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At least 343 records · Page 19

Symmetries of the TDNLS equations for weakly nonlinear dispersive MHD waves

In this paper we consider the symmetries and conservation laws for the TDNLS equations derived by Hada (1993) and Brio, Hunter and Johnson, to describe the propagation of weakly nonlinear dispersive MHD waves in beta approximately 1 plasmas. The equations describe the interaction of the Alfven and magnetoacoustic modes near the triple umbilic, where the fast magnetosonic, slow magnetosonic and Alfven speeds coincide and a(g)(exp 2) = V(A)(exp 2) where a(g) is the gas sound speed and V(A) is the Alfven speed. We discuss Lagrangian and Hamiltonian formulations, and similarity solutions for the equations.

Webb, G. M.↗

On the nonlinear three dimensional instability of Stokes layers and other shear layers to pairs of oblique waves

The nonlinear evolution of a pair of initially oblique waves in a high Reynolds Number Stokes layer is studied. Attention is focused on times when disturbances of amplitude epsilon have O(epsilon(exp 1/3)R) growth rates, where R is the Reynolds number. The development of a pair of oblique waves is then controlled by nonlinear critical-layer effects. Viscous effects are included by studying the distinguished scaling epsilon = O(R(exp -1)). This leads to a complicated modification of the kernel function in the integro-differential amplitude equation. When viscosity is not too large, solutions to the amplitude equation develop a finite-time singularity, indicating that an explosive growth can be introduced by nonlinear effects; we suggest that such explosive growth can lead to the bursts observed in experiments. Increasing the importance of viscosity generally delays the occurrence of the finite-time singularity, and sufficiently large viscosity may lead to the disturbance decaying exponentially. For the special case when the streamwise and spanwise wavenumbers are equal, the solution can evolve into a periodic oscillation. A link between the unsteady critical-layer approach to high-Reynolds-number flow instability, and the wave vortex approach is identified.

Wu, Xuesong↗

Shock wave structure using nonlinear model Boltzmann equations

The structure of a strong plane shock wave in a monatomic rarefied perfect gas is one of the simplest problems able to be posed in kinetic theory, and one of the hardest to solve. Its simplicity lies in the absence of solid boundaries, geometrical complications, or internal molecular energy. Its difficulty arises from the great departure of the gas from equilibrium within the shock, which invalidates many of the techniques used successfully elsewhere in kinetic theory. In addition to this theoretical challenge, the modern development of ballistics and hypersonic flight has helped to stimulate extensive theoretical and experimental interest in the shock problem. The experimenters in turn have encountered great difficulties on account of the very small physical dimensions of shocks. In fact, until very recently indeed, any close comparisons of theoretical and experimental shock structure results have been rather unprofitable due to the inadequacies of both theory and experiment. During the last few years this situation has been appreciably improved by development of the Monte Carlo method. This allows idealized 'experiments' to be performed on large computers instead of in wind tunnels, using a known intermolecular force law. The most developed of these methods has been shown to be equivalent theoretically to the Boltzmann equation and to give results which agree extremely closely with measurements of high accuracy. Thus Monte Carlo results not only form the soundest basis for our present theoretical knowledge of shock wave structure, but, for purposes of developing other theories, can also be considered a very valuable experimental resource. However, such results remain very expensive to obtain. In this thesis we develop more economical kinetic theory methods for the approximate prediction of shock structure, and compare our results with those of the Monte Carlo method.

Segal, Ben Maurice↗

Structure and Dynamics of the Quiet Solar Chromosphere

The grant supported research on the structure of the quiet, nonmagnetic chromosphere and on wave excitation and propagation in both the nonmagnetic chromosphere and the magnetic network. The work on the structure of the chromosphere culminated in the recognition that between two competing views of the solar chromosphere, older models by Avrett and collaborators (referred to as VAL) and the newer, dynamical model by Carlsson & Stein (referred to as CS), the clear decision is in favor of the older models, and this in spite of the evident lack of physics, which does not include wave motion and oscillations. The contrast between the static VAL models and the dynamical CS model can be stated most succinctly by comparing the temperature variation implied by the VAL models and the temperature fluctuations of the CS model, which are, respectively, of the order of 10% for the VAL model (at heights where hydrogen is 50% ionized) and a factor of 10 (at the upper boundary of their chromospheric model). The huge fluctuations of the CS model have never been observed, whereas the smaller temperature variations of the VAL models are consistent with ground-based and space-based observations. While it should be obvious which model describes the Sun and which one fails, the case is far from settled in the minds of solar physicists. Thus, much educational work remains to be done and, of course, more research to develop arguments that make the case more convincing. The research on waves and oscillations has been based on a unified theory of excitation of acoustic waves in the field-free atmosphere and of transverse and longitudinal waves in magnetic flux tubes located in the magnetic network by noting, first, that impulsive excitation of all these waves in gravitationally stratified media leads to oscillations at the respective cutoff frequencies and, second, that the observed oscillation frequencies in the nonmagnetic and magnetic parts of the chromosphere match corresponding cutoff frequencies in the upper solar photosphere. The dynamical simulations by Carlsson and Stein have been most instructive and of fundamental importance for understanding wave propagation in a stratified medium by their "flaws", the most important of which is an intensity excess at the H2v emission peak in the H line of Ca II, which is surprising since the observed intensity should have been an upper limit to the simulated intensity. The only plausible explanation for a predicted intensity that is higher than observed is that energy is spread horizontally in upward propagation in the Sun, but not in the plane-wave modeling of CS (as well as by almost everyone else). Investigations of the horizontal size of the region disturbed by the upward-propagating shock in the acoustic-wave propagation implies that the waves in H2v bright-point oscillations emanate from a point source with a diameter corresponding to the width of an intergranular lane, about 100 km, and reach a size of about 4000 km in the upper layers of the chromosphere. Linear, analytic modeling of waves emanating from a point source in a stratified atmosphere shows that the upward-expanding propagation channel does not have sharp boundaries and that the shape of the wave front depends on the order of the wave behind the initial pulse. Otherwise, the behavior of the linear waves resembles that of the nonlinear shock waves observed in the Sun. Research that needs to be done to firm up the conclusions reached above concerns the numerical simulations of nonlinear waves and oscillations in a three-dimensional stratified atmosphere with impulsive excitation, and observations linking directly the horizontal size of the disturbed area in upward propagation to individual waves.

Kalkofen, Wolfgang↗

Discrete phase changes within nonlinear steepened magnetosonic waves - Comet Giacobini-Zinner

Some features of steepened magnetosonic waves are discussed with reference to the Giacobini-Zinner data set. In particular, attention is given to the discovery of discrete intervals of both phase rotation and lack of phase rotation within a single wavelength and also to the presence of intervals of 'backward' rotations (right-hand polarized in the spacecraft frame) within the magnetosonic wave. Possible explanations of these features are reviewed, and it is suggested that these features are nonlinear manifestations of the wave steepening process.

Tsurutani, Bruce T.↗

Electron acceleration via kinetic Alfven waves

Obliquely propagating shear Alfven waves are effected by kinetic effects. The polarization and dispersion of these waves are discussed and it is shown that electrons can be effectively accelerated along field lines by these waves. Several nonlinear effects such as solitary waves, nonlinear damping due to current-driven instabilities, and anomalous resistivity are also discussed. Recent observations of electric and magnetic field perturbations on auroral field lines which seem to be related to these waves are described. However, the evidence for the existence of these kinetic Alfven waves is not firm.

Goertz, C. K.↗

Frequency-domain computing using nonlinear acoustic-wave device on lithium niobate

Abstract Multiply-accumulation are crucial computing operations in signal processing, numerical simulations, and machine learning. In recent years, optical analog approaches have demonstrated higher computing performance and better power efficiency than their digital counterparts. However, analog computing chips usually need large areas and complex structures for parallel computing, as a single device element only executes one computing operation at a single time. Here, we demonstrate frequency-domain computing using the nonlinear acoustic-wave devices on lithium niobate, featuring a normalized external second-harmonic generation conversion efficiency of ~ 5.7 × 10-4 W-1. The second-order sum-frequency nonlinear process of lithium niobate enables multiplication of inputs encoded in the frequency domain. Compared to the analog schemes, our device features a notably simpler design, and nanofabrication requires only one lift-off. Using a single acoustic-wave device within an area of 0.03 mm2, we can simultaneously conduct over 130,000 multiply-accumulation operations. Our acoustic-wave device shows applications in real and complex vector convolutions and image processing. This demonstration sets the stage for experimental realizations into frequency-domain integrated nonlinear acoustic computing systems, potentially shaping future developments in acoustic neural networks and quantum computing.

chai, mingzhao (ORCID:0009000466226341)↗

Behavior of solitary waves of coupled nonlinear Schrödinger equations subjected to complex external periodic potentials with odd-$\mathcal{PT}$ symmetry

In this work, we discuss the response of both moving and trapped solitary wave solutions of a two-component nonlinear Schrödinger system in 1 + 1 dimensions to an odd-$\mathcal{PT}$ external periodic complex potential. The dynamical behavior of perturbed solitary waves is explored by conducting numerical simulations of the nonlinear system and using a collective coordinate variational approximation. We present case examples corresponding to choices of parameter values and initial conditions involved therein. The results of the collective coordinate approximation are compared against numerical simulations where we observe qualitatively good agreement between the two. Unlike the case for a single-component solitary wave in a complex periodic $\mathcal{PT}$-symmetric potential, the collective coordinate equations do not have a small oscillation regime, and initially the height of the two components changes in opposite directions often causing instability. We find that the dynamic stability criteria we have used in the one-component case are a good indicator for the onset of dynamic instabilities in the present setup.

97 MATHEMATICS AND COMPUTING↗

Nonlinear evolution of longitudinal plasma waves

Long-time nonlinear behavior of single-mode longitudinal plasma waves is studied on the basis of the Vlasov equation with Fokker-Planck collision terms. The resonant layer, trapped island, collisional sublayers, and X-point neighborhoods are analyzed. A nonlinear evolution equation is obtained and the wave-generated current is also evaluated.

Pao, Young-Ping↗

An Efficient Three-Dimensional CFD-Based Numerical Wave Tank for a Wave Energy Converter in Extreme Irregular Waves

A numerical wave tank approach for computational fluid dynamics (CFD) modelling of an extreme irregular seastate is presented. The technique couples a potential flow solution with a CFD solver for more efficient numerical predictions. This method has recently become attractive both for the research community and the industry working with offshore structures. The model is used to determine the response of a submerged pressure differential wave energy converter (WEC) in a fully nonlinear irregular wave condition using the high-fidelity CFD code, STAR-CCM+. Potential flow based numerical models are commonly used to predict motions and performance of wave energy converters. Wave kinematics can deviate from potential flow predictions for extreme wave conditions; the excitation loads on an absorber can also be increasingly influenced by viscous effects, not predicted by potential flow engineering level models. In these extreme conditions, a Reynolds-averaged Navier-Stokes CFD model can better predict motions and loads for a WEC. Long time series with varying random seed numbers can be used to identify singular extreme wave events from a stochastic irregular sea state. This approach simulates a more realistic wave series for a given sea state than a regular wave or a focused wave. However, it is computationally infeasible to run these long time series for three-dimensional (3D) CFD simulations. In this work, two-dimensional (2D) CFD simulations with a long domain allow the full development of an extreme nonlinear wave condition. The results are used to identify extreme events from a 50-year storm condition for the PacWave site off the coast of Oregon. A relatively short time window including this extreme event is then mapped to a 3D simulation using a user defined wave methodology. Convergence studies for domain length, wave forcing lengths, and time before the extreme event were conducted.

CFD↗

An Efficient Three-Dimensional CFD-Based Numerical Wave Tank for a Wave Energy Converter in Extreme Irregular Waves: Preprint

A numerical wave tank approach for computational fluid dynamics (CFD) modelling of an extreme irregular seastate is presented. The technique couples a potential flow solution with a CFD solver for more efficient numerical predictions. This method has recently become attractive both for the research community and the industry working with offshore structures. The model is used to determine the response of a submerged pressure differential wave energy converter (WEC) in a fully nonlinear irregular wave condition using the high fidelity CFD code, STAR-CCM+. Potential flow based numerical models are commonly used to predict motions and performance of wave energy converters. Wave kinematics can deviate from potential flow predictions for extreme wave conditions; the excitation loads on an absorber can also be increasingly influenced by viscous effects, not captured in engineering level models. In these extreme conditions, a Reynolds-averaged Navier-Stokes CFD model can better predict motions and loads for a WEC. Long time series with varying random seed numbers can be used to identify singular extreme wave events from a stochastic irregular sea state. This approach simulates a more realistic wave series for a given sea state than a regular wave or a focused wave. However, it is computationally infeasible to run these long time series for three-dimensional (3D) CFD simulations. In this work, two-dimensional (2D) CFD simulations with a long domain allow the full development of an extreme nonlinear wave condition. The results are used to identify extreme events from a 50-year storm condition for the PacWave site off the coast of Oregon. A relatively short time window including this extreme event is then mapped to a 3D simulation using a user defined wave methodology. Convergence studies for domain length, wave forcing lengths, and time before the extreme event were conducted.

cfd↗

Uncertainty Assessment of CFD Investigation of the Nonlinear Difference-Frequency Wave Loads on a Semisubmersible FOWT Platform

Current mid-fidelity modeling approaches for floating offshore wind turbines (FOWTs) have been found to underpredict the nonlinear, low-frequency wave excitation and the response of semisubmersible FOWTs. To examine the cause of this underprediction, the OC6 project is using computational fluid dynamics (CFD) tools to investigate the wave loads on the OC5-DeepCwind semisubmersible, with a focus on the nonlinear difference-frequency excitation. This paper focuses on assessing the uncertainty of the CFD predictions from simulations of the semisubmersible in a fixed condition under bichromatic wave loading and on establishing confidence in the results for use in improving mid-fidelity models. The uncertainty for the nonlinear wave excitation is found to be acceptable but larger than that for the wave-frequency excitation, with the spatial discretization error being the dominant contributor. Further, unwanted free waves at the difference frequency have been identified in the CFD solution. A wave-splitting and wave load-correction procedure are presented to remove the contamination from the free waves in the results. A preliminary comparison to second-order potential-flow theory shows that the CFD model predicted significantly higher difference-frequency wave excitations, especially in surge, suggesting that the CFD results can be used to better calibrate the mid-fidelity tools.

17 WIND ENERGY↗

Nonlinear evolution of oblique waves on compressible shear layers

The effects of critical-layer nonlinearity on spatially growing oblique instability waves on compressible shear layers between two parallel streams are considered. The analysis shows that mean temperature nonuniformities cause nonlinearity to occur at much smaller amplitudes than it does when the flow is isothermal. The nonlinear instability wave growth rate effects are described by an integrodifferential equation which bears some resemblance to the Landau equation, in that it involves a cubic-type nonlinearity. The numerical solutions to this equation are worked out and discussed in some detail. Inviscid solutions always end in a singularity at a finite downstream distance, but viscosity can eliminate this singularity for certain parameter ranges.

Goldstein, M. E.↗

Collisional broadening of nonlinear resonant wave-particle interactions

A general procedure for understanding plasma behavior 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 principle 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 process.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Evidence of Nonlinear Seismic Effects in the Earth from Downhole Distributed Acoustic Sensors

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.

58 GEOSCIENCES↗