulation are very similar to those observed by GEOTAIL and suggest that the nonlinear dynamics of the electron beam play an essential role in the generation of ESW.

Matsumoto, H.↗

NASA NTRS1989

Nonlinear evolution of high frequency R-mode waves excited by water group ions near comets - Computer experiments

An ion beam resonates with R-mode waves at a high-frequency RH mode and a low-frequency RL mode. The nonlinear evolution of ion beam-generated RH waves is studied here by one-dimensional hybrid computer experiments. Both wave-particle and subsequent wave-wave interactions are examined. The competing process among coexisting RH and RL mode beam instabilities and repeated decay instabilities triggered by the beam-excited RH mode waves is clarified. It is found that the quenching of the RH instability is not caused by a thermal spreading of the ion beam, but by the nonlinear wave-wave coupling process. The growing RH waves become unstable against the decay instability. This instability involves a backward-traveling RH electromagnetic wave and a forward-traveling longitudinal sound wave. The inverse cascading process is found to occur faster than the growth of the RL mode. Wave spectra decaying from the RH waves weaken as time elapses and the RL mode waves become dominant at the end of the computer experiment.

Kojima, H.↗

NASA NTRS1988

The strong nonlinear interaction of Tollmien-Schlichting waves and Taylor-Goertler vortices in curved channel flow

Viscous fluid flows with curved streamlines can support both centrifugal and viscous traveling wave instabilities. Here the interaction of these instabilities in the context of the fully developed flow in a curved channel is discussed. The viscous (Tollmein-Schlichting) instability is described asymptotically at high Reynolds numbers and it is found that it can induce a Taylor-Goertler flow even at extremely small amplitudes. In this interaction, the Tollmein-Schlichting wave can drive a vortex state with wavelength either comparable with the channel width or the wavelength of lower branch viscous modes. The nonlinear equations which describe these interactions are solved for nonlinear equilibrium states.

Bennett, J.↗

NASA NTRSDate not supplied

Observations and 3D MHD Modeling of Small-scale Solar Prominence Oscillations

Small scaleoscillations were recently observed in prominences with high resolution Hinode/SOT and IRIS SJI in unprecedented detailand identified as fast magnetosonic waves. The high-resolution observations provide evidence of flows of cool material, fluid instabilities such as Kelvin-Helmholtz and Rayleigh-Taylor, and the spectroscopic information provides evidence of Doppler shifts, heating, and cooling of the prominence material. Recently nonlinear fast magnetosonic waves were observed withperiods in the range of 5–11 minutes and wavelengths in the plane of the sky (POS) of ~2000kmand flows, and the flows in narrow threads withPOS speed ∼16–46 km/s. Thenonlinear fast magnetosonic waves and flows were modeled using 2.5D MHD (Ofman & Kucera 2020). Here, we extend the studyof the nonlinear fast magnetosonic waves using more realistic 3D MHD model. The model includes the 3D structure of the density and the magnetic fieldas well as mode coupling anddemonstrate the propagating density compressions associated with the nonlinear fast magnetosonicwaves, as well as the guided modesin the pillar. The 3DMHD modelingimprove understanding ofthe POSeffects in limb prominence oscillations observations.The results of the modeling are useful for coronal seismology of the prominence structure.

Leon Ofman↗

NASA NTRS1988

The nonlinear interaction of Tollmien-Schlichting waves and Taylor-Goertler vortices in curved channel flows

The development of Tollmien-Schlichting waves (TSWs) and Taylor-Goertler vortices (TGVs) in fully developed viscous curved-channel flows is investigated analytically, with a focus on their nonlinear interactions. Two types of interactions are identified, depending on the amplitude of the initial disturbances. In the low-amplitude type, two TSWs and one TGV interact, and the scaled amplitudes go to infinity on a finite time scale; in the higher-amplitude type, which can also occur in a straight channel, the same singularity occurs if the angle between the TSW wavefront and the TGV is greater than 41.6 deg, but the breakdown is exponential and takes an infinite time if the angle is smaller. The implications of these findings for external flow problems such as the design of laminar-flow wings are indicated. It is concluded that longitudinal vortices like those observed in the initial stages of the transition to turbulence can be produced unless the present interaction mechanism is destroyed by boundary-layer growth.

Hall, P.↗

NASA NTRS2014

Magnetic Untwisting in Solar Jets that Go into the Outer Corona in Polar Coronal Holes

We present results from 14 exceptionally high‐reaching large solar jets observed in the polar coronal holes. EUV movies from SDO/AIA show that each jet is similar to many other similar‐size and smaller jets that erupt in coronal holes, but each is exceptional in that it goes higher than most other jets, so high that it is observed in the outer corona beyond 2.2 R(sub Sun) in images from the SOHO/LASCO/C2 coronagraph. For these high‐reaching jets, we find: (1) the front of the jet transits the corona below 2.2 R(sub Sun) at a speed typically several times the sound speed; (2) each jet displays an exceptionally large amount of spin as it erupts; (3) in the outer corona, most jets display oscillatory swaying having an amplitude of a few degrees and a period of order 1 hour. We conclude that these jets are magnetically driven, propose that the driver is a magnetic‐untwisting wave that is grossly a large‐amplitude (i.e., nonlinear) torsional Alfven wave that is put into the reconnected open magnetic field in the jet by interchange reconnection as the jet erupts, and estimate from the measured spinning and swaying that the magnetic‐untwisting wave loses most of its energy in the inner corona below 2.2 R(sub Sun). From these results for these big jets, we reason that the torsional magnetic waves observed in Type‐II spicules should dissipate in the corona in the same way and could thereby power much of the coronal heating in coronal holes.

Moore, Ronald L.↗

NASA NTRS1987

The nonlinear interaction of Tollmien-Schlichting waves and Taylor-Goertler vortices in curved channel flows

It is known that a viscous fluid flow with curved streamlines can support both Tollmien-Schlichting and Taylor-Goertler instabilities. In a situation where both modes are possible on the basis of linear theory a nonlinear theory must be used to determine the effect of the interaction of the instabilities. The details of this interaction are of practical importance because of its possible catastrophic effects on mechanisms used for laminar flow control. This interaction is studied in the context of fully developed flows in curved channels. A part form technical differences associated with boundary layer growth the structures of the instabilities in this flow are very similar to those in the practically more important external boundary layer situation. The interaction is shown to have two distinct phases depending on the size of the disturbances. At very low amplitudes two oblique Tollmein-Schlichting waves interact with a Goertler vortex in such a manner that the amplitudes become infinite at a finite time. This type of interaction is described by ordinary differential amplitude equations with quadratic nonlinearities.

Hall, P.↗

NASA NTRS1991

Resonant Triad in Boundary-Layer Stability: Composite Solution and Comparison with Observations - Part 2

Here, numerical results are computed from an asymptotic near-resonance triad analysis. The analysis considers a resonant triad of instability waves consisting of a plane fundamental wave and a pair of symmetrical oblique subharmonic waves. The relevant scaling ensures that nonlinearity is confined to a distinct critical layer. The analysis is first used to form a composite solution that accounts for both the flow divergence and nonlinear effects. It is shown that the backreaction on the plane Tollmien Schlichting (TS) fundamental wave, although fully accounted for, is of little significance. The observed enhancement at the fundamental frequency disturbance is not in the plane TS wave, but is caused by nonlinearly generated waves at the fundamental frequency that result from nonlinear interactions in the critical layer. The saturation of the oblique waves is caused by their self-interaction. The nonlinear phase-locking phenomenon, the location of resonance with respect to the neutral stability curve, low frequency effects, detuning in the streamwise wave numbers, and nonlinear distortion of the mode shapes are discussed. Nonlinearity modifies the initially two dimensional Blasius profile into a fuller one with spanwise periodicity. The interactions at a wide range of unstable spanwise wave numbers are considered, and the existence of a preferred spanwise wave number is explained by means of the vorticity distribution in the critical layer. Besides presenting novel features of the phenomena and explaining the delicate mechanisms of the interactions, the results of the theory are in excellent agreement with experimental and numerical observations for all stages of the development and for various input parameters.

Mankbadi, Reda R.↗

NASA NTRS1996

Generation of Squeezed Light Using Photorefractive Degenerate Two-Wave Mixing

We present a quantum nonlinear model of two-wave mixing in a lossless photorefractive medium. A set of equations describing the quantum nonlinear coupling for the field operators is obtained. It is found that, to the second power term, the commutation relationship is maintained. The expectation values for the photon number concur with those of the classical electromagnetic theory when the initial intensities of the two beams are strong. We also calculate the quantum fluctuations of the two beams initially in the coherent state. With an appropriate choice of phase, quadrature squeezing or number state squeezing can be produced.

Lu, Yajun↗

NASA NTRS1992

Nonlinear elastic effects on the energy flux deviation of ultrasonic waves in gr/ep composites

The effects of nonlinear elasticity on energy flux deviation in undirectional gr/ep composites are examined. The shift in the flux deviation is modeled using acoustoelasticity theory and the second- and third-order elastic stiffness coefficients for T300/5208 gr/ep. Two conditions of applied uniaxial stress are considered. In the first case, the direction of applied uniaxial stress was along the fiber axis (x3), while in the second case it was perpendicular to the fiber axis along the laminate stacking direction (x1). For both conditions, the change in the energy flux deviation angle from the condition of zero applied stress is computed over the range of propagation directions of 0 to 60 deg from the fiber axis at two-degree intervals. A positive flux deviation angle implies the energy deviates away from the fiber direction toward the x1 axis, while a negative deviation means that the energy deviates toward the fibers. Over this range of fiber orientation angles, the energy of the quasi-longitudinal and pure mode transverse waves deviates toward the fibers, while that of the quasi-transverse mode deviates away from the fibers.

Prosser, William H.↗

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↗

NASA NTRS1992

A fully nonlinear, mixed spectral and finite difference model for thermally driven, rotating flows

Finite difference in time and the meridional plane, in conjunction with a spectral technique in the azimuthal direction, are used to approximate the Navier-Stokes equations in a model that can simulate a variety of thermally driven rotating flows in cylindrical and spherical geometries. Axisymmetric flow, linearized waves relative to a fixed or changing axisymmetric flow, nonlinear waves without wave-wave interaction, and fully nonlinear 3D flow, can in this way be calculated. A reexamination is conducted of the steady baroclinic wave case previously treated by Williams (1971) and Quon (1976).

Miller, Timothy L.↗

NASA NTRS1972

Solitary waves in concentrated vortices.

A nonlinear integrodifferential equation governing finite amplitude wave propagation on concentrated vortices is solved numerically. The solution to the Cauchy problem shows a solitary wave development qualitatively similar to solutions of the Korteweg-de Vries equation. A perturbation solution of the stationary form of the evolution equation confirms the unsteady calculation.

Leibovich, S.↗

NASA NTRS1983

A compressible model for the simulation of moist mountain waves

A two-dimensional, nonlinear, nonhydrostatic model is described which allows the calculation of moist airflow in mountainous terrain. The model is compressible, uses a terrain-following coordinate system, and employs lateral and upper boundary conditions which minimize wave reflections. The model's accuracy and sensitivity are examined. These tests suggest that in numerical simulations of vertically propagating, highly nonlinear mountain waves, a wave absorbing layer does not accurately mimic the effects of wave breakdown and dissipation at high levels in the atmosphere. In order to obtain a correct simulation, the region in which the waves are physically absorbed must generally be included in the computational domain (a nonreflective upper boundary condition should be used as well). The utility of the model is demonstrated in two examples (linear waves in a uniform atmosphere and the Jan. 11, 1972 Boulder windstorm) which illustrate how the presence of moisture can influence propagating waves. In both cases, the addition of moisture to the upstream flow greatly reduces the wave response.

Durran, D. R.↗

NASA NTRS1988

Nonlinear 3-D evolution of bounded kinetic Alfven waves due to shear flow and collisionless tearing instability

The three-dimensional nonlinear simulation of the evolution of a kinetic Alfven wave is presented for simple boundary conditions that resemble those of a discrete auroral breakup arc. The model used is a variant of the reduced megnetohydrodynamic description that includes, in addition, the important dispersive effect of electron inertia. It is found that with a 'generator' boundary condition corresponding to a current generator and a fully conducting 'load' boundary, the wave evolves three-dimensionally through a combination of shear flow and collisionless tearing mode instability.

Seyler, Charles E., Jr.↗