Showing papers on "Longitudinal wave published in 1999"

Nonlinear gravity and capillary-gravity waves

Abstract: This review deals primarily with the bifurcation, stability, and evolution of gravity and capillary-gravity waves. Recent results on the bifurcation of various types of capillary-gravity waves, including two-dimensional solitary waves at the minimum of the dispersion curve, are reviewed. A survey of various mechanisms (including the most recent ones) to explain the frequency downshift phenomenon is provided. Recent significant results are given on “horseshoe” patterns, which are three-dimensional structures observable on the sea surface under the action of wind or in wave tank experiments. The so-called short-crested waves are then discussed. Finally, the importance of surface tension effects on steep waves is studied.

A solution to diffraction biases in sonoelasticity: The acoustic impulse technique

Abstract: Several methods have been proposed to estimate the viscoelastic properties of soft biological tissues using forced low-frequency vibrations (10-500 Hz). Those methods are based on the measurement of phase velocity of the shear waves (approximately 5 m/s). It is shown in this article that the measurements of velocity as well as attenuation are subjected to biases. These biases are related to reflected waves created at boundaries, to the nonnegligible size of the piston source which causes diffraction effects and to the influence of a low-frequency compressional wave. Indeed, a theoretical analysis of the field radiated by a point source explains how mechanical vibrations of a piston generate a shear wave with a longitudinal component and how this component can interfere with a low-frequency compressional wave. However, by using a low-frequency transient excitation, these biases can be avoided. Then the precise numerical values of elasticity and viscosity can be deduced. Experiments in phantoms and beef muscles are shown. Moreover, a relative hardness imaging of a phantom composed of two media with different elasticities is presented.

Slow Magnetosonic Waves in Coronal Plumes

Abstract: Recent observations of polar plumes in the southern solar coronal hole by the Extreme-Ultraviolet Imaging Telescope (EIT) on board the SOHO spacecraft show signatures of quasi-periodic compressional waves with periods of 10-15 minutes. The relative wave amplitude was found to increase with height in the plumes up to about 1.2 R☉. Using a one-dimensional linear wave equation for the magnetosonic wave, we show that the waves are propagating and that their amplitude increases with height. The observed propagation velocity agrees well with the expected sound velocity inside the plumes. We present the results of the first nonlinear, two-dimensional, magnetohydrodynamic (MHD) simulation of the magnetosonic waves in plumes for typical coronal conditions consistent with observations and gravitationally stratified solar corona. We find numerically that outward-propagating slow magnetosonic waves are trapped, and nonlinearly steepen in the polar plumes. The nonlinear steepening of the magnetosonic waves may contribute significantly to the heating of the lower corona by compressive dissipation.

Solitonlike Electromagnetic Waves behind a Superintense Laser Pulse in a Plasma

Abstract: We present strong evidence, based on 2(1/2)D particle-in-cell simulations of the interaction of ultrashort, high-intensity laser pulses with underdense plasmas, of the formation of long-lived, slowly moving $(0.1c)$, low-frequency solitonlike electromagnetic waves. These nonlinear waves consist of electron-density depressions and intense cylindrical electromagnetic field concentrations with a larger amplitude and a lower frequency than those of the laser pulse.

Two-dimensional reactive flow dynamics in cellular detonation waves

Abstract: This investigation deals with the two-dimensional unsteady detonation characterized by the cellular structure resulting from trajectories of triple-shock configurations formed by the transverse waves and the leading shock front. The time-dependent reactive shock problem considered here is governed by a system of nonlinear hyperbolic conservation laws coupled to a polytropic equation of state and a one-step Arrhenius chemical reaction rate with heat release. The numerical solution obtained allowed us to follow the dynamics of the cellular detonation front involving the triple points, transverse waves and unreacted pockets. The calculations show that the weak tracks observed inside the detonation cells around the points of collision of the triple-shock configurations arise from interactions between the transverse shocks and compression waves generated by the collision. The unreacted pockets of gas formed during the collisions of triple points change form when the activation energy increases. For the self-sustained detonation considered here, the unreacted pockets burn inside the region independent of the downstream rarefaction, and thus the energy released supports the detonation propagation. The length of the region independent of the downstream is approximately the size of one or two detonation cell.

Dynamic Response and Wave Propagation in Plane Trusses and Frames

Abstract: The dynamics of planar frames and trusses is analyzed in terms of the propagation of axial (longitudinal) and flexural (transverse) stress waves being structural members. The waves are multiscattered at the joints, and scattering coefficients representing the reflection and transmission of both types of waves at each joint are derived from the dynamics and compatibility conditions of the joint. The complex multireflected waves within the structure are evaluated in the frequency domain by a newly developed reverberation matrix, which is formulated from scattering coefficients and propagating phase factors. Transient waves are then analyzed by Fourier synthesis and evaluated by a fast Fourier transform algorithm. Transient responses for the axial and bending strains in all structural members are calculated over a long duration for a model truss with rigid joints. Comparison to experimental data of the model truss under a step loading shows good agreement for the early as well as considerably long time responses.

Rayleigh-wave attenuation by a semi-infinite two-dimensional elastic-band-gap crystal

Abstract: In this paper, we report experiments on the scattering of surface-elastic waves by a periodic array of cylindrical holes. The experiments were performed in a marble quarry by drilling cylindrical holes in two different configurations: honeycomb and triangular lattices. The attenuation spectra of the surface waves show the existence of absolute band gaps for elastic waves in these semi-infinite two-dimensional crystals. Results are compared with theoretical calculations based on a scalar-wave approach. The scaling property of the underlying theory has led us to explore the possible application of the results obtained to the attenuation of surface waves in seismic movements. @S0163-1829~99!07419-6#

Rayleigh–Bloch surface waves along periodic gratings and their connection with trapped modes in waveguides

Abstract: Rayleigh–Bloch surface waves are acoustic or electromagnetic waves which propagate parallel to a two-dimensional diffraction grating and which are exponentially damped with distance from the grating. In the water-wave context they describe a localized wave having dominant wavenumber β travelling along an infinite periodic array of identical bottom-mounted cylinders having uniform cross-section throughout the water depth. A numerical method is described which enables the frequencies of the Rayleigh–Bloch waves to be determined as a function of β for an arbitrary cylinder cross-section. For particular symmetric cylinders, it is shown how a special choice of β produces results for the trapped mode frequencies and mode shapes in the vicinity of any (finite) number of cylinders spanning a rectangular waveguide or channel. It is also shown how one particular choice of β gives rise to a new type of trapped mode near an unsymmetric cylinder contained within a parallel-sided waveguide with locally-distorted walls. The implications for large forces due to incident waves on a large but finite number of such cylinders in the ocean is discussed.

Shock waves for a model system of the radiating gas

Abstract: This paper is concerned with the existence and the asymptotic stability of traveling waves for a model system derived from approximating the one-dimensional system of the radiating gas. We show the existence of smooth or discontinuous traveling waves and also prove the uniqueness of these traveling waves under the entropy condition, in the class of piecewise smooth functions with the first kind discontinuities. Furthermore, we show that the C3 -smooth traveling waves areasymptotically stable and that the rate of convergence toward these waves is t-1/4 , which looks optimal. The proof of stability is given by applying the standard energy method to the integrated equation of the original one.

Propagation of Alfvén waves through the ionosphere: Dependence on ionospheric parameters

Abstract: Waves in the 1-Hz frequency band are often seen by both ground observations of magnetic fields and satellite observations of electric and magnetic fields. Comparison between the ground and satellite observations of these waves is complicated by the fact that such waves must pass through the strongly inhomogeneous and collisional ionosphere. While this is true for ULF waves at lower frequencies as well, waves near 1 Hz are more strongly affected since their wavelength is comparable with the scale size of the ionospheric minimum in the Alfven speed; therefore they can be trapped and, in the case of compressional waves, ducted in this region of low Alfven speed. A model is developed to describe the propagation of waves in this frequency range through the ionosphere. A variety of ionospheric models for this propagation have been used to assess the ground signatures of these waves under various conditions. This model is used to study the transient response of the ionosphere to an increase in the field-aligned current. The strength of the ground signal depends strongly on both the Pedersen and Hall conductivities of the ionosphere. Ground signatures are strongest when the Hall conductivity is greater than the Pedersen conductivity. An underdamped signature is seen when the conductivities are high, while an overdamped waveform results for low conductivities. The fundamental mode of the shear mode Alfven resonator is found not to couple to a ducted compressional wave, while higher harmonics of the wave are readily ducted through the ionospheric waveguide.

Modulated Waves: Theory and Applications

Abstract: The authors consider a wide and very important class of waves that are referred to as modulated waves - those characterized by a slow variation of the macroscopic parameters of amplitude, frequency and profile. Most of the fundamentals of wave theory may be understood by considering this class of waves. The authors characterize linear and nonlinear wave propagation in terms of a common approach based on slowly varying parameters (modulations). They expand the concept of modulation to include a wide class of wave processes. After examining the nature of waves and wave dispersion, the authors turn to modulated waves in linear dispersive media and then to modulated waves in nonlinear media. Theoretical analysis is supported by examples from different branches of physics: electrodynamics, fluid mechanics, acoustics and the mechanics of solids.

Excitation of Oscillations in Photospheric Flux Tubes through Buffeting by External Granules

Abstract: We examine the excitation of transverse (kink) and longitudinal (sausage) waves in magnetic flux tubes by granules in the solar photosphere The investigation is motivated by the interpretation of network oscillations in terms of flux tube waves We model the interaction between a granule, with a specified transverse velocity, and a vertical flux tube in terms of the Klein-Gordon equation, which we solve analytically as an initial value problem for both wave modes, assuming the same external impulse The calculations show that for magnetic field strengths typical of the network, the energy flux in transverse waves is higher than in longitudinal waves by an order of magnitude, in agreement with the chromospheric power spectrum of network oscillations observed by Lites, Rutten, & Kalkofen But for weaker fields, such as those that might be found in internetwork regions, the energy fluxes in the two modes are comparable This result implies that if there are internetwork oscillations in magnetic flux tubes, they must show the cutoff periods of both longitudinal and transverse modes at 3 minutes and at 7 minutes or longer We also find that granules with speeds of about 2 km s-1 can efficiently excite transverse oscillations in frequent short-duration (typically 1 minute) bursts that can heat the corona

An introduction to the mathematical theory of waves

Abstract: Introduction: Introduction to waves A mathematical representation of waves Partial differential equation Traveling and standing waves: Traveling waves The Korteweg-de Vries equation The Sine-Gordon equation The wave equation D'Alembert's solution of the wave equation Vibrations of a semi-infinite string Characteristic lines of the wave equation Standing wave solutions of the wave equation Standing waves of a nonhomogeneous string Superposition of standing waves Fourier series and the wave equation Waves in conservation laws: Conservation laws Examples of conservation laws The method of characteristics Gradient catastrophes and breaking times Shock waves Shock wave example: Traffic at a red light Shock waves and the viscosity method Rarefaction waves An example with rarefaction and shock waves Nonunique solutions and the entropy condition Weak solutions of conservation laws Bibliography Index.

Closed-form integration of singular terms for constant, linear and quadratic boundary elements. Part 2. SV-P wave propagation

Abstract: One of the most important aspects in the application of boundary element techniques to wave propagation problems is the accurate representation of the singular terms at the points of application of the virtual loads. It is current practice to carry out this task by means of numerical quadrature. This paper presents an analytical evaluation of the singular integrals for constant, linear and quadratic boundary elements involving SH waves, the results of which are then used to model inclusions in a two-dimensional acoustic medium illuminated by dynamic anti-plane line sources. Finally, the BEM results are compared with the known analytical solutions for cylindrical inclusions.

Laser-Doppler-based acoustic-to-seismic detection of buried mines

Abstract: Airborne acoustic waves coupled into the surface of the ground excite Biot Type I and II compressional and shear waves. This coupling of airborne sound into the ground is termed acoustic-to-seismic coupling. If a land mine or other inhomogeneity is presented below the surface, the ground surface vibrational velocity or S/A ratio will increase due to reflection and scattering of the Type II compressional wave. The dispersion characteristics of this wave in solids determines the mine detection limits. The S/A ratio is read with a laser doppler vibrometer (LDV). The loud speaker and LDV were mounted onto a large forklift at Fort AP Hill. This system was used to scan patches of ground at the Fort AP Hill calibration mine lanes. An investigation on the variability of surface velocity over different background types and mine types is described. The results of these initial field exercises are described.

Formation of pressure‐balanced structures and fast waves from nonlinear Alfvén waves

Abstract: In the solar wind, Alfvenic fluctuations are typically observed in association with small fluctuations of the density (ρ) and magnetic field strength (B), which tend to be anticorrelated and in approximate pressure balance. One would not expect any finite δρ and δB among pure Alfven waves propagating strictly outward from the Sun. Our paper shows how Alfven waves can nonlinearly produce structures in pressure balance. We present a second-order analysis of the pure magnetohydrodynamic equations and hybrid simulations which show that nonlinear Alfven waves traveling in different directions but with equal group velocity can generate pressure-balanced structures with wave vectors perpendicular to the background magnetic field B 0 . Homogeneous fast waves are also generated in this direction in order to satisfy initial conditions. They cannot be Landau or transit-time damped and so cause the values of B and ρ to vary with time as they beat with the pressure-balanced structures. However, we find δρδB < 0 is satisfied most of the time, and this can partly explain the tendency for anticorrelation observed in the solar wind. In directions away from the perpendicular one, Alfven waves produce driven fast waves which give constant B and ρ to second order. Homogeneous fast and slow waves are also produced in these directions but Landau damp away in large β plasmas. Thus an equilibrium or steady propagating waveform at second order can be produced where B and ρ vary only in the perpendicular direction. If transverse magnetic structures with wave vectors perpendicular to B 0 are included at the same order as the initial Alfven waves, then these evolve to pressure-balanced structures and can also coexist with the Alfven waves. However, an equilibrium is obtained generally only when these structures also have velocity fluctuations equivalent of those of the Alfven waves.

Bound waves and bragg scattering in a wind-wave tank

Abstract: We present optical and microwave measurements that show the presence of bound waves traveling at the speed of the dominant wave in a wind-wave tank. We suggest that when these bound waves are much shorter than the dominant waves, they are preferentially located on the leeward face of the dominant wave and hence have a mean tilt. We hypothesize that the turbulence associated with these bound waves suppresses freely propagating, wind-generated waves where bound waves are present so that we may divide the rough water surface into patches containing free and patches containing bound waves. This model is shown to account for the observed histograms of slope measured in the tank and, at least qualitatively, for the observed decrease in the probability of finding bound waves with increasing wind speed. Furthermore, if we add these bound, tilted waves to the free waves of the standard Bragg/composite-surface scattering model for microwave scattering from rough water surfaces, then the model can account for many otherwise unexplained features of the scattering. Principal among these features are the rapid decrease in polarization ratio and rapid increase in the first moment of the microwave Doppler spectrum with increasing wind speed when the antenna is directed upwind, features that occur to a much lesser extent when the antenna looks downwind.

Compressional MHD waves in the magnetosphere: A new approach

Abstract: Dynamics of compressional MHD wave propagation is theoretically studied in the dayside and nightside magnetosphere. In order to analytically examine the MHD wave equation, we adopt the quantum mechanical approach which is often used in the problem of the Schrodinger's equation. The wave solutions are obtained for dayside and nightside Alfven speed profiles, respectively, without any arbitrary boundary condition at the magnetopause or the bow shock. The result shows that the previous cavity/waveguide models are found to be inappropriate for studying compressional wave properties in the magnetosphere. We discuss the role of virtual resonances which generally represent any possible compressional modes in the magnetosphere.

Experimental revealing of polarization waves.

Abstract: Stationary and traveling waves of the states of optical polarization are considered in the framework of Jones vector formalism. The feasibility of revealing these waves in holographic and interference arrangements is substantiated and demonstrated.

Validation of the Slow Compressional Wave in Porous Media: Comparison of Experiments and Numerical Simulations

Abstract: We perform numerical simulation of ultrasonic experiments on poroelastic samples, in which Biot's slow compressional wave had been observed. The simulation is performed using OASES modeling code, which allows to compute elastic wave fields in layered poroelastic media. Modeled were the experiments of Plona (1980), Rasolofosaon (1988), and our own measurements. In all the three situations, a good agreement between experiment and simulations has been observed. This further confirms the fact that Biot's theory of poroelasticity, on which the simulations were based, adequately describes the behavior of the porous materials under investigations at ultrasonic frequencies.

Parametrically excited surface waves: two-frequency forcing, normal form symmetries, and pattern selection.

Abstract: Motivated by experimental observations of exotic standing wave patterns in the two-frequency Faraday experiment, we investigate the role of normal form symmetries in the pattern selection problem. With forcing frequency components in ratio m/n, where m and n are co-prime integers, there is the possibility that both harmonic and subharmonic waves may lose stability simultaneously, each with a different wavenumber. We focus on this situation and compare the case where the harmonic waves have a longer wavelength than the subharmonic waves with the case where the harmonic waves have a shorter wavelength. We show that in the former case a normal form transformation can be used to remove all quadratic terms from the amplitude equations governing the relevant resonant triad interactions. Thus the role of resonant triads in the pattern selection problem is greatly diminished in this situation. We verify our general results within the example of one-dimensional surface wave solutions of the Zhang-Vinals model of the two-frequency Faraday problem. In one-dimension, a 1:2 spatial resonance takes the place of a resonant triad in our investigation. We find that when the bifurcating modes are in this spatial resonance, it dramatically effects the bifurcation to subharmonic waves in the case of forcing frequencies are in ratio 1/2; this is consistent with the results of Zhang and Vinals. In sharp contrast, we find that when the forcing frequencies are in ratio 2/3, the bifurcation to (sub)harmonic waves is insensitive to the presence of another spatially-resonant bifurcating mode.

Theoretical and experimental studies of surface waves on solid-fluid interfaces when the value of the fluid sound velocity is located between the shear and the longitudinal ones in the solid

Abstract: The existence of two surface waves propagating on a plane solid–fluid interface is demonstrated when the value of the fluid sound velocity is located between the shear and the longitudinal ones in the solid. First, the Scholte–Stoneley dispersion equation is studied analytically and numerically to find the roots corresponding to the Stoneley and the Rayleigh waves. The anatomy of each one is then described with the formalism of the evanescent plane waves: both waves are unleaky. Finally, the results are confirmed experimentally by measuring the times of flight on a Plexiglas–water interface and on a PVC–water interface.

Waves generated by a moving source in a two-layer ocean of finite depth

Abstract: The velocity potentials of a point source moving at a constant velocity in the upper layer of a two-layer fluid are obtained in a form amenable to numerical integration. Each fluid layer is of finite depth, and the density difference between the two layers is not necessarily small. The far-field asymptotic behavior of the surface waves and internal waves are also derived using the method of stationary phase. They show that the wave system at the free surface or at the interface each contains contributions from two different modes: a surface-wave mode and an internal-wave mode. When the density difference between the two layers is small or the depth of the upper layer is large, the surface-wave mode mainly affects the surface waves while the internal-wave mode mainly affects the internal waves. However, for large density difference, both modes contribute to the surface wave or internal wave system. For each mode, both divergent and transverse waves are present if the total depth Froude number is less than a certain critical Froude number which is mode-dependent. For depth Froude number greater than the critical Froude number, only divergent waves exist for that mode. This classification is similar to that of a uniform fluid of finite depth, where the critical Froude number is simply unity. The surface waves and internal waves are also calculated using the full expressions of the source potentials. They further confirm and illustrate the features observed in the asymptotic analysis.

Nonlinear surface acoustic waves in crystals

Abstract: A theory for nonlinear surface acoustic waves in isotropic solids [E. A. Zabolotskaya, J. Acoust. Soc. Am. 91, 2569–2575 (1992)] is generalized to include the anisotropy of crystals. There is no restriction to material symmetry, orientation of the free surface with respect to crystal axes, or propagation direction in the plane of the free surface. Numerical simulations of waveform distortion, shock formation, and harmonic propagation curves are presented for two different cuts of potassium chloride.

Generation of Tollmien-Schlichting waves by convecting gusts interacting with sound

Abstract: A new mechanism is proposed for the generation of Tollmien–Schlichting (T–S) waves by free-stream turbulence. For definiteness and self-consistency, the mechanism is described mathematically by using a triple-deck formalism. The free-stream turbulence is represented by convecting gusts consisting of the so-called vortical and entropy waves of small amplitude. We show that suitable convecting gusts can interact with sound waves in the free stream to produce a forcing that has the same time and length scales as those of the T–S waves, thereby exciting such waves in the vicinity of the lower branch of the neutral stability curve. The T–S waves so produced have the order of magnitude of e2R5/16, where e is the amplitude of the free-stream disturbance and R the global Reynolds number. The scale conversion is achieved without resorting to any non-homogeneity on the wall, and hence the mechanism operates in a flat boundary layer. Furthermore, the T–S waves so generated do not undergo any immediate decay, as they may do in some other receptivity processes. For homogeneous isotropic free-stream turbulence, the spectrum of the T–S waves is obtained. The efficiency of the receptivity mechanism is assessed by parametric studies.

Numerical study of internal wave reflection from sloping boundaries

Abstract: The breaking of internal waves propagating in a stratified fluid of constant buoyancy frequency on a sloping boundary was investigated numerically. It was found that at the boundary, nonlinear non-resonant interactions between the incident and reflected waves produced higher-mode waves. These modes had frequencies greater than the local buoyancy frequency and so could not radiate from the interaction region. The energy level of trapped waves increased with time and subsequently led to overturning of the density field. At the critical frequency, when the reflected wave propagated in a direction parallel to the slope, wave overturning occurred near the wall, but the point of overturning moved off the bottom as the propagation angle changed away from that of the bottom slope as the waves became increasingly supercritical. The internal wave reflection coefficient generally increased as the effects of nonlinearity and viscosity decreased, but depended strongly on the forcing frequency and the angle of the sloping boundary.

Turbulent shear flow over fast-moving waves

Abstract: We divide the interaction between wind and ocean surface waves into three parameter regimes, namely slow, intermediate and fast waves, that are distinguished by the ratio c/u. (c is the wave phase speed and u. is the friction velocity in the wind). We develop here an analytical model for linear changes to the turbulent air flow caused by waves of small slope that is applicable to slow and to fast waves. The wave-induced turbulent shear stress is parameterized here with a damped mixing-length model, which tends to the mixing-length model in an inner region that lies close to the surface, and is then damped exponentially to zero in an outer region that lies above the inner region. An adjustable parameter in the damped mixing-length model controls the rate of decay of the wave-induced stress above the inner region, and shows how the results vary from a model with no damping, which corresponds to using the mixing-length model throughout the flow, to a model with full damping, which, following previous suggestions, correctly represents rapid distortion of the wave-induced turbulence in the outer region. Solutions for air flow over fast waves are obtained by analysing the displacement of streamlines over the wave; they show that fast waves are damped, thereby giving their energy up to the wind. There is a contribution to this damping from a counterpart of the non-separated sheltering mechanism that gives rise to growth of slow waves (Belcher & Hunt 1993). This sheltering contribution is smaller than a contribution from the wave-induced surface stress working against the orbital motions in the water. Solutions from the analysis for both slow and fast waves are in excellent agreement with values computed by Mastenbroek (1996) from the nonlinear equations of motion with a full second-order closure model for the turbulent stresses. Comparisons with data for slow and intermediate waves show that the results agree well with laboratory measurements over wind-ruffled paddle-generated waves, but give results that are a factor of about two smaller than measurements of purely wind-generated waves. We know of no data for fast waves with which to compare the model. The damping rates we find for fast waves lead to e-folding times for the decay of the waves that are a day or longer. Although this wind-induced damping of fast waves is small, we suggest that it might control low-frequency waves in a fully-developed sea.