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Nonlinear analysis of electrostatic drift Kelvin-Helmholtz instability is performed. It is shown that the analysis leads to the propagation of the weakly nonlinear dispersive waves, and the nonlinear behavior is governed by the nonlinear Burger's equation.
Temperature variation is often considered an undesirable factor in ultrasonic testing, as wave velocity is highly sensitive to thermal fluctuations. However, completely eliminating the temperature effect is difficult, particularly in tests requiring precise velocity measurements. Recently, a method called Thermal Modulation of Nonlinear Ultrasonics (TMNL) has been developed. Instead of eliminating the thermal effect, the TMNL method leverages the temperature variation as a driving force to stimulate the nonlinear response of the medium and modulate the ultrasonic waves propagating in it. These modulated waves can then be used to evaluate the nonlinear behaviours of the test medium. This paper presents a focused review of the TMNL technique, including its theoretical foundations, particularly the conceptual challenges in integrating thermal effects into classical acoustoelastic theory, and recent applications in non-destructive evaluation (NDE). Three case studies are presented to demonstrate TMNL’s application in detecting microcracking in concrete, assessing ageing in polymer materials, and enabling temperature compensation in acoustoelastic tests. In conclusion, the review also summarises related studies, including photothermal crack modulation, and discusses current limitations and future directions of TMNL in elastic media.
The solar atmosphere and solar wind are magnetically structured. The structuring can include tangential discontinuities, which can support surface waves. Such waves can be dispersive. This means that dispersion and nonlinearity can balance in such a way that solitary waves (or solitons) can result. This general point is illustrated by a two-dimensional nonlinear analysis which explicitly demonstrates the presence of long-wavelength solitary waves propagating on tangential discontinuities. If the waves are only weakly nonlinear, then they obey the Korteweg-de Vries equation and are true solitons.
Some nonlinear aspects of Alfvenic pulses propagating in coronal loops and the underlying chromosphere are numerically investigated. Heat conduction and radiation are included. The Alfvenic pulses are modeled as axisymmetric twists on a vertical cylindrical flux tube. They nonlinearly couple into acoustic-gravity waves propagating along the flux tube. A single Alfvenic pulse is found to leave two acoustic-gravity pulses in its wake. These pulses can result in significant motions of the transition region and underlying chromosphere. These motions do not resemble spicules, but they may correspond to a variety of observations indicating that the solar atmosphere is in a continual dynamic state. It is suggested that a dynamic chromosphere and transition region may be the inevitable consequence of the coronal heating process itself.
The nonlinear evolution of the magnetohydrodynamic (MHD) parametric instability of wave fluctuations propagating along an unperturbed magnetic field is investigated. Both a magnetohydrodynamic perturbation-theoretical approach and a nonlinear MHD simulation are used. It is shown that high harmonic waves are rapidly excited by wave-wave coupling, and that the wave spectrum evolves from a state containing a small number of degrees of freedom in k space to one which contains a large number of degrees of freedom. It is found that the spectral evolution prior to nonlinear saturation is well described by the prturbation theory. During this stage, the ratio of the growth rate of the nth harmonic wave to the linear growth rate of the fundamental wave is n. The nonlinear saturation stage is characterized by a frequency shift of the fundamental wave that destroys the wave-wave resonance condition which, in turn, causes the wave amplitude to cease its growth.
Projection-based model order reduction allows for the parsimonious representation of full order models (FOMs), typically obtained through the discretization of a set of partial differential equations (PDEs) using conventional techniques (e.g., finite element, finite volume, finite difference methods) where the discretization may contain a very large number of degrees of freedom. As a result of this more compact representation, the resulting projection-based reduced order models (ROMs) can achieve considerable computational speedups, which are especially useful in real-time or multi-query analyses. One known deficiency of projection-based ROMs is that they can suffer from a lack of robustness, stability and accuracy, especially in the predictive regime, which ultimately limits their useful application. Another research gap that has prevented the widespread adoption of ROMs within the modeling and simulation community is the lack of theoretical and algorithmic foundations necessary for the “plug-and-play” integration of these models into existing multi-scale and multi-physics frameworks. This paper describes a new methodology that has the potential to address both of the aforementioned deficiencies by coupling projection-based ROMs with each other as well as with conventional FOMs by means of the Schwarz alternating method [41]. Leveraging recent work that adapted the Schwarz alternating method to enable consistent and concurrent multiscale coupling of finite element FOMs in solid mechanics [35, 36], we present a new extension of the Schwarz framework that enables FOM-ROM and ROM-ROM coupling, following a domain decomposition of the physical geometry on which a PDE is posed. In order to maintain efficiency and achieve computation speed-ups, we employ hyper-reduction via the Energy-Conserving Sampling and Weighting (ECSW) approach [13]. We evaluate the proposed coupling approach in the reproductive as well as in the predictive regime on a canonical test case that involves the dynamic propagation of a traveling wave in a nonlinear hyper-elastic material.
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.
The mean dyadic Green's function for a two-layer random medium with arbitrary three-dimensional correlation functions has been obtained with the zeroth-order solution to the Dyson equation by applying the nonlinear approximation. The propagation of the coherent wave in the random medium is similar to that in an anisotropic medium with different propagation constants for the characteristic transverse electric and transverse magnetic polarizations. In the limit of a laminar structure, two propagation constants for each polarization are found to exist.
Expressions for the density response of neutral atmospheric layers to propagating waves are derived. The expressions include nonlinear effects and are used to compute the response of the mesospheric sodium layer to low-frequency internal gravity waves. The results are compared with lidar observations of the sodium layer and used to deduce gravity wave parameters. It is shown that because of the large sodium density gradients and the relatively high amplitudes of gravity waves at mesospheric heights the nonlinear components of the layer density response must be considered in interpreting sodium lidar data.
The objectives of the Superboom Caustic Analysis and Measurement (SCAMP) Program were to develop and validate, via flight-test measurements, analytical models for sonic boom signatures in and around focal zones as they are expected to occur during commercial aircraft transition from subsonic to supersonic flight, and to apply these models to focus boom prediction of low-boom aircraft designs. The SCAMP program has successfully investigated sonic boom focusing both analytically and experimentally, while gathering a comprehensive empirical flight test and acoustic dataset, and developing a suite of focused sonic boom prediction tools. An experimental flight and acoustic measurement test was designed during the initial year of the SCAMP program, with execution of the SCAMP flight test occurring in May 2011. The current SCAMP team, led by Wyle, includes partners from the Boeing Company, Pennsylvania State University, Gulfstream Aerospace, Eagle Aeronautics, and Central Washington University. Numerous collaborators have also participated by supporting the experiment with human and equipment resources at their own expense. The experiment involved precision flight of a McDonnell Douglas (now Boeing) F-18B executing different maneuvers that created focused sonic booms. The maneuvers were designed to center on the flight regime expected for commercial supersonic aircraft transonic transition, and also span a range of caustic curvatures in order to provide a variety of conditions for code validations. The SCAMP experiment was designed to capture concurrent F-18B on-board flight instrumentation data, high-fidelity ground-based and airborne acoustic data, and surface and upper air meteorological data. Close coordination with NASA Dryden resulted in the development of new experimental instrumentation and techniques to facilitate the SCAMP flight-test execution, including the development of an F-18B Mach rate cockpit display, TG-14 powered glider in-flight sonic boom measurement instrumentation and "Where's the Focus?" (WTF) software for near-real time way-point computation accounting for local atmospherics. In May 2011, 13 F-18B flights were conducted during 5 flying days over a 2 week period. A densely populated 10,000 ft-long ground acoustic array with 125-ft microphone spacing was designed to capture pre-, focus, and post-focus regions. The ground-based acoustic array was placed in a nominally east-west orientation in the remote Cuddeback lakebed region, north of Edwards AFB. This area was carefully selected to avoid placing focused booms on populated areas or solar power facilities. For the SCAMP measurement campaign, approvals were obtained to temporarily extend the Black Mountain supersonic corridor northward by three miles. The SCAMP flight tests successfully captured 70 boom events, with 61 focus passes, and 9 calibration passes. Seventeen of the focus passes and three of the calibration passes were laterally offset; with the others being centerline flights. Airborne incoming sonic boom wave measurements were measured by the TG-14 for 10 of the F-18B flight passes including one maximum focus signature, several N-u combinations, several overlapped N-u signatures, and several evanescent waves. During the 27-month program, the SCAMP team developed a suite of integrated computer codes with sonic boom focusing predictive capabilities: PCBoom, Lossy Nonlinear Tricomi Equation Method (LNTE) and the Nonlinear Progressive wave Equation (NPE) method. PCBoom propagates the rays through the atmosphere and, in addition to legacy focus signature prediction based on the Gill-Seebass method, provides input source characteristics and propagation parameters to LNTE and NPE. LNTE, a Tricomi solver that incorporates atmospheric losses, computes the focus signature at the focus, and computes the focus signature in the vicinity of the focal zone, including the evanescent and post-focus zones. LNTE signature auralization from low-boom vehicle designs has been demonstrated in the NASA Langley Interior Effects Room (IER). The NPE has also been validated for use in prediction of focused ground boom signatures in sonic boom focal zones. The NPE formulation has the capability to incorporate atmospheric turbulence in the predictions. This has been applied to sonic boom propagation in the past. Prediction of turbulence effects on focal zone signatures was not, however, explored during the SCAMP program.
The propagation of orographic gravity waves into an atmosphere with exponentially decreasing density is simulated with a two-dimensional, nonlinear, time-dependent numerical model. After the stationary wave is established over the mountain, the model predicts that wave breaking causes a large reduction of the vertical momentum flux in the flow, not only at levels where wave breaking is present, but also far below the lowest occurrence of overturning. More than half of the decrease in momentum flux is explained by the presence of large amplitude, downward propagating waves, which are generated in regions of wave breaking. The downward propagating waves appear almost simultaneously with overturning, and have nonzero phase speeds, suggesting a strongly nonlinear generation mechanism that depends on local wave properties. The generation of these downward propagating waves is a robust process, insensitive to mountain height, mountain width, or density scale height. These results have important implications for observational studies of orographically generated waves as well as for schemes that seek to parameterize the effects of orogoraphy in large-scale models.
Numerical simulations of the Farley-Buneman instability in 2-1/2 dimensions using particle ions and fluid electrons show the growth, saturation and nonlinear behavior of two-stream waves. This hybrid technique models the saturated state of the instability for a much longer period of time than the pure particle codes that preceded it. While focusing principally on modeling the topside E region equatorial electrojet, many of these results apply to the auroral two-stream instability as well. The following features are seen in all our hybrid simulations: (1) wave growth at an angle offset from the electron drift direction where the angle depends on the strength of the driving electric field, (2) nonlinear coupling to waves traveling perpendicular to the propagation direction of the principal two-stream waves, (3) a saturated wave phase velocity at or above the sound speed but well below the velocity predicted by linear theory and (4) phase velocities which remain almost constant as a simulated radar sweeps from a horizontal direction to nearly vertical. The nonlinear electron motion dominates the behavior of these waves. Further, these simulations indicate that ion kinetic effects are not essential for the saturation of the instability and that electron temperature effects have a minor impact on the final saturated state.
Seismic velocities and elastic moduli of rocks are known to vary significantly with applied stress, which indicates that these materials exhibit nonlinear elasticity. Monochromatic waves in nonlinear elastic media are known to generate higher harmonics and combinational frequencies. Such effects have the potential to be used for broadening the frequency band of seismic sources, characterization of the subsurface, and safety monitoring of civil engineering infrastructure. However, knowledge on nonlinear seismic effects is still scarce, which impedes the development of their practical applications. To explore the potential of nonlinear seismology, we performed three experiments: two in the field and one in the laboratory. The first field experiment used two vibroseis sources generating signals with two different monochromatic frequencies. The second field experiment used a surface orbital vibrator with two eccentric motors working at different frequencies. In both experiments, the generated wavefield was recorded in a borehole using a fiber-optic distributed acoustic sensing cable. Both experiments showed combinational frequencies, harmonics, and other intermodulation products of the fundamental frequencies both on the surface and at depth. Laboratory experiments replicated the setup of the field test with vibroseis sources and showed similar nonlinear combinations of fundamental frequencies. Amplitudes of the nonlinear signals observed in the laboratory showed variation with the saturating fluid. These results confirm that nonlinear components of the wavefield propagate as body waves, are likely to generate within rock formations, and can be potentially used for reservoir fluid characterization.
The most common form of magnetar activity is short X-ray bursts, with durations from milliseconds to seconds, and luminosities ranging from 10 36 –10 43 erg s -1 . Recently, an X-ray burst from the galactic magnetar SGR 1935+2154 was detected to be coincident with two fast radio burst (FRB) like events from the same source, providing evidence that FRBs may be linked to magnetar bursts. Using fully 3D force-free electrodynamics simulations, we show that such magnetar bursts may be produced by Alfvén waves launched from localized magnetar quakes: a wave packet propagates to the outer magnetosphere, becomes nonlinear, and escapes the magnetosphere, forming an ultra-relativistic ejecta. The ejecta pushes open the magnetospheric field lines, creating current sheets behind it. Magnetic reconnection can happen at these current sheets, leading to plasma energization and X-ray emission. The angular size of the ejecta can be compact, ≲1 sr if the quake launching region is small, ≲0.01 sr at the stellar surface. We discuss implications for the FRBs and the coincident X-ray burst from SGR 1935+2154.
Theoretical and experimental studies of space related plasma wave propagation and resonance phenomena cover whistler emissions and instabilities, low frequency plasma instabilities, nonlinear wave interactions and scattering from plasma column, and the resonance come of dipole antenna immersed in cold overdense magnetoplasma.
We present what are to our knowledge first-time calculations from vector nonlinear Maxwell's equations of femtosecond soliton propagation and scattering, including carrier waves, in two-dimensional dielectric waveguides. The time integration efficiently implements linear and nonlinear convolutions for the electric polarization, and the nonlinear convolution accounts for two quantum effects, the Kerr and Raman interactions. By retaining the optical carrier, the new method solves for fundamental quantities - optical electric and magnetic fields in space and time - rather than a nonphysical envelope function. It has the potential to provide an unprecedented two- and three-dimensional modeling capability for millimeter-scale integrated-optical circuits with submicrometer engineered inhomogeneities.
A previous interpretation of strong fluctuations in the intensity of a radio source observed during its occultation by the plasma tail and head of Comet Kohoutek a few days after the latter's perihelion passage is examined to explain the consequence of this interpretation that plasma irregularities moved toward the cometary nucleus with speeds of between 66 and 94 km/sec. It is shown that this reversed velocity may be associated with a nonlinear wave coupled to the turbulent plasma and propagating toward the nucleus with a typical Alfven speed. The reported abrupt cessation of the radio intensity fluctuations at a distance of 80,000 km from the nucleus is shown to be due to a rather abrupt change in the plasma density.
Relevant research projects conducted by faculty and graduate students in the general area of aeroacoustics to further the understanding of noise generation by aircraft and to aid in the development of practical methods for noise suppression are listed. Special activities summarized relate to the nonlinear acoustic wave theory and its application to several cases including that of the acoustic source located at the throat of a near-sonic duct, a computer program developed to compute the nonlinear wave theory, and a parabolic approximation for propagation of sounding in moving stratified media.