Showing papers on "Longitudinal wave published in 1992"

Waves in plasmas

Abstract: Wave normal surfaces waves in a cold uniform plasma causality, acoustic waves and simple drift waves energy flow and accessibility Kruskal-Schwarzschild solutions for a bounded plasma oscillations in bonded plasmas plasma models with discrete structure longitudinal oscillations in a plasma of continuous structure absolute and convective instability susceptibilities for a hot plasma in a magnetic field waves in magnetized uniform media effects on waves from weak collisions reflection, absorption and mode conversion nonuniform plasmas the straight-trajectory approximation quasilinear diffusion quasilinear diffusion in a magnetized plasma bounce-averaged quasilinear diffusion in a magnetized plasma bounce-averaged quasilinear diffusion.

Ultrasonic classification of imperfect interfaces

Abstract: Ultrasonic reflection measurements from material interfaces are commonly used to detect and quantitatively characterize boundary imperfections of different kinds. Either shear or longitudinal waves can be used to assess the degree of the interface imperfection in acoustical terms. On the other hand, the evaluation of this data in terms of strength-related mechanical properties requiresa priori knowledge of the physical nature of the imperfection. It is shown in this paper that the ratio between the normal and transverse interfacial stiffnesses can be used to classify the interface imperfection. This ratio is readily measured, e.g., by comparing the longitudinal and shear reflection coefficients at normal incidence. Both theoretical and experimental results indicate that different types of imperfections, such as kissing, partial, and slip bonds, can be distinguished by this simple technique.

Intense Dynamic Loading Of Condensed Matter

Abstract: MECHANICS OF CONTINUOUS MEDIA Stresses and Strains in a Solid Body Equations of One-Dimensional Motion of Compressible Media, Shock Waves Interpretation of Detection Data on Compression and Rarefaction Waves EXPERIMENTAL TECHNIQUES OF THE PHYSICS OF HIGH DYNAMIC PRESSURE Explosive Generation of Dynamic Pressure Ballistic Experiments with a Shock Wave Promising Sources of High Dynamic Pressure Discrete Measurement of Wave and Mass Velocities Pressure Profiles Recorded with Manganin Sensors Measurement of the Velocity of Matter ELASTOPLASTIC PROPERTIES OF SHOCK-LOADED SOLIDS Basic Relationships and Models Moduli of Elasticity and the Velocity of Sound in Shock Compressed Metals Dynamic Yield Point Structure of Plastic Compression Waves Compression and Rarefaction Waves in Shock-Compressed Metals Compaction of Porous Media in Shock Waves Catastrophic Thermoplastic Shear under Dynamic Deformation. Impact Compression of Brittle Materials Methods of Studying High Dynamic Deformations Microscopic Models of Strain Dynamics EVOLUTION OF LOAD PULSES IN MEDIA WITH POLYMORPHIC PHASE TRANSITIONS The Structure of Compression and Release Waves in Iron The Graphite to Diamond Transition under Shock Compression Properties of the Phase Transition Induced by Shock FRACTURE UNDER PULSED LOADING. SPALLING STRENGTH Dynamics of Wave Interactions During Spalling Spalling Strength of Metals Work of Spalling Fracture Determination if Tensile Stress Behind the Spall Plane Resistance of Polymers, Brittle Materials, and Liquids to Spalling Fracture Mechanism and Kinetics of Dynamic Fracture of Metals SHOCK AND DETONATION WAVES IN SOLID EXPLOSIVES Basic Concepts and Models Kinetics of Dissociation of Explosives Deduced from Analyses of Evolution of Shock Waves Semiempirical Macrokinetic Equations of Solid Explosives MODEL EQUATIONS OF STATE FOR A WIDE RANGE OF PRESSURE AND TEMPERATURE General Analysis of Phase Diagram Quasi-Harmonic Model of a Solid Equation of State for Condensed Phase at High Temperatures Evaporation Effects and Generalized Equations of State Tabulated and Approximate Equations of States GENERALIZED EQUATIONS OF STATE FOR METALS Cold Compression Curve Electron Component Thermal Excitation of the Crystal Lattice Liquid Phase Procedure for Constructing Semiempirical Equations of State for Metals THERMODYNAMIC PROPERTIES OF METALS Aluminum Copper Lead Lithium FURTHER BRIEF NOTES ON CONTINUUM MECHANICS Equation of Motion Shock Waves Characteristic Form of Gas-Dynamic Equations. Simple Waves The Structure of a Shock Wave Decay of a Random Discontinuity in Hydrodynamics Equation of Motion for Porous Condensed Media DYNAMICS OF CONDENSED MEDIA WITH ALLOWANCE FOR THEIR STRENGTH Equations of Motion. Divergence Form Characteristics Form on Equations of Motion Simple Waves Shock Waves in a Hyperelastic Medium Decay of an Arbitrary Discontinuity Equations of Motion for a Hyperelastic Medium in an Arbitrary Curvilinear Set of Coordinates Equations of Motion of a Maxwell Viscoelastic Medium Nonlinear Waves in a Viscoelastic Medium BRIEF REVIEW OF COMPUTATIONAL TECHNIQUES FOR THE DYNAMICS OF CONDENSED MEDIA Method of Particles in Cells Method of Large Particles Godunov's Method Lagrangian Methods NUMERICAL MODELING OF CONDENSED MEDIA UNDER INTENSIVE PULSED LOADING Tabulated Form of the Equation of State High-Speed Collisions Irregular Collisions of Strong Shock Waves in Metals Numerical Modeling of the Effect of Relativistic High-Current and High-Energy Ion Beams on Metal Targets Effect of an Explosion on an Iron Plate Impactor Penetration of an Obstacle of Finite Thickness Impact of a Micrometerorite on a Spacecraft Shield References Index

Funnel-shaped, low-frequency equatorial waves

Abstract: Funnel-shaped, low-frequency radiation, as observed in frequency time spectrograms, is frequently found at the earth's magnetic equator which extends from the proton-cyclotron frequency up to the lower hybrid frequency. Ray-tracing calculations can qualitatively reproduce the observed frequency-time characteristics of these emissions if the waves are propagating in the fast magnetosonic mode starting with wave normal angles of about 88 deg at the magnetic equator. The funnel-shaped emissions are consistent with generation by protons with a ring-type velocity space distribution. A ring-shaped region of positive slope in the velocity space density distribution of protons is observed near the Alfven velocity, indicating that the ring protons strongly interact with the waves. Ray-tracing calculations show that for similar equatorial wave normal angles lower-frequency fast magnetosonic waves are more closely confined to the magnetic equator than higher-frequency fast magnetosonic waves. For waves refracted back toward the equator at similar magnetic latitudes, the lower-frequency waves experience stronger damping in the vicinity of the equator than higher-frequency waves. Also, wave growth is restricted to higher frequencies at larger magnetic latitudes. Wave damping at the equator and wave growth off the equator favors equatorial wave normal angle distributions which lead to the funnel-shaped frequency time characteristic.

A model for the generation of two-dimensional surf beat

Abstract: A finite difference model predicting group-forced long waves in the nearshore is constructed with two interacting parts: an incident wave model providing time-varying radiation stress gradients across the nearshore, and a long-wave model which solves the equations of motion for the forcing imposed by the incident waves. Both shallow water group-bound long waves and long waves generated by a time-varying breakpoint are simulated. Model-generated time series are used to calculate the cross correlation between wave groups and long waves through the surf zone. The cross-correlation signal first observed by Tucker [1950] is well predicted. For the first time, this signal is decomposed into the contributions from the two mechanisms of leaky mode forcing. Results show that the cross-correlation signal can be explained by bound long waves which are amplified, though strongly modified, through the surf zone before reflection from the shoreline. The breakpoint-forced long waves are added to the bound long waves at a phase of π/2 and are a secondary contribution owing to their relatively small size.

Response of the dipole magnetosphere to pressure pulses

Abstract: The response of the magnetosphere to pressure pulses at the magnetopause has been studied using a three-dimensional model of ULF waves in a dipole geometry. Pressure pulses at the magnetosphere directly excite compressional waves, which then convert to shear mode Alfven waves due to inhomogeneity. The behavior of the system depends on the frequency of the source at the magnetopause, with vortex structure tending to form on field lines resonant with the source frequency. The perturbations between the vortices are skewed toward noon, in agreement with observations.

The role of upstream waves in supercritical quasi‐parallel shock re‐formation

Abstract: It has been demonstrated by hybrid simulations of collisionless shocks that the shock itself is not stationary but exhibits a cyclic behavior. We have performed a number of one-dimensional hybrid simulations of collisionless shocks and of the interaction of two plasma streams in order to assess the role of upstream waves in the re-formation process. We found that when upstream waves and reflected ions are present, the waves inevitably steepen up and lead to shock re-formation. To investigate the interaction of the reflected ions with upstream waves, the hybrid code is then used in two stages. In the first stage a shock together with upstream diffuse particles and waves is generated. In the second stage, upstream wave trains are isolated, and their subsequent interaction with a finite length ion beam as well as with ions emitted from a moving point source is investigated. The results show that the original wave amplitude grows and the wave steepens. This is due to a deceleration and deflection of the beam ions once they encounter a wave crest with a large local value of the angle ΘBn between the magnetic field and the direction of beam propagation: the deflection leads to a local density increase and due to the compressibility to a corresponding magnetic field increase. This sets up a positive feedback loop during which the background ions are also decelerated and can even get reflected. It is concluded that shock re-formation can be caused by the interaction of reflected ions with low-frequency upstream waves.

Inhomogeneous waves in solids and fluids

Abstract: The book may be viewed as an introduction to time-harmonic waves in dissipative bodies, notably viscoelastic solids and fluids. The inhomogeneity of the waves, which is due to the fact that planes of constant phase are not parallel to planes of constant amplitude, is shown to be strictly related to the dissipativity of the medium. A preliminary analysis is performed on the propagation of inhomogeneous waves in unbounded media and of reflection and refraction at plane interfaces. Then emphasis is given to those features that are of significance for applications. In essence, they regard surface waves, scattering by (curved) obstacles, wave propagation in layered heterogeneous media, and ray methods. The pertinent mathematical techniques are discussed so as to make the book reasonably self-contained.

On the evolution of roll waves

Abstract: An amplitude evolution equation is derived for roll waves that occur in a uniform open-channel flow down an incline. A periodic series of roll waves, which is a manifestation of the instability of high-velocity turbulent flow, is shown to be itself unstable to subharmonic disturbances. These disturbances develop into longer and higher roll waves. In this way roll waves tend to increase in size as time goes on, in agreement with experimental evidence.

Flexure waves in elastic rods

Abstract: The order‐1 theory of the dynamics of homogeneous elastic rods is treated with the emphasis on twist‐free bending motions of inextensible rods. Various forms of the governing equations for such planar motions are presented, and their traveling wave solutions are shown to result in curves of the same form as those in Euler’s theory of equilibrium configurations. Traveling waves are called subsonic or supersonic in accord with whether their speed is less than or greater than (E/ρ)1/2 with E the tensile modulus and ρ the density. The solitary traveling waves are loops and are given by elementary functions. At each prescribed level of tension below a critical value, for both subsonic and supersonic waves, the larger the loop the faster the wave. The periodic traveling waves, both with and without inflexion points, are given by elliptic functions and integrals. Small amplitude sinusoidal waves are a limiting case of inflexional waves. The solitary waves are obtainable as appropriate limits of both inflexional and noninflexional waves. Although, in general, traveling waves are motions of rods of infinite length, there are traveling waves that are possible planar modes of motion for rods of finite length with joined ends. A rod with such a traveling wave forms a figure eight in the inflexional case and a circular ring in the noninflexional case.

The nonlinear evolution of high-frequency resonant-triad waves in an oscillatory Stokes layer at high Reynolds number

Abstract: The nonlinear evolution of high-frequency disturbances in high-Reynolds-number Stokes layers is studied. The disturbances are composed of a two-dimensional wave (2α, 0) of magnitude δ, and a pair of oblique waves (α, ± β) of magnitude e, where α, β are the streamwise and spanwise wavenumbers respectively. We assume that β = √3α so that the waves form a resonant triad when they are nearly neutral. It is shown that the growth rate of the disturbance is controlled by nonlinear interactions inside ‘critical layers’. In order for there to be a nonlinear feedback mechanism between the two-dimensional and the three-dimensional waves, the former is required to have a smaller magnitude than the latter, namely .As in Goldstein & Lee (1992), the amplitude equations turn out to be significantly different from those of Raetz (1959), Craik (1971) and Smith & Stewart (1987) in two respects. Firstly, they are integro-differential equations, i.e. the local growth rate depends on the whole history of the evolution. Secondly the back reaction of the oblique waves on the two-dimensional wave is represented by two cubic terms and one quartic term, rather than by one quadratic term. Our numerical investigations show that the amplitudes of the two- and three-dimensional waves can develop a finite-time singularity, a result of some importance. The structure of the finite-time singularity is identified, and it is found that the two-dimensional wave has a ‘more singular’ structure than the three-dimensional waves. The finite-time singularity implies that explosive growth is induced by nonlinear effects. We suggest that this nonlinear blow-up of high-frequency disturbances is related to the bursting phenomena observed in oscillatory Stokes layers and can lead to transition to turbulence.

Scattering of an obliquely incident acoustic wave by an infinite hollow cylindrical shell

Abstract: Acoustic scattering from an isotropic elastic hollow cylindrical shell of infinite length excited by an obliquely incident plane acoustic wave is investigated. The form functions of an aluminum cylindrical shell immersed in water have been calculated by the direct summation of the Rayleigh series. Computations are made at angles (with the normal to the cylinder axis) between α=0° and α=35°. The results of the theoretical calculation are in good agreement with the results of experiments. The experimental results have shown in a frequency range of k1a=0 –20 that the resonances are related to three wave families: the circumferential wave (l=2) detected for angles smaller than the ‘‘angle of longitudinal wave in thin rods’’ (αl), the guided wave (p=1) detected for angles smaller than the second critical angle (αT), and the Scholte–Stoneley wave (l=0). The evolution of the resonance frequencies is followed for different angles and one can note experimentally, that at an angle superior to the Rayleigh critical ...

Use of the multidimensional WKB method to describe propagation of lower hybrid waves in tokamak plasma

Abstract: The influence of diffraction on the propagation of lower hybrid (LH) waves in tokamak plasma was studied. This effect has not been investigated before owing to a lack of suitable methods for solving the wave equation. An asymptotic method is developed which, while using a quasi-classical description in the direction of the group velocity, retains a wave description perpendicular to that direction. This method reduces the general wave equation to a system of ordinary differential equations. It is shown that allowance for the wave properties results in significant diffractional blurring of LH wave beams. This effect occurs in both configurational space and spectral space. In the first, it causes broadening of the absorbed power profile. In the second, it enriches the spectrum with slow waves, increasing interaction with electrons. The effect of diffraction is greater than the effects of the geometrical optics usually taken into account

Ray-tracing simulation of the global propagation of inertia gravity waves through the zonally averaged middle atmosphere

Abstract: The global propagation of large-horizontal-wavelength inertia gravity waves through a zonally averaged geostrophic wind and temperature climatology of the middle atmosphere is investigated using numerical ray-tracing techniques. Strong meridional shear in the zonal wind acts to refract waves horizontally (azimuthally), leading to changes in the local propagation azimuth, horizontal wavelength, and ground-based horizontal phase speed of the wave. Unlike other identified mechanisms which can produce such changes, this refraction effect is linear and does not require (nor forbid) that the wave amplitude be unstable for it to occur. Careful treatment of wave amplitudes indicates that such refracted waves are suppressed in amplitude far less by radiative damping and saturation than previous modeling has suggested, due to the use of a more accurate radiative damping parameterization. Refraction therefore is potentially important in modifying the waves' characteristics as they propagate through the middle atmosphere, and simulations reveal modifications which agree broadly with some observational data. Multiray simulations, using a horizontally isotropic source “spectrum” of waves with equal initial amplitudes, produce wave amplitudes at a height of 60 km which exhibit variations with latitude, season, and vertical wavenumber which have much in common with observations. A dearth of waves with large horizontal wavelengths also arises, in agreement with collated observations in the upper middle atmosphere. Significant differences in the latitude-season structure of the mean wave amplitudes of the northern and southern hemisphere are simulated. The simulations reproduce the well-known change in mean azimuthal wave propagation from eastward in summer to westward in winter, but the simulated westward phase invariably exceeds 6 months in duration, and in places the eastward summer phase is very weak and of limited duration. In addition, a smaller but nonetheless distinct poleward component to the mean propagation directions arises, due in part to horizontal refraction. Comparison of measured and simulated distributions of wave propagation azimuths reveals good agreement at some locations. Mid-latitude winter distributions around North America are well simulated when only c = 0 waves are retained. However, significant differences also occur, which may reflect the importance of features omitted from this model, such as zonal atmospheric variability and/or wave source effects. These and other limitations of the present model are highlighted; it is recommended that subsequent simulations incorporate zonal refraction due to planetary Rossby wave structure, and that higher-frequency waves be included so that the impact of refraction on the vertical flux of horizontal wave momentum can be assessed.

Evidences for elastic isotropy and ultrasonic-attenuation anisotropy in Al-Mn-Pd quasi-crystals

Abstract: Very accurate ultrasonic experiments have been performed to check the elastic isotropy of Al-Mn-Pd quasi-crystals. The velocities of ultrasonic waves propagating along a twofold or a fivefold axis have been found equal to (6521 ± 10) m · s-1 for longitudinal waves and (3292 ± 3) m · s-1 for shear waves. The accuracy of these measurements is one order of magnitude better than previous results. In addition, when the polarization of the shear waves propagating along a twofold axis is changed, the velocity is constant within an experimental uncertainty of 10-4. In this paper, we also report the first experimental evidence for anisotropic ultrasonic attenuation. Such an anisotropy is expected to occur for instance if phasons and phonons are coupled in the crystal.

Transverse and longitudinal waves at the air-liquid interface in the presence of an adsorption barrier

Abstract: Sternling and Scriven1 showed that the Marangoni elasticity induced by the isothermal transfer of a surface active solute between two adjacent immiscible bulks could result in convective motion.

Nonlinear reflection of bulk acoustic waves at an interface

Abstract: A theory as the basis for solving nonlinear boundary value problems is described. A new analysis is presented for nonlinear reflection, which reveals that there is a two‐dimensional spatial increase of the second‐harmonic wave. The accretion along the propagation direction is the result of the self‐interaction of the primary wave; the one in the wave front is due to the boundary restriction.

Over-reflection and shear instability in a shallow-water model

Abstract: The characteristics of shallow-water waves in a linear shear flow are studied, and the relationship between waves and unstable modes is examined. Numerical integration of the linear shallow-water equations shows that over-reflection occurs when a wave packet is incident at the turning surface. This phenomenon can be explained by the conservation of momentum as discussed by Acheson (1976). The unstable modes of linear shear flow in a shallow water found by Satomura (1981) are described in terms of the properties of wave propagation as proposed by Lindzen and others. Ripas's (1983) theorem, which is the sufficient condition for stability of flows in shallow water, is also related to the wave geometry. The Orr mechanism, which is proposed by Lindzen (1988) as the primary mechanism of wave amplification, cannot explain the over-reflection of shallow-water waves. The amplification of these waves occurs in the opposite sense to that of Orr's solution.

From sine waves to square waves in delay equations

Abstract: Suppose fλ: ℝ→ℝ, fλ(0) = 0 and the fixed point zero undergoes a generic supercritical period doubling bifurcation at λ = 0. We characterise those small values of e > 0, λ ∈ ℝ for which there are periodic solutions of period approximately two of the equationAs e → 0, these solutions approach square waves.

Wave phenomena in the upstream region of Saturn

Abstract: A search was carried out for the signatures of waves associated with both the electron and the ion foreshocks in the upstream region of Saturn, using magnetic-field data obtained by Voyager 1 and 2 during transit through this region. Two distinct bands of wave activity were found at frequencies around 0.5-mHz and 2-mHz in the upstream region. The two classes of waves differ considerably in their properties: the 0.5-mHz waves are righthanded and strongly elliptically polarized, while the 2-mHz waves are elliptically or circularly polarized in the left-handed sense. It is suggested that the two waves may be associated with two different backstreaming particle distributions, possibly those reflected from the shock and those leaking from the hot magnetic field at frequencies between 90 and 150 mHz.

Finite-amplitude waves in deformed mooney-rivlin materials

Abstract: In a previous paper (3), Currie and Hayes showed that two linearly polarized finite-amplitude shear waves, polarized in directions orthogonal to each other and to the direction of propagation n, may propagate along any direction in a Mooney-Rivlin material which is maintained in a state of arbitrary static finite homogeneous deformation.Here, we recover this result and obtain explicit expressions for the speeds of the two waves in terms of the angles that n makes with special directions, called 'acoustic axes'. These are the only directions such that the two wave speeds are equal. They are determined only by the basic static deformation of the material. There are two such directions if this deformation is triaxial, and one if it is biaxial.Then, it is shown that, although the theory is nonlinear, the superposition of the two waves propagating along any direction is also a solution. In particular, for propagation along an acoustic axis, elliptically and circularly polarized finite-amplitude waves are possible.Finally, the energy flux and energy density of the waves are considered. © 1992 Oxford University Press.

Surface waves in an inhomogeneous elastic medium under the influence of gravity

Abstract: The present paper is concerned with the investigation of surface waves under the influence of gravity field in a non-homogeneous elastic solid medium. The theory of generalised surface waves has firstly been developed and then it is employed to investigate particular cases of waves viz. a) Rayleigh, b) Love and c) Stonely under the influence of gravity, the medium being non-homogeneous. It has been shown that the gravity field has no effect on Love waves and the velocity of Love wave lies between two quantities which are dependent on the non-homogeneities of two media

Observations of a new class of upstream waves with periods near 3 seconds

Abstract: A new class of ULF waves with periods near 3 s in the earth's upstream region is found by examining the high time resolution magnetic field data from the ISEE spacecraft. These waves are observed in the part of the upstream region which is magnetically connected to the bow shock, but only when the solar wind plasma beta is high (greater than 1). The waves are always right-handed, nearly circularly polarized in the spacecraft frame. The directions of the wave vectors are in the general direction of the average magnetic field, and the waves are convected downstream in the spacecraft frame. This study of these waves has shown that they appear to be intrinsically left-handed ion cyclotron waves in the plasma rest frame.

Wave–turbulence interaction in free‐surface channel flows

Abstract: Wave–turbulence interaction in turbulent channel flows has been studied using microbubble tracers and visualization. In the experiments, two‐dimensional waves of different lengths and amplitudes have been superimposed on a turbulent channel flow via a wavemaker. The conditions were chosen to be such that the frequencies of the interfacial waves were in the range of the ejection frequencies in the undisturbed flow. The results show that the waves cause an increase in the number of wall ejections, giving rise to an increase in the measured values of the turbulence intensities and Reynolds stresses. However, the increases in ejection frequency do not appear to be directly related to wave frequency. They correlate better with wave amplitude. Conditional averaging of the velocity fields shows that while turbulence is increased in the region below the crest of the waves (extending to the wall), it is decreased in the wave troughs. The overall effect of the surface waves, over the range of conditions investigated is, however, to increase turbulence levels.

Shallow water sediment properties derived from high‐frequency shear and interface waves

Abstract: Low-frequency sound propagation in shallow water environments is not restricted to the water column but also involves the subbottom. Thus, as well as being important for geophysical description of the seabed, subbottom velocity/attenuation structure is essential input for predictive propagation models. To estimate this structure, bottom-mounted sources and receivers were used to make measurements of shear and compressional wave propagation in shallow water sediments of the continental shelf, usually where boreholes and high-resolution reflection profiles give substantial supporting geologic information about the subsurface. This colocation provides an opportunity to compare seismically determined estimates of physical properties of the seabed with the “ground truth” properties. Measurements were made in 1986 with source/detector offsets up to 200 m producing shear wave velocity versus depth profiles of the upper 30–50 m of the seabed (and P wave profiles to lesser depths). Measurements in 1988 were made with smaller source devices designed to emphasize higher frequencies and recorded by an array of 30 sensors spaced at 1-m intervals to improve spatial sampling and resolution of shallow structure. These investigations with shear waves have shown that significant lateral and vertical variations in the physical properties of the shallow seabed are common and are principally created by erosional and depositional processes associated with glacial cycles and sea level oscillations during the Quaternary. When the seabed structure is relatively uniform over the length of the profiles, the shear wave fields are well ordered, and the matching of the data with full waveform synthetics has been successful, producing velocity/attenuation models consistent with the subsurface lithology indicated by coring results. Both body waves and interface waves have been modeled for velocity/attenuation as a function of depth with the aid of synthetic seismograms and other analytical techniques. Some results give strong evidence of anisotropy and lateral heterogeneity in shear velocity of the upper 5–10 m of sediments and of extremely high velocity gradients in the topmost 1–2 m, possibly exceeding 30 s−1.