Showing papers on "Longitudinal wave published in 2015"

Hybrid waves localized at hyperbolic metasurfaces

Abstract: The authors show theoretically that hyperbolic metasurfaces support simultaneous propagation of both quasi-TE and quasi-TM plasmon surface modes of ``hybrid''' polarization at the same frequency --- a two-dimensional analog of D'yakonov surface waves. The shape of their equal-frequency contours depends drastically on the frequency and changes from elliptical to hyperbolic, and so a topological transition takes place.

Evidence of thermal conduction suppression in a solar flaring loop by coronal seismology of slow-mode waves

Abstract: Analysis of a longitudinal wave event observed by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory is presented. A time sequence of 131 A images reveals that a C-class flare occurred at one footpoint of a large loop and triggered an intensity disturbance (enhancement) propagating along it. The spatial features and temporal evolution suggest that a fundamental standing slow-mode wave could be set up quickly after meeting of two initial disturbances from the opposite footpoints. The oscillations have a period of ~12 minutes and a decay time of ~9 minutes. The measured phase speed of 500 ± 50 km s−1 matches the sound speed in the heated loop of ~10 MK, confirming that the observed waves are of slow mode. We derive the time-dependent temperature and electron density wave signals from six AIA extreme-ultraviolet channels, and find that they are nearly in phase. The measured polytropic index from the temperature and density perturbations is 1.64 ± 0.08 close to the adiabatic index of 5/3 for an ideal monatomic gas. The interpretation based on a 1D linear MHD model suggests that the thermal conductivity is suppressed by at least a factor of 3 in the hot flare loop at 9 MK and above. The viscosity coefficient is determined by coronal seismology from the observed wave when only considering the compressive viscosity dissipation. We find that to interpret the rapid wave damping, the classical compressive viscosity coefficient needs to be enhanced by a factor of 15 as the upper limit.

Laboratory study on the mechanical behaviors of an anisotropic shale rock

Abstract: Shale gas is becoming an important energy source worldwide. The geomechanical properties of shale rocks can have a major impact on the efficiency of shale gas exploration. This paper studied the mineralogical and mechanical characteristics of a typical gas shale in Ohio, USA. Scanning electron microscope (SEM) with energy dispersive X-ray (EDX) analyses was employed to measure the microstructure and material composition of the shale rock. The anisotropic behaviors of shale rock, including compressive and tensile strengths, were experimentally measured. The characteristics of shale rock were also studied by nondestructive wave speed measurements. The shale demonstrated strong anisotropic behaviors with the tensile strengths perpendicular to the bedding plane around 300–360 times of that parallel to bedding plane. Results of ultrasonic tests indicated that both compression and shear wave velocities show strong anisotropic patterns. The compression wave speed was the smallest in the direction perpendicular to the bedding plane; while the shear wave speed was the smallest in the direction parallel to the bedding plane. The ratio of wave speed anisotropy is around 1.3–1.4 for compression wave; the ratio of shear wave speed anisotropy is larger and more diverse compared with the compression wave anisotropy. This might be related to the larger variability in the frictional adhesive strength along bedding plane than the compressive adhesive strength.

Shock wave formation in the collapse of a vapor nanobubble.

Abstract: In this Letter, the dynamics of a collapsing vapor bubble is addressed by means of a diffuse-interface formulation The model cleanly captures, through a unified approach, all the critical features of the process, such as phase change, transition to supercritical conditions, thermal conduction, compressibility effects, and shock wave formation and propagation Rather unexpectedly for pure vapor bubbles, the numerical experiments show that the process consists in the oscillation of the bubble associated with the emission of shock waves in the liquid, and with the periodic disappearance and reappearance of the liquid-vapor interface due to transition to super- or subcritical conditions The results identify the mechanism of shock wave formation as strongly related to the transition of the vapor to the supercritical state, with a progressive steepening of a focused compression wave evolving into a shock which is eventually reflected as an outward propagating wave in the liquid

Nonlocal resonances in weak turbulence of gravity-capillary waves.

Abstract: We report a laboratory investigation of weak turbulence of water surface waves in the gravity-capillary crossover. By using time-space-resolved profilometry and a bicoherence analysis, we observe that the nonlinear processes involve three-wave resonant interactions. By studying the solutions of the resonance conditions, we show that the nonlinear interaction is dominantly one dimensional and involves collinear wave vectors. Furthermore, taking into account the spectral widening due to weak nonlinearity explains why nonlocal interactions are possible between a gravity wave and high-frequency capillary ones. We observe also that nonlinear three-wave coupling is possible among gravity waves, and we raise the question of the relevance of this mechanism for oceanic waves.

2-D arterial wall motion imaging using ultrafast ultrasound and transverse oscillations

Abstract: Ultrafast ultrasound is a promising imaging modality that enabled, inter alia, the development of pulse wave imaging and the local velocity estimation of the so-called pulse wave for a quantitative evaluation of arterial stiffness. However, this technique only focuses on the propagation of the axial displacement of the artery wall, and most techniques are not specific to the intima–media complex and do not take into account the longitudinal motion of this complex. Within this perspective, this paper presents a study of two-dimensional tissue motion estimation in ultrafast imaging combining transverse oscillations, which can improve motion estimation in the transverse direction, i.e., perpendicular to the beam axis, and a phase-based motion estimation. First, the method was validated in simulation. Two-dimensional motion, inspired from a real data set acquired on a human carotid artery, was applied to a numerical phantom to produce a simulation data set. The estimated motion showed axial and lateral mean errors of 4.2 ± 3.4 μm and 9.9 ± 7.9 μm, respectively. Afterward, experimental results were obtained on three artery phantoms with different wall stiffnesses. In this study, the vessel phantoms did not contain a pure longitudinal displacement. The longitudinal displacements were induced by the axial force produced by the wall’s axial dilatation. This paper shows that the approach presented is able to perform 2-D tissue motion estimation very accurately even if the displacement values are very small and even in the lateral direction, making it possible to estimate the pulse wave velocity in both the axial and longitudinal directions. This demonstrates the method’s potential to estimate the velocity of purely longitudinal waves propagating in the longitudinal direction. Finally, the stiffnesses of the three vessel phantom walls investigated were estimated with an average relative error of 2.2%.

Shear-horizontal surface waves in a half-space of piezoelectric semiconductors

Abstract: We study the propagation of shear-horizontal waves near the surface of a piezoelectric semiconductor half-space of crystals of class 6 mm with the presence of a biasing electric field in the propagation direction. The three-dimensional equations of linear piezoelectric semiconductors are used. A transcendental equation that determines the dispersion relation is obtained and solved numerically. Results show that the semiconduction affects the wave speed and causes wave dispersion as well as attenuation, and that the waves can be amplified by the biasing electric field.

Dispersive and diffusive-dispersive shock waves for nonconvex conservation laws

Abstract: We consider two physically and mathematically distinct regularization mechanisms of scalar hyperbolic conservation laws. When the flux is convex, the combination of diffusion and dispersion are known to give rise to monotonic and oscillatory traveling waves that approximate shock waves. The zero-diffusion limits of these traveling waves are dynamically expanding dispersive shock waves (DSWs). A richer set of wave solutions can be found when the flux is non-convex. This review compares the structure of solutions of Riemann problems for a conservation law with non-convex, cubic flux regularized by two different mechanisms: 1) dispersion in the modified Korteweg--de Vries (mKdV) equation; and 2) a combination of diffusion and dispersion in the mKdV-Burgers equation. In the first case, the possible dynamics involve two qualitatively different types of DSWs, rarefaction waves (RWs) and kinks (monotonic fronts). In the second case, in addition to RWs, there are traveling wave solutions approximating both classical (Lax) and non-classical (undercompressive) shock waves. Despite the singular nature of the zero-diffusion limit and rather differing analytical approaches employed in the descriptions of dispersive and diffusive-dispersive regularization, the resulting comparison of the two cases reveals a number of striking parallels. In contrast to the case of convex flux, the mKdVB to mKdV mapping is not one-to-one. The mKdV kink solution is identified as an undercompressive DSW. Other prominent features, such as shock-rarefactions, also find their purely dispersive counterparts involving special contact DSWs, which exhibit features analogous to contact discontinuities. This review describes an important link between two major areas of applied mathematics, hyperbolic conservation laws and nonlinear dispersive waves.

An acoustic metasurface design for wave motion conversion of longitudinal waves to transverse waves using topology optimization

Abstract: This letter presents an acoustic metasurface that converts longitudinal acoustic waves into transverse elastic waves in an acoustic-elastic coupled system. Metasurface configurations are obtained by a level set-based topology optimization method, and we describe the mechanism that changes the direction of the wave motion. Numerical examples of 2D problems with prescribed frequencies of incident acoustic waves are provided, and transverse elastic wave amplitudes are maximized by manipulating the propagation of the acoustic waves. Frequency analysis reveals that each of the different metasurface designs obtained for different wavelengths of incident waves provides peak response at the target frequency.

Bright, dark, and singular solitons in magneto-electro-elastic circular rod

Abstract: In this article, the bright, dark, and singular solitons are being constructed for nonlinear longitudinal wave equation with dispersion caused by transverse Poisson’s effect in a magneto-electro-elastic circular rod. The solitary wave ansatz is used to carry out these solutions. The constraint conditions, for the existence of the soliton solutions, are also listed. This article provides a lot of encouragement for the researchers in this era.

Frequency tunable surface magneto elastic waves

Abstract: We use the transient grating technique to generate narrow-band, widely tunable, in-plane surface magnetoelastic waves in a nickel film. We monitor both the structural deformation of the acoustic wave and the accompanying magnetic precession and witness their intimate coupling in the time domain. Strikingly, when an in plane magnetic field is applied parallel to the acoustic propagation direction, we witness its resonant coupling to the ferromagnetic resonance.

MHD wave propagation from the sub-photosphere to the corona in an arcade-shaped magnetic field with a null point

Abstract: The aim of this work is to study the energy transport by means of MHD waves propagating in quiet Sun magnetic topology from layers below the surface to the corona Upward propagating waves find obstacles, such as the equipartition layer with plasma b=1 and the transition region, and get converted, reflected and refracted Understanding the mechanisms by which MHD waves can reach the corona can give us information about the solar atmosphere and the magnetic structures We carry out two-dimensional numerical simulations of wave propagation in a magnetic field structure that consists of two vertical flux tubes separated by an arcade shaped magnetic field This configuration contains a null point in the corona, that significantly modifies the behaviour of the waves We describe in detail the wave propagation through the atmosphere under different driving conditions We also present the spatial distribution of the mean acoustic and magnetic energy fluxes and the spatial distribution of the dominant frequencies in the whole domain We conclude that the energy reaches the corona preferably along vertical magnetic fields, inside the flux tubes, and it has an acoustic nature Most of the magnetic energy keeps concentrated below the transition region due to the refraction of the magnetic waves and the continuous conversion of acoustic-like waves into fast magnetic waves in the equipartition layer located in the photosphere However, part of the magnetic energy reaches the low corona when propagating in the region where the arcades are located, but waves are sent back downwards to the lower atmosphere at the null point surroundings This phenomenon, together with the reflection and refraction of waves in the TR and the lower turning point, act as a re-feeding of the atmosphere In the frequency distribution, we find that high frequency waves can reach the corona outside the vertical flux tubes

On magnetostrophic inertia-less waves in quasi-geostrophic models of planetary cores

Abstract: We investigate quasi-geostrophic waves in a rotating spherical shell permeated by an imposed magnetic field B¯. A projection of the momentum equation onto a well chosen class of velocity fields results in a quasi-geostrophic reduced model where, in contrast with previous such models, the evolution of the velocity is not prescribed by an equation for the axial vorticity. We consider fields B¯ that may be longitudinally dependent. Increasing the angular rotation frequency, we find that the non-axisymmetric Alfven waves that are present at low rotation morph into inertial waves, torsional Alfven waves and low frequency magnetostrophic waves that satisfy Taylor’s constraint (i.e. vanishing acceleration of the geostrophic cylinders by the magnetic forces).

Nonlinear guided wave propagation in prestressed plates

Abstract: The measurement of stress in a structure presents considerable interest in many fields of engineering. In this paper, the diagnostic potential of nonlinear elastic guided waves in a prestressed plate is investigated. To do so, an analytical model is formulated accounting for different aspects involved in the phenomenon. The fact that the initial strains can be finite is considered using the Green Lagrange strain tensor, and initial and final configurations are not merged, as it would be assumed in the infinitesimal strain theory. Moreover, an appropriate third-order expression of the strain energy of the hyperelastic body is adopted to account for the material nonlinearities. The model obtained enables to investigate both the linearized case, which gives the variation of phase and group velocity as a function of the initial stress, and the nonlinear case, involving second-harmonic generation as a function of the initial state of stress. The analysis is limited to Rayleigh-Lamb waves propagating in a plate. Three cases of initial prestress are considered, including prestress in the direction of the wave propagation, prestress orthogonal to the direction of wave propagation, and plane isotropic stress.

On the application of Wentzel–Kramer–Brillouin theory for the simulation of the weakly nonlinear dynamics of gravity waves

Abstract: The dynamics of internal gravity waves is modelled using Wentzel–Kramer–Brillouin (WKB) theory in position–wave number phase space. A transport equation for the phase-space wave-action density is derived for describing one-dimensional wave fields in a background with height-dependent stratification and height- and time-dependent horizontal-mean horizontal wind, where the mean wind is coupled to the waves through the divergence of the mean vertical flux of horizontal momentum associated with the waves. The phase-space approach bypasses the caustics problem that occurs in WKB ray-tracing models when the wave number becomes a multivalued function of position, such as in the case of a wave packet encountering a reflecting jet or in the presence of a time-dependent background flow. Two numerical models were developed to solve the coupled equations for the wave-action density and horizontal mean wind: an Eulerian model using a finite-volume method and a Lagrangian ‘phase-space ray tracer’ that transports wave-action density along phase-space paths determined by the classical WKB ray equations for position and wave number. The models are used to simulate the upward propagation of a Gaussian wave packet through a variable stratification, a wind jet and the mean flow induced by the waves. Results from the WKB models are in good agreement with simulations using a weakly nonlinear wave-resolving model, as well as with a fully nonlinear large-eddy-simulation model. The work is a step toward more realistic parametrizations of atmospheric gravity waves in weather and climate models.

Variational symplectic particle-in-cell simulation of nonlinear mode conversion from extraordinary waves to Bernstein waves

Abstract: In this paper, the nonlinear mode conversion of extraordinary waves in nonuniform magnetized plasmas is studied using the variational symplectic particle-in-cell simulation. The accuracy of the nonlinear simulation is guaranteed by the long-term accuracy and conservativeness of the symplectic algorithm. The spectra of the electromagnetic wave, the evolution of the wave reflectivity, the energy deposition profile, and the parameter-dependent properties of radio-frequency waves during the nonlinear mode conversion are investigated. It is illustrated that nonlinear effects significantly modify the physics of the radio-frequency injection in magnetized plasmas. The evolutions of the radio-frequency wave reflectivity and the energy deposition are observed, as well as the self-interaction of the Bernstein waves and mode excitations. Even for waves with small magnitude, nonlinear effects can also become important after continuous wave injections, which are common in the realistic radio-frequency wave heating and current drive experiments.

On the existence of steady-state resonant waves in experiments

Abstract: This paper describes an experimental investigation of steady-state resonant waves. Several co-propagating short-crested wave trains are generated in a basin at the State Key Laboratory of Ocean Engineering (SKLOE) in Shanghai, and the wavefields are measured and analysed both along and normal to the direction of propagation. These steady-state resonant waves are first calculated theoretically under the exact resonance criterion with sufficiently high nonlinearity, and then are generated in the basin by means of the main wave components that contain at least 95 % of the wave energy. The steady-state wave spectra are quantitatively observed within the inherent system error of the basin and identified by means of a contrasting experiment. Both symmetrical and anti-symmetrical steady-state resonant waves are observed and the experimental and theoretical results show excellent agreement. These results offer the first experimental evidence of the existence of steady-state resonant waves with multiple solutions.

2D finite element modeling of the non-collinear mixing method for detection and characterization of closed cracks

Abstract: The non-collinear mixing technique is applied for detection and characterization of closed cracks. The method is based on the nonlinear interaction of two shear waves generated with an oblique incidence, which leads to the scattering of a longitudinal wave. A Finite Element model is used to demonstrate its application to a closed crack. Contact acoustic nonlinearity is modeled using unilateral contact law with Coulomb׳s friction. The method is shown to be effective and promising when applied to a closed crack. Scattering of the longitudinal wave also enables us to image the crack, giving its position and size.

The interaction between steep waves and a surface-piercing column

Abstract: Experimental observations are presented of a single surface-piercing column subject to a wide range of surface gravity waves. With the column diameter, D, chosen such that the flow lies within the ...

Nonlinear dynamics of wave-groups in random seas: Unexpected walls of water in the open ocean

Abstract: This paper investigates the size and structure of large waves on the open ocean. We investigate how nonlinear physics modifies waves relative to those predicted by a linear model. We run linear random simulations and extract extreme waves and the surrounding sea-state. For each extreme event, we propagate the waves back in time under linear evolution before propagating the wave-field forward using a nonlinear model. The differences between large linear and nonlinear wave-groups are then examined. The general trends are that under nonlinear evolution, relative to linear evolution, there is, on average, little or no extra amplitude in the nonlinear simulations; that there is an increase in the width of the crest of the wave-group and a contraction of large wave-groups in the mean wave direction; that large waves tend to move to the front of a wave-packet meaning that the locally largest wave is relatively bigger than the wave preceding it; and that nonlinearity can increase the duration of extreme wave events. In all these trends, there is considerable scatter, although the effects observed are clear. Our simulations show that nonlinearity does play an important part in the formation of extreme waves on deep water.

Faraday waves: their dispersion relation, nature of bifurcation and wavenumber selection revisited

Abstract: In the current literature, the dispersion relation of parametrically-forced surface waves is often identified with that of free unforced waves. We revisit here the theoretical description of Faraday waves, showing that forcing and dissipation play a significant role in the dispersion relation, rendering it bi-valued. We then determine the instability thresholds and the wavenumber selection in cases of both short and long waves. We show that the bifurcation can be either supercritical or subcritical, depending on the depth.

Gravity wave propagation through a vertically and horizontally inhomogeneous background wind

Abstract: A combination of ray theory and 2-D time-dependent simulations is used to investigate the linear effects of a time-dependent, vertically, and horizontally inhomogeneous background horizontal wind field on the propagation, refraction, and reflection of small-scale gravity wave packets. Interactions between propagating waves of different scales are likely to be numerous and important. We find that a static medium-scale wave wind field of sufficient amplitude can channel and/or critical-level filter a small-scale wave or cause significant reflection, depending upon both waves' parameters. However, the inclusion of a time-dependent phase progression of the medium-scale wave can reduce energy loss through critical-level filtering by up to ∼70% and can also reduce reflection by up to ∼60% for the cases simulated. We also find that the relative direction of propagation between the small-scale and medium-scale wave can significantly affect small-scale wave filtering. When the phases are progressing in the same horizontal direction, the small-scale wave is far more likely to become trapped and ultimately critical-level filtered than if the phases are propagating in opposite horizontal directions unless reflection occurs first. Considerations of time-dependent winds associated with medium-scale-propagating waves and their directionality are important for assessing the propagation and dispersion of small-scale waves over large horizontal distances.

On the wave propagation in the time differential dual-phase-lag thermoelastic model

Abstract: We study the propagation of plane time harmonic waves in the infinite space filled by a time differential dual-phase-lag thermoelastic material. There are six possible basic waves travelling with distinct speeds, out of which, two are shear waves, and the remaining four are dilatational waves. The shear waves are found to be uncoupled, undamped in time and travels independently with the speed that is unaffected by the thermal effects. All the other possible four dilatational waves are found to be coupled, damped in time and dispersive due to the presence of thermal properties of the material. In fact, there is a damped in time longitudinal quasi-elastic wave whose amplitude decreases exponentially to zero when the time is going to infinity. There is also a quasi-thermal mode, like the classical purely thermal disturbance, which is a standing wave decaying exponentially to zero when the time goes to infinity. Furthermore, there are two possible longitudinal quasi-thermal waves that are damped in time with different decreasing rates or there is one plane harmonic in time longitudinal thermal wave, depending on the values of the time delays. The surface wave problem is studied for a half space filled by a dual-phase-lag thermoelastic material. The surface of the half space is free of traction and it is free to exchange heat with the ambient medium. The dispersion relation is written in an explicit way and the secular equation is established. Numerical computations are performed for a specific model, and the results obtained are depicted graphically.