Nonlinear Wave Interactions Research Articles

Experimental monitoring of nonlinear wave interactions in crab orchard sandstone under uniaxial load

Abstract When two waves interact within a rock sample, the interaction strength depends strongly on the sample’s microstructural properties, including the orientation of the sample layering. The study that established this dependence on layering speculated that the differences were caused by cracks aligned with the layers in the sample. To test this, we applied a uniaxial load to similar samples of Crab Orchard Sandstone and measured the nonlinear interaction as a function of the applied load and layer orientation. We show that the dependence of the nonlinear signal changes on applied load is exponential, with a characteristic load of 11.4–12.5 MPa that is independent of sample orientation and probe wavetype (P or S); this value agrees with results from the literature, but does not support the cracks hypothesis.

Convergence, bounded variation properties and Kruzhkov solution of a fully discrete Lagrangian–Eulerian scheme via weak asymptotic analysis for 1D hyperbolic problems

AbstractWe design and implement an effective fully discrete Lagrangian–Eulerian scheme for a class of scalar, local and nonlocal models, and systems of hyperbolic problems in 1D. We propose statements, via a weak asymptotic analysis, which include existence, uniqueness, regularity, and numerical approximations of entropy‐weak solutions computed with the scheme for the corresponding nonlinear initial value problem for the local scalar case. We study both convergence and weak bounded variation (BV) properties of the scheme to the entropy solution (for the local and scalar case) in the sense of Kruzhkov. The approach is based on the improved concept of no‐flow curves, as introduced by the authors, and we highlight the strengths of the method: (i) the scheme for systems of hyperbolic problems does not require computation of the eigenvalues (exact or approximate) either to the numerical flux function or the weak CFL stability condition (wCFL) and (ii) we prove the properties: positivity‐preserving, total variation nonincreasing, and maximum principle subject to the wCFL. We present numerical experiments to evaluate the shock capturing capabilities of the scheme in resolving the main features for hyperbolic problems: shock waves, rarefaction waves, contact discontinuities, positivity‐preserving properties, and nonlinear wave formations and interactions.

An element-based homogenized model for nonlinear wave interaction with 2D distributed microcracks

An element-based homogenized model for nonlinear wave interaction with 2D distributed microcracks

Mixed localized waves and their dynamics for a matrix Lakshmanan–Porsezian–Daniel equation

Interactions between different localized waves are of great significance to physical systems. In this paper, we study the mixed localized waves and their dynamics based on the matrix Lakshmanan–Porsezian–Daniel equation. First, we construct the Nth-order mixed localized solutions describing the interactions between the (N−1) th-order rogue waves and breathers. Using these solutions, we discuss the second- and third-order mixed localized waves, as well as their dynamics. Furthermore, we describe five types of interactions between rogue waves and breathers: between the first-order rogue waves and temporal period breathers, the first-order rogue waves and spatial period breathers, the first-order rogue waves and spatial-temporal period breathers, the second-order rogue waves and temporal period breathers, and the second-order rogue waves and spatial period breathers. These results may be useful for the study of nonlinear wave interactions in physical systems.

Correction to: A 3D Homogenized Model for Nonlinear Wave Interaction with Randomly Distributed Microcracks

Correction to: A 3D Homogenized Model for Nonlinear Wave Interaction with Randomly Distributed Microcracks

Skill assessment of different quadruplet wave-wave interaction formulations in the WAVEWATCH-III model with application to the Gulf of Mexico

In this study, the Gaussian Quadrature Method (GQM) method was implemented in the WAVEWATCH-III model and used along with embedded formulations for estimating the nonlinear wave interactions. The results of DIA, GMD, GQM and WRT methods were compared for ideal test cases. The GQM was in good agreement with the exact WRT method while its medium resolution conjuration was ∼10 times faster than WRT. The GMD was more than 50 times faster than GQM but it could not reproduce WRT results for slanting fetch condition. Two different packages named ST3 and ST6, were employed for calculating the wind input and energy dissipation formulations over the Gulf of Mexico. The high quality ERA5 wind data from August to September in 2017 blended with Holland parametric model were used to run the wave model. The simulation period includes both fair weather condition and extreme events of Hurricanes Harvey and Irma. The performance of wave model using different nonlinear wave interaction terms was assessed against bulk wave parameters measured by in-situ buoys as well as altimeter-derived data by introducing a new error index. The general features of in-situ directional wave spectra were well captured by all DIA, GMD, GQM and WRT methods; however, the spectra produced by GMD and GQM were closer to the results by WRT method. Interestingly, the DIA method with calibrated whitecap dissipation term outperformed other methods in reproducing in-situ data (i.e. wave bulk parameters and wave spectra) during both fair weather and extreme events; indicating overfitting in the white capping or/and wind input terms in the wave model.

Detection of magnetohydrodynamic waves by using convolutional neural networks

Nonlinear wave interactions in magnetohydrodynamics (MHD), such as shock refraction at an inclined density interface, lead to a plethora of wave patterns with numerous wave types. Identification of different types of MHD waves is an important and challenging task in such complex wave patterns. Moreover, owing to the multiplicity of solutions and their admissibility for different systems, especially for intermediate-type MHD shock waves, the identification of MHD wave types is complicated if one relies on the Rankine–Hugoniot jump conditions. MHD wave detection is further exacerbated by nonphysical smearing of discontinuous shock waves in numerical simulations. This paper proposes two MHD wave detection methods based on convolutional neural network to enable wave classification and identify their locations. The first method separates the output into regression (location prediction) and classification problems, assuming the number of waves for each training data is fixed. In contrast, the second method does not specify the number of waves a priori, and the algorithm predicts wave locations and classifies types using only regression. We use one-dimensional input data (density, velocity, and magnetic fields) to train the two models that successfully reproduce a complex two-dimensional MHD shock refraction structure. The first fixed output model efficiently provides high precision and recall, achieving total neural network accuracy up to 99%, and the classification accuracy of some waves approaches unity. The second detection model has relatively low performance, with more sensitivity to the setting of parameters, such as the number of grid cells Ngrid and the thresholds of confidence score and class probability, etc. The detection model achieves better than 90% accuracy with F1 score >0.95. The proposed two methods demonstrate very strong potential for MHD wave detection in complex wave structures and interactions.

A radiometer to diagnose parametric instabilities during linear excitation of electron Bernstein waves in the Mega Amp Spherical Tokamak (MAST) Upgrade.

Highly overdense magnetically confined fusion plasmas, such as the Mega Amp Spherical Tokamak (MAST) Upgrade, cannot easily be heated using conventional electron cyclotron resonance heating because high density cutoffs block microwave access to the plasma core. Instead, electromagnetic waves can be coupled to electron Bernstein waves (EBWs) through the O-X-B mode coupling scheme, and the EBWs can then be absorbed at higher densities. The excitation of EBWs occurs at the upper hybrid (UH) layer where nonlinear wave interactions, called parametric decay instabilities (PDIs), are known to occur at reduced power thresholds. We present a design for a radiometer to detect PDIs during O-X-B in MAST Upgrade. The radiometer will aid in determining at what power levels PDIs become important as well as inferring various parameters about both electrons and ions near the UH layer. We estimate a gyrotron power density threshold for PDI and expected frequency shifts to be produced in them. The design allows for shifts from several decays involving lower hybrid (LH) waves to be observed.

On the Interaction of Azimuthal Modes of Capillary Waves on the Surface of an Elliptical Jet in a Uniform Electrostatic Field

Nonlinear interaction of capillary waves for the first azimuthal modes of an elliptical jet in an electric cross-section field is examined by the product of two independent small parameters. The interaction itself arises due to the ellipticity of the section perpendicular to the jet. Three azimuth modes participate in the interaction: either even or odd ones. When compared with a jet in a radial electrostatic field, the stability of the jet in a perpendicular uniform electrostatic field is reduced. It turned out that the characteristic time for implementing instability decreases with an increase in the initial amplitudes of the interacting modes and with an increase in the intensity of the external electrostatic field, and it also depends on the value of the wave number.

Off-equatorial effects of the nonlinear interaction of VLF chorus waves with radiation belt electrons

Nonlinear processes are involved in both the growth of VLF chorus waves and the energization of radiation belt electrons trapped in the wave potential. Nonlinear theory has led to analytic formulae describing both these processes. To investigate these processes, observations from the Van Allen Probes twin spacecraft provide simultaneous in situ information on VLF chorus waves, radiation belt and injected electrons, and local plasma parameters. We combine the theoretical treatment summarized by Omura (2021) with these in situ observations to investigate the characteristics and effects of nonlinear radiation belt processes at the off-equatorial location of the spacecraft observations. We show the smooth phase transition between initial subpackets of chorus wave elements, conducive to extended trapping and enhancement of resonant electrons. The structure of the chorus wave element changes as it propagates away from the equator. Frequency dispersion due to the variation of parallel wave group velocity with frequency contributes to the chorus waveform frequency sweep rate observed at an off-equatorial location. Nonlinear damping at the local value of ½ fce progressively erodes wave amplitude at frequencies above ½ fceEQ. We examine the important dependencies of the nonlinear inhomogeneity factor on the time rate of change of the wave frequency and the field-aligned gradient of the magnetic field and discuss their implication for the energization of trapped non-relativistic and MeV electrons. The 0.5–2% energy gain we find for 3–6 MeV seed electrons indicates that prompt local acceleration of highly relativistic and ultra-relativistic radiation belt electrons can take place directly through their nonlinear interaction with an individual VLF chorus wave element.

Absolute parametric decay instabilities of X2 microwave beams in reduced models and fully kinetic codes

Nonlinear wave interactions known as parametric decay instabilities (PDIs) have been known to occur in fusion plasmas for many years. In the past, they have generally been considered of little importance in the context of high power microwave beams aimed for X2 heating due to high thresholds. Experimental evidence suggests that non-monotonic density structures, such as islands and ELMs, can lead to low thresholds absolute PDIs. The consequences include degraded electron cyclotron resonance heating performance, absorption into unintended modes and the production of strong scattering, which may damage microwave sensitive equipment. We present a reduced analytical 1D model for absolute PDI of an X-mode microwave beam into a cascade of electrostatic eigenmodes of a non-monotonic density structure. The model is solved numerically and compared with fully kinetic particle-in-cell (PIC) simulations which are computationally much more expensive. The primary decay, which initiates cascade, shows good agreement with the PIC simulations in terms of daughter frequencies, growth rates and saturation, in particular in a weakly nonlinear pump intensity regime. The secondary daughter waves of the reduced model, while visible, do not appear to be the dominant processes in the PIC simulations.

Five-linear singular integral estimates of Brascamp–Lieb-type

We prove the full range of estimates for a five-linear singular integral of Brascamp-Lieb type. The study is methodology-oriented with the goal to develop a sufficiently general technique to estimate singular integral variants of Brascamp-Lieb inequalities that do not obey H\"older scaling. The invented methodology constructs localized analysis on the entire space from local information on its subspaces of lower dimensions and combines such tensor-type arguments with the generic localized analysis. A direct consequence of the boundedness of the five-linear singular integral is a Leibniz rule which captures nonlinear interactions of waves from transversal directions.

The envelope soliton for the nonlinear interaction of Langmuir waves with electron acoustic waves in the Earth's inner magnetosphere

The nonlinear coupling of Langmuir waves with electron-acoustic waves is investigated using the kinetic theory, where the hot electron component is modeled by the kappa distribution with an exponential cutoff at high energy tail, i.e., the cutoff kappa distribution. The one dimensional structure of envelope Langmuir solitons is analyzed by the numerical calculation with parameters typical of the Earth's inner magnetosphere. In the case of hot electrons with a cutoff kappa distribution, envelope Langmuir solitons have larger width and slower speed than that in the case of hot electrons with a Maxwellian distribution. The envelop Langmuir soliton with density depletion obtained in the Earth's inner magnetosphere propagates at a speed lower than the electron-acoustic velocity. At a given amplitude of electrostatic field, the envelope Langmuir soltions have a speed comparable with the ones of electron-acoustic wave solitons, but a wider scale in the case of hot electrons with a cutoff kappa distribution.

A 3D Homogenized Model for Nonlinear Wave Interaction with Randomly Distributed Microcracks

A 3D Homogenized Model for Nonlinear Wave Interaction with Randomly Distributed Microcracks

Parametrically Tunable Mid-Infrared Resonant Radiation by Four-Wave Mixing in Silicon Nitride Nanophotonic Waveguides

The direct generation of mid-infrared light is of significant interest for various applications including spectroscopy, detection system, optical sensing and biophotonics. Ultrashort-pulse nonlinear interaction can be viewed as four-wave mixing process, which can generate new spectral components under appropriate conditions. Here, we numerically demonstrate a fully, yet effective, spectral conversion scheme where the effective portion and components of femtosecond pulses can access the mid-infrared region directly by four-wave mixing process in silicon nitride integrated photonics waveguide. Wideband conversions occur mainly towards the mid-infrared region around the traditional red-shift phase-matching point without the adjustment of waveguide geometry. The corresponding conversion mechanisms can be attributed to nonlinear interaction of optical waves, resulting in the dispersive wave generation, the soliton-probe collision and the phase-sensitive scattering process. Our results provide an alternative route to realize wideband tunable mid-infrared frequency conversion in silicon nitride system on a chip.

Three-dimensional rogue waves and dust-acoustic dark soliton collisions in degenerate ultradense magnetoplasma in the presence of dust pressure anisotropy

A three-dimensional Thomas–Fermi dense anisotropic magnetized plasma having Fermi–Dirac distributed ions and electrons as well as classical fluid negative dust impurities is considered to analyze oblique modulational instability (MI) and head-on collisions among dust-acoustic dark solitons. The Chew–Golberger–Low description is employed to define the anisotropic dust pressure. The linear analysis is investigated. It is found that for larger wavelengths, the pressure anisotropy has a strong effect on the wave frequency. Following the multiscale reductive perturbation technique, a (3 + 1)-dimensional nonlinear Schrödinger equation is derived. Also, the MI criterion is identified, and the regions of (un)stable modulated waves are determined precisely. In addition to that, (un)stable domains of the modulated structures as well as the profile of the dust-acoustic rogue waves are found to be strongly affected by dust grain density, pressure anisotropy, and the strength of the magnetic field. In the stable regions, the face-to-face dark soliton collision and their phase shifts as well as their analytical trajectories are reported by applying the extended Poincare–Lighthill–Kuo method. Numerical analysis reveals that the phase shifts increase with dust concentration but decrease with dust pressure anisotropy. The present results may be applicable in exploring the nonlinear wave dynamics and solitary wave interactions in dense astrophysical plasmas especially to white dwarfs, interiors of the neutron stars, and magnet stars.

Impact of Wavy Wall Surface on Hypersonic Boundary-Layer Instability of Sharp Cone Model

A comprehensive investigation of the impact of wavy wall on hypersonic boundary layers is carried out in a Mach 6 Ludwieg tube based on a 7 deg half-angle sharp cone. Linear stability theory is applied on the cone base flow with both smooth and wavy surfaces first. The evaluation of amplification rate as well as the frequency of instability waves reveals that the second mode instability is suppressed downstream of the wavy wall region. The development of instabilities is then characterized using surface flush-mounted pressure sensors and focused laser differential interferometer (FLDI). The FLDI measurement is conducted within the wavy wall zone both at troughs and at crests. Good agreement is found between the surface pressure measurement and computation, except that instability waves are invisible shortly downstream of the wavy wall. Additionally, bispectral analysis indicates that the nonlinear interaction of instability waves downstream of the wavy wall region is suppressed. FLDI measurement along the streamwise direction shows that the second mode instability waves disappear in the wavy wall region, and the boundary-layer transition process is delayed. Spatial measurement with FLDI of boundary layer identifies various types of disturbance at the troughs and crests; moreover, the co-existence of low-frequency and high-frequency disturbances is observed off the wall surface downstream of the wavy wall.

A Nonlinear Radio-Photon Conversion Device

The article analyzes existing materials and structures with quadratic-nonlinear optical properties that can be used to generate a difference frequency in the terahertz and sub-terahertz frequency ranges. The principle of constructing a nonlinear optical-radio converter, based on an optical focon (a focusing cone), is proposed. Based on the assumption that this focon can be implemented from the metal-organic framework (MOF), we propose a technique for modeling its parameters. The mathematical model of the process of propagation and nonlinear interaction of waves inside the focon is based on a simplification of the nonlinear wave equation. Within the framework of the developed model, the following parameters are approximately determined: the 3D gradient of the linear refractive index and the function determining the geometric profile of the focon, which provide a few-mode-based generation of the difference frequency. The achieved theoretical efficiency of radio frequency generation is at least 1%; the proposed device provides a guiding structure for both optical and radio signals in contrast to the known solutions.

On using nonlinear wave interactions in multi-directional seas for energy conversion on the ocean floor

This paper investigates possible utilization of energy in interacting surface waves on the seafloor. Theory suggests that resonant wave interactions in confused open seas can cause energetic downward traveling second-order pressure waves, which during stormy conditions can be large enough to excite seafloor microseisms (Longuet-Higgins, 1950). Our analysis of contemporaneous data from seafloor pressure and velocity sensors from an Ocean Observatories Initiative (OOI) installation in the Northern Pacific and collocated surface-wave hindcasts showed evidence of the theoretically predicted vertical resonances (Longuet-Higgins, 1950). We observed that area-averaged predicted dynamic pressures and particle velocities 200 m below the water surface and their measured counterparts 2.6 km below at the seafloor were well correlated at the predicted resonance frequencies. Our results further revealed occurrence of net vertical power transfer at resonance from surface to seafloor by means of the predicted double-frequency pressure waves. Motivated by these findings, we estimated year-long seafloor power availability at five selected deep-sea locations. Next, we evaluated upper bounds on potentially convertible area averaged yearly-mean power amounts by a small flexible sphere type device at the seafloor. At ∼400 mW m−2 to ∼15 Wm−2, these power levels could assist sensor operations on and from the deep ocean floor.

On the Nonlinear Interaction of Low-Frequency Kinetic Plasma Waves in the Preflare Atmosphere of the Solar Active Region

On the Nonlinear Interaction of Low-Frequency Kinetic Plasma Waves in the Preflare Atmosphere of the Solar Active Region