Showing papers on "Longitudinal wave published in 1998"

Ultrasonic Band Gap in a Periodic Two-Dimensional Composite.

Abstract: The first experimentally observed ultrasonic full band gap in periodic bidimensional composites for the longitudinal wave mode is described in this Letter. The structure consists of an aluminum alloy plate with a square periodic arrangement of cylindrical holes filled with mercury. No propagation wave exists at the frequency range between 1000--1120 kHz irrespective of the measurement direction. The experiment was performed by means of an ultrasonic transmission technique, and a measurement of the position dependence of the acoustic amplitude was also performed.

Observation of ‘third sound’ in superfluid 3 He

Abstract: Waves on the surface of a fluid provide a powerful tool for studying the fluid itself and the surrounding physical environment. For example, the wave speed is determined by the force per unit mass at the surface, and by the depth of the fluid1: the decreasing speed of ocean waves as they approach the shore reveals the changing depth of the sea and the strength of gravity. Other examples include propagating waves in neutron-star oceans2 and on the surface of levitating liquid drops3. Although gravity is a common restoring force, others exist, including the electrostatic force which causes a thin liquid film to adhere to a solid. Usually surface waves cannot occur on such thin films because viscosity inhibits their motion. However, in the special case of thin films of superfluid 4He, surface waves do exist and are called ‘third sound’. Here we report the detection of similar surface waves in thin films of superfluid 3He. We describe studies of the speed of these waves, the properties of the surface force, and the film's superfluid density.

Acoustic anisotropy in bovine cancellous bone

Abstract: This paper presents the experimental results on the acoustic anisotropy in bovine cancellous bone. The propagation of both fast and slow longitudinal waves in bovine cancellous bone was experimentally examined in relation to the structural anisotropy, or the trabecular arrangement. Propagation speeds of the fast and slow waves were measured as a function of the propagation angle to the trabecular alignment, and theoretically estimated by use of Biot’s theory for an isotropic medium.

Experimental study of interfacial solitary waves

Abstract: A small-scale experiment was conducted (in a 3 m long flume) to study interfacial long-waves in a two-immiscible-fluid system (water and petrol were used). Experiments and nonlinear theories are compared in terms of wave profiles, phase velocity and mainly frequency--amplitude relationships. As expected, the KdV solitary waves match the experiments for small-amplitude waves for all layer thickness ratios. The characteristics of 'large'-amplitude waves (that is when the crest is close to the critical level - approximately located at mid-depth) asymptotically tend to be predicted by a 'KdV-mKdV' equation containing both quadratic and cubic nonlinear terms. In addition a numerical solution of the complete Euler equations, based on Fourier series expansions, is devised to describe solitary waves of intermediate amplitude. In all cases, solitary interfacial waves in this numerical theory tally with the experimental data. When the layer thicknesses are almost equal (ratio of lower layer to total depth equal to 0.4 or 0.63) both the KdV-mKdV and the numerical solutions match the experimental points.

Traveltimes for infrasonic waves propagating in a stratified atmosphere

Abstract: SUMMARY The tau‐p method of Buland & Chapman (1983) is reformulated for sound waves propagating in a stratified atmosphere under the influence of a height-dependent wind velocity profile. For a given launch angle along a specified azimuth, the ray parameter is redefined to include the influence of the horizontal wind component along the direction of wave propagation. Under the assumption of negligible horizontal wind shear, the horizontal wind component transverse to the ray propagation does not aVect the direction of the wave normal, but displaces the reference frame of the moving wavefront, thus altering the observed incidence azimuth. Expressions are derived for the time, horizontal range, and transverse range of the arriving waves as a function of ray parameter. Algorithms for the location of infrasonic wave sources using the modified tau‐p formulation in conjunction with regional atmospheric wind and temperature data are discussed.

Properties of seismic fault zone waves and their utility for imaging low-velocity structures

Abstract: A two-dimensional solution for the scalar wave equation in a model of two vertical layers between two quarter spaces is used to study properties of seismic waves in a laterally heterogeneous low-velocity structure. The waves, referred to as seismic fault zone waves, include head waves, internal fault zone reflections, and trapped waves. The analysis aims to clarify the dependency of the waves on media velocities, media attenuation coefficients, layer widths, and source-receiver geometry. Additional calculations with extreme low-velocity layers provide examples that may be relevant for volcanic and geothermal domains. The interference patterns controlling seismic fault zone waves change with the number of internal reflections in the low-velocity structure. This number increases with propagation distance along the structure, decreases with fault zone width, and increases (for given length scales) with the velocity contrast. The relative lateral position of the source within the low-velocity layer modifies die length scales associated with internal reflections and influences the resulting interference pattern. Low values of Q affect considerably the dominant period and overall duration of the waves. Thus there are significant tradeoffs between propagation distance along the structure, fault zone width, velocity contrast, source location within the fault zone, and Q. The lateral and depth receiver coordinates determine the particular point where the interference pattern is sampled and observed motion is a strong function of both coordinates. The zone connecting sources generating fault zone waves and observation points with appreciable wave amplitude can be over an order of magnitude larger than the fault zone width. Calculations for cases with layer P wave velocity of ∼200 m s−1, modeling a vertical dike or crack with fluid and gas, show conspicuous persisting oscillations. The results resemble aspects of seismic data in volcanic domains. If these waves exist in observed records, their explicit recognition and modeling will help to separate source and structural effects and aid in the interpretation of volcano-seismology signals. Although the tradeoffs in parameters governing seismic fault zone waves are significant, each variable has its own signature, and the parameters may be constrained by additional geophysical data. Simultaneous modeling of many waveforms with an appropriate solution can resolve the various parameters and provide a high-resolution structural image.

Modulational instability of dust-acoustic and dust-ion-acoustic waves

Abstract: Using the standard reductive perturbation technique, a nonlinear Schr\"odinger equation is derived to study the modulational instability of finite amplitude dust-acoustic (DA) and dust-ion-acoustic (DIA) waves against oblique perturbations (with respect to the propagation direction of the carrier waves) in an unmagnetized dusty plasma. It is shown that both the DA and DIA waves are modulationally unstable. Possible stationary states of the wave packets can appear as envelope solitons.

Electrodynamics: A Modern Geometric Approach

Abstract: Special relativity Maxwell's equation(s) Lorentz-Force equations electromagnetic waves in 1-D electromagnetic waves in vacuum polarization waves in media waves at boundaries the field of a moving charge the Lorrentz-Dirac equation rotations and spherical harmonics radiation multipoles.

Gravity waves on ice‐covered water

Abstract: Gravity waves propagating on the surface of ice-covered water of finite depth are considered. The ice layer is viewed as a suspension, with an effective viscosity much greater than that of water and a density slightly less than that of water. It is treated as a viscous liquid, and the water beneath it is treated as an inviscid liquid. The linearized motion of gravity waves is analyzed for this two-layer model, and the dispersion equation is obtained. It is solved numerically for waves of any length. It is also simplified for waves short compared to the layer thickness and for waves long compared to the layer thickness. This equation yields dispersion and strong attenuation, both of which depend upon the effective viscosity of the suspension.

On the determination of the onset of breaking for modulating surface gravity water waves

Abstract: Determining the onset of wave breaking in unforced nonlinear modulating surface gravity wave trains on the basis of a threshold variable has been an elusive problem for many decades. We have approached this problem through a detailed numerical study of the fully nonlinear two-dimensional inviscid problem on a periodic spatial domain. Two different modes of behaviour were observed for the evolution of a sufficiently steep wave group: either recurrence of the initial state or the rapid onset of breaking, each of these involving a significant deformation of the wave group geometry. For both of these modes, we determined the behaviour of dimensionless growth rates constructed from the rates of change of the local mean wave energy and momentum densities of the wave train, averaged over half a wavelength. These growth rates were computed for wave groups with three to ten carrier waves in the group and also for two modulations with seven carrier waves and three modulations with ten carrier waves. We also investigated the influence of a background vertical shear current.Two major findings arose from our calculations. First, due to nonlinearity, the crest–trough asymmetry of the carrier wave shape causes the envelope maxima of these local mean wave energy and momentum densities to fluctuate on a fast time scale, resulting in a substantial dynamic range in their local relative growth rates. Secondly, a universal behaviour was found for these local relative growth rates that determines whether subsequent breaking will occur.

The elastodynamic finite integration technique for waves in cylindrical geometries

Abstract: This paper deals with the elastodynamic finite integration technique for axisymmetric wave propagation in a homogeneous and heterogeneous cylindrical medium (CEFIT). This special variant of a finite difference time domain (FDTD) scheme offers a suitable method to calculate real three-dimensional problems in a two-dimensional staggered grid. In order to test the accuracy of the numerical CEFIT code, problems for which analytical solutions are available are presented. These solutions involve wave propagation in an elastic plate, the scattering of a plane longitudinal wave by a spherical obstacle, and ultrasound generation by a thermoelastic laser source. For the latter problem experimental results are included. The CEFIT code also allows the treatment of more complicated problems. Further possible applications are the investigation of elastic waves generated in an acoustic microscope, the simulation of impact-echo measurements in multi-layer systems, axisymmetric wave propagation in arbitrary bodies of revo...

Lattice BGK simulation of sound waves

Abstract: We consider the application of the lattice Boltzmann BGK model to simulate sound waves in situations where the density variation is small compared to the mean density. Linear sound waves are simulated in two different situations: a plane wave propagating in an unbound region; and a wave in a tube. For both cases the behaviour of the simulated waves is found to be in good agreement with analytic expressions. Non-linear sound waves are also simulated and are seen to display the expected features.

Inertia–Gravity Wave Breaking in Three Dimensions. Part II: Convectively Unstable Waves

Abstract: The three-dimensional breakdown of a large-amplitude, convectively unstable inertia‐gravity wave is examined numerically as a function of primary-wave frequency and amplitude The results confirm that near-inertial waves break down preferentially via shear instability even when the primary wave is initially overturned As in the convectively stable near-inertial regime, the spectrum of instability energy is approximately isotropic in azimuthal orientation At intermediate frequencies, wave breakdown is triggered by a transverse shear instability in the region of overturning This behavior, displaying a clear preference for instability with horizontal component of wavevector in the transverse direction, is different from the breakdown of convectively stable waves at intermediate frequency examined in Part I As the primary-wave frequency is increased further, shear instabilities once again develop in the transverse direction, but they are modified by convective instability as the billows reach finite amplitude The influence of transverse vertical shear becomes progressively weaker as the wave frequency approaches the buoyancy frequency In this limit, transverse convection leads to wave collapse, and there is no preferred scale of instability

Velocity‐shear‐driven ion‐cyclotron waves and associated transverse ion heating

Abstract: Recent sounding rocket experiments, such as SCIFER, AMICIST, and ARCS-4, and satellite data from FAST, Freja, DE-2, and HILAT, provide compelling evidence of a correlation between small-scale spatial plasma inhomogeneities, broadband low-frequency waves, and transversely heated ions. These naturally arising, localized inhomogeneities can lead to sheared cross-magnetic-field plasma flows, a situation that has been shown to have potential for instability growth. Experiments performed in the Naval Research Laboratory's Space Physics Simulation Chamber demonstrate that broadband waves in the ion-cyclotron frequency range can be driven solely by a transverse, localized electric field, without the dissipation of a field-aligned current. Significant perpendicular ion energization resulting from these waves has been measured. Detailed comparisons with both theoretical predictions and space observations of electrostatic waves found in the presence of sheared cross-magnetic-field plasma flow are made.

Analysis and experiments on stress waves in planar trusses

Abstract: The dynamics of planar trusses are investigated in terms of axial (longitudinal) stress waves, which propagate along structural members and scatter at the joints. The scattering coefficients representing the reflection and transmission of axial waves at each joint are derived from the dynamics and compatibility conditions of the joint. The complex multiple reflections of waves within the structure are evaluated in the frequency domain with a newly developed reverberation matrix, which is formulated from the scattering coefficients and propagating phase factors. Transient waves are then derived by Fourier synthesis, and evaluated by a Fast Fourier Transform algorithm. Experimental results of propagating broad band pulses are presented for a truss model excited by a step loading. Comparison between theoretical results and transient wave records indicate that the axial wave theory is valid only for the response at the very early time. The discrepancy is much reduced if the scattering coefficients are modifie...

Stability and Instability of Fourth-Order Solitary Waves

Abstract: We study ground-state traveling wave solutions of a fourth-order wave equation. We find conditions on the speed of the waves which imply stability and instability of the solitary waves. The analysis depends on the variational characterization of the ground states rather than information about the linearized operator.

Sound generation in gradient coil structures for MRI

Abstract: When supporting plates of plastic material are subjected to alternating transverse Lorentz forces while in a strong magnetic field normal to the plate surface, compressional waves within the solid produce a modulation of the plate surface that launches an acoustic wave in air along the magnetic field axis. We have extended our previous theory describing this process to include a detailed description of the formation of an acoustic interference pattern in air described by Fraunhofer diffraction at a distance from the plate surface. The extended theory predicts that the observed acoustic signal midpoint and normal to the plate surface gives a variation with frequency in approximate agreement with our previous measurements. The acoustic output off axis shows acoustic blazing that produces two main diffraction peaks with a splitting inversely proportional to the velocity of sound in the plate material. The new results could have important ramifications for the minimization of sound output in gradient coil design for MRI. A new arrangement of coils is proposed to ameliorate the acoustic output problem centrally and normal to the plate by extending the frequency response of the supporting plates to much higher frequencies. Also presented are estimates of the compressional wave velocities deduced from frequency response data recorded at the center-point of a number of different plates.

Theory of compressional and shear waves in fluidlike marine sediments

Abstract: An unconsolidated, saturated marine sediment consists of a more or less loose assemblage of mineral grains in contact, with seawater in the interstices. It is postulated that the two-phase medium possesses no skeletal frame, implying that the elastic rigidity modulus of the material is zero. A theory of wave propagation in such a sediment is developed, in which the medium is treated as a fluid that supports a specific form of intergranular dissipation. Two important equations emerge from the analysis, one for compressional wave propagation and the second describing transverse disturbances. For the type of dissipation considered, which exhibits hysteresis or memory, the shear equation admits a wavelike solution, and is thus a genuine wave equation, even though the sediment shows no elastic rigidity. In effect, the medium possesses a “dissipative” rigidity, which is capable of supporting shear. This behavior is distinct from that of a viscous fluid, for which the shear equation is diffusionlike in character...

Guided Wave Tuning Principles for Defect Detection in Tubing

Abstract: Dispersion diagrams for longitudinal modes and several flexural modes are given. A partial loading oblique incidence technique was introduced for non-axisymmetric guided wave generation. Acoustic fields for partially loaded generation of guided waves were obtained along a sample Inconel steam generator tube surface. The axial field and the circumferential fields were non uniform. Even though the acoustic field was much more complicated than in the case of axisymmetric modes, the study of non-axisymmetric mode cannot be avoided; excitation of a single symmetric mode is often difficult due to limited access and transducer efficiency and there is also mode conversion after scattering from defects. For 100% inspection coverage of tubing and piping, three dimensional tuning (distance, frequency, and incident angle tuning), was employed. A single combination of incident angle, position, and frequency may miss defects in “blind spots”. However, complete inspection coverage of a whole cross sectional area over a certain distance of tubing was successfully demonstrated through a multi crack detection experiment by using the three dimensional tuning concepts. Also, the use of non-axisymmetric guided waves for a large distance inspection capability was successfully demonstrated.

Longitudinal Dispersion in Sinuous Channel with Changes in Shape

Abstract: Results are presented from a series of laboratory experiments conducted on a large scale channel with sinuous planform geometry. These have been used to obtain the magnitude of the longitudinal dispersion coefficient. A constant trapezoidal cross section and a variable cross-sectional "natural" shape under different discharges have been studied. Temporal concentration distributions recorded for the trapezoidal section tend towards Gaussian form and provide values of a longitudinal dispersion coefficient comparable with previous similar studies. The more "natural" cross-sectional geometry channel exhibits strongly skewed distributions and increases the value of a longitudinal dispersion parameter by over 150%. Variation of a longitudinal dispersion coefficient with discharge has been observed and has been explained by the effects of the longitudinally varying cross-sectional shape. A comparison between observed and predicted distributions from a simple routing procedure emphasizes the need for an improved method for incorporating the effects of longitudinal variations in cross-sectional shape.

Internal wave excitation from stratified flow over a thin barrier

Abstract: We perform laboratory experiments in a recirculating shear flow tank of non-uniform salt-stratified water to examine the excitation of internal gravity waves (IGW) in the wake of a tall, thin vertical barrier. The purpose of this study is to characterize and quantify the coupling between coherent structures shed in the wake and internal waves that radiate from the mixing region into the deep, stationary fluid. In agreement with numerical simulations, large-amplitude internal waves are generated when the mixing region is weakly stratified and the deep fluid is sufficiently strongly stratified. If the mixing region is unstratified, weak but continuous internal wave excitation occurs. In all cases, the tilt of the phase lines of propagating waves lies within a narrow range. Assuming the waves are spanwise uniform, their amplitude in space and time is measured non-intrusively using a recently developed 'synthetic schlieren' technique. Using wavelet transforms to measure consistently the width and duration of the observed wavepackets, the Reynolds stress is measured and, in particular, we estimate that when large-amplitude internal wave excitation occurs, approximately 7% of the average momentum across the shear depth and over the extent of the wavepacket is lost due to transport away from the mixing region by the waves. We propose that internal waves may act back upon the mean flow modifying it so that the excitation of waves of that frequency is enhanced. A narrow frequency spectrum of large-amplitude waves is observed because the feedback is largest for waves with phase tilt in a range near 45°. Numerical simulations and analytic theories are presented to further quantify this theory.

Review of shear surface acoustic waves in solids

Abstract: General considerations about physical reasons for the existence of surface acoustic waves and, in particular, shear surface acoustic waves in solids are presented. The results of calculations for various types of shear surface acoustic waves are described, and corresponding physical explanations are given.

The compression wave produced by a high-speed train entering a tunnel

Abstract: An analytical investigation is made of the compression wave produced when a high–speed train enters a tunnel. The wave propagates ahead of the train within the tunnel at about the speed of sound. In very long tunnels it is transformed by nonlinear steepening into a shock whose amplitude is about one or two per cent of atmospheric pressure. The emergence of the shock from the far end of the tunnel produces an environmental disturbance analogous to the sonic boom generated by an aircraft in supersonic flight. In this paper the train is modeled by a continuous distribution of monopole sources whose strengths are determined by the train nose profile. The initial wavelength greatly exceeds the tunnel diameter at typical train Mach numbers of about 0.2 and the analytical problem of wave generation by interaction of the monopoles with the tunnel can be solved by use of a compact Gree9s function. The functional form of Gree9s function depends on the tunnel entrance geometry and on the proximity of other inhomogeneities, such as embankments, buildings and bridge structures. Detailed predictions are given for axisymmetric ‘rain’ entering a long circular cylindrical tunnel. The results are found to be in excellent agreement with experimental data for this configuration available in the literature.

Lamb waves as thickness vibrations superimposed on a membrane carrier wave

Abstract: Classical Lamb waves in an homogeneous, isotropic linearly elastic plate are reconsidered. The displacement components are obtained in terms of thickness motions superimposed on a membrane carrier wave which defines the propagation along the plate. The carrier wave can be any solution of the reduced wave equation for a membrane. The analysis of the thickness motions results in the usual Rayleigh–Lamb frequency equation. A number of special cases for the carrier wave are considered.

Radio wave propagation along mixed paths through a four-layered model of rain forest: an analytic approach

Abstract: This paper presents a novel full-wave analysis of the radio waves that are excited from a dipole antenna located in the trunk layer and propagate inside a four-layered forest medium The dyadic Green's functions for the four-layered geometry are applied first to derive the integral expression of the electric fields The closed form of the electric fields is then obtained by using the quasi-static approximation, saddle-point technique, and branch-cut integrations in the complex plane and, hence, expressed in terms of direct waves, multiple reflected waves, and lateral waves Two kinds of images, ie, the quasi-dynamic and complex images, are considered in the integration in the complex plane Among those waves excited by a dipole antenna in the four-layered medium, it is shown theoretically and numerically that the lateral wave along the upper-side air-canopy interface plays a role of dominant modes The propagation mechanism of other lateral waves due to the air-canopy, canopy-trunk, and trunk-ground interfaces is also discussed and analyzed so as to gain an insight into the wave characteristics Transmission losses of the lateral waves are calculated numerically

Lamb waves in highly attenuative plastic plates

Abstract: The influence of material attenuation on Lamb wave dispersion behavior has been studied analytically. As the attenuation is increased, keeping the ratio of the bulk longitudinal to bulk shear wave attenuation constant at the value measured in high-density polyethylene, the degree of coupling between the shear and longitudinal partial waves decreases and the phase velocity dispersion curves for different modes of the same symmetry can cross; this is not possible for an elastic plate. With increasing attenuation, some modes become asymptotic to the bulk longitudinal velocity at high frequency, rather than to the bulk shear velocity. At high values of attenuation, there is minimal coupling between the longitudinal and shear partial waves and the behavior of the longitudinal modes is analogous to that of a “fluid plate.” The predicted group velocities and attenuations of selected modes in a high-density polyethylene plate have been checked experimentally, and good agreement was obtained.