Showing papers on "Longitudinal wave published in 1980"

Internal solitons in the andaman sea.

Abstract: The solitary wave is a localized hydrodynamic phenomenon that can occur because of a balance between nonlinear cohesive and linear dispersive forces in a fluid. It has been shown theoretically, and observed experimentally, that some solitary waves have properties analogous to those of elementary particles, and the waves have therefore been named solitons. During a measurement program in the Andaman Sea near northern Sumatra, large-amplitude, long internal waves were observed with associated surface waves called tide rips. Using theoretical results from the physics of nonlinear waves, it is shown that the internal waves are solitons and their interactions with surface waves are described.

Observation of a second bulk compressional wave in a porous medium at ultrasonic frequencies

Abstract: A second bulk compressional wave has been observed in a water‐saturated porous solid composed of sintered glass spheres using an ultrasonic mode conversion technique. The speed of this second compressional wave was measured to be 1040 m/sec in a sample with 18.5% porosity. The theory of Biot, which predicts two bulk compressional waves in porous media, provides a qualitative explanation of the observations. To the author’s knowledge, this type of bulk wave has not been observed at ultrasonic frequencies.

Confirmation of Biot’s theory

Abstract: Plona’s recent measurements of elastic‐wave speeds in a water‐saturated porous structure of sintered glass beads are compared quantitatively to the predictions of Biot’s theory. The theoretical predictions lie within the bounds of experimental error (3%) for the fast compressional wave and for the shear wave in all cases. For the slow compressional wave, the theoretically predicted speeds lie within about 10% of the experimental values and increase with increase in porosity as observed. Our model achieves this agreement with no significant free parameters. The frame moduli are estimated using a recently developed self‐consistent theory of composite materials. The induced mass of the frame in a water environment is also estimated theoretically.

Narrow-band nonlinear sea waves

Abstract: Probabilistic description of nonlinear waves with a narrow-band spectrum is simplified to a form in which each realization of the surface displacement becomes an amplitude-modulated Stokes wave with a mean frequency and random phase. Under appropriate conditions this simplification provides a convenient yet rigorous means of describing nonlinear effects on sea surface properties in a semiclosed or closed form. In particular, it is shown that surface displacements are non-Gaussian and skewed, as was previously predicted by the Gram-Charlier approximation; that wave heights are Rayleigh distributed, just as in the linear case; and that crests are non-Rayleigh.

On head-on collisions between two solitary waves

Abstract: We consider a head-on collision between two solitary waves on the surface of an inviscid homogeneous fluid. A perturbation method which in principle can generate an asymptotic series of all orders, is used to calculate the effects of the collision. We find that the waves emerging from (i.e. long after) the collision preserve their original identities to the third order of accuracy we have calculated. However a collision does leave imprints on the colliding waves with phase shifts and shedding of secondary waves. Each secondary wave group trails behind its primary, a solitary wave. The amplitude of the wave group diminishes in time because of dispersion. We have also calculated the maximum run-up amplitude of two colliding waves. The result checks with existing experiments.

Non‐WKB Alfvén waves in the solar wind

Abstract: We treat, both analytically and numerically, small-amplitude, undamped, toroidal Alfven waves in a model of axisymmetric solar wind flow in which solar rotation is neglected. There is no restriction to WKB waves; the waves may have any frequency. By transforming in simple ways the equations governing the waves we are able to obtain exact formal solutions to the general time-dependent problem as well as to the Fourier-analyzed problem. We discuss the equations and their solutions in terms of coupled inward and outward propagating waves. One integral of the equations for the Fourier amplitudes is obtained; it relates the amplitudes of the ingoing and outgoing waves. The integral is a special case of a general law of conservation of wave action, which we show to hold for finite wavelengths. The statement of the conservation of wave action is shown to be analogous to the conservation of particle-antiparticle pairs in relativistic quantum theory. We obtain the condition required for WKB waves and show that it depends on the coupling of waves in a flowing medium. The solar wind problem is discussed in terms of the Fourier amplitudes. It is shown that there is a singularity in the equations, at the Alfven point, which determines physically acceptable solar wind solutions. A qualitative account of the amplitudes far from the sun is given based on an exact solution for a model with constant solar wind flow speed. A conservation equation for the wave energy is obtained, and the relations among the wave energy density, energy flux density, force, and acceleration are stated. Numerical solutions, based on realistic solar wind profiles, are given. We show that non-WKB waves with wave periods of about a day or two have somewhat greater wave energy densities, up to a factor of 2 or so, in the corona than do WKB waves with the same amplitude at 1 A.U. On the other hand, non-WKB waves of any wave period are no more effective in accelerating the plasma than are WKB waves; they are much less effective for wave periods of a day or more. We conclude that, for conditions actually existing in the corona, WKB estimates quite accurately account throughout the corona for the wave energy density, energy flux density, and wave acceleration of the plasma for Alfven waves with periods less than about 0.05, 1, and 0.01 day, respectively; the corresponding periods in the solar wind are about 1, 1, and 0.5 day.

The gross features of the lithosphere-asthenosphere system in Europe from seismic surface waves and body waves

Abstract: Long-period recordings of dispersive Rayleigh waves along numerous station lines, or ‘profiles’, in Europe have for the first time permitted a uniform inversion of these observations based on a new method of phase velocity regionalization. Regional dispersion relations obtained by this method have then been subjected to a complete inversion procedure commonly known as the ‘hedgehog’ method. The results are presented in a map outlining the thickness of the lower lithosphere (‘lid’) and the shear (S) velocities in both the ‘lid’ and the asthenosphere ‘channel’. A comparison of these results with the minimum compressional (P) wave velocities in the asthenosphere and their corresponding depths provides an estimate of theV p /V s ratio for the asthenosphere in the European area.

The Excitation and Propagation of Elastic Waves

Abstract: Keywords: Propriete dynamique Reference Record created on 2004-09-07, modified on 2016-08-08

Solitary-wave interaction

Abstract: The interaction of solitary‐wave solutions of a model equation for long waves in dispersive media is examined numerically. It is found that the waves do not emerge from the interaction unscathed. Instead, two new solitary waves, having slightly different amplitudes from the original waves, together with a small dispersive tail are generated as a result of the interaction.

Equatorial Solitary Waves. Part I: Rossby Solitons

Abstract: Using the method of multiple scales, I show that long, weakly nonlinear, equatorial Rossby waves are governed by either the Korteweg-deVries (KDV) equation (symmetric modes of odd mode number n) or the modified Korteweg-deVries (MKDV) equation. From the same localized initial conditions, the nonlinear and corresponding linearized waves evolve very differently. When nonlinear effects are neglected, the whole solution is an oscillatory wavetrain which decays algebraically in time so that the asymptotic solution as t→∝ is everywhere zero. The nonlinear solution consists of two parts: solitary waves plus an oscillatory tail. The solitary waves are horizontally localized disturbances in which nonlinearity and dispersion balance to create a wave of permanent form. The solitary waves are important because 1) they have no linear counterpart and 2) they are the sole asymptotic solution as t→∝. The oscillatory wavetrain, which lags behind and is well-separated from the solitary waves for large time, dies o...

Long nonlinear waves in stratified shear flows

Abstract: The propagation of finite-amplitude internal waves in a shear flow is considered for wavelengths that are long compared to the shear-layer thickness. Both singular and regular modes are investigated, and the equation governing the amplitude evolution is derived. The theory is generalized to allow for a radiation condition when the region outside the stratified shear layer is unbounded and weakly stratified. In this case, the evolution equation contains a damping term describing energy loss by radiation which can be used to estimate the persistence of solitary waves or nonlinear wave packets in realistic environments. A continuous three-layer model is studied in detail and closed-form expressions are obtained for the phase speed and the coefficients of the nonlinear and dispersive terms in the amplitude equation as a function of Richardson number.

Compressional to shear wave conversion in oceanic crust

Abstract: Summary Mode conversion for compressional to shear waves or vice versa, occurs most efficiently where the seismic wave encounters a large change in seismic velocities over a distance of less than half a wavelength. In the oceanic crust, the interface between water or sediment and the volcanic basement is frequently the site of considerable mode conversion. We examine the effect of changes in the sediment and the basement properties on the efficiency of mode conversion over a range of horizontal phase velocities assuming that the interface is a first order discontinuity. We then show with the aid of synthetic seismograms calculated using the reflectivity method that a small transition zone at the top of the basement over which the velocities increase with depth may have a considerable effect on the amount of conversion. In particular, small changes in the shear wave velocity structure over thicknesses of around half the shear wavelength may markedly change the amplitudes of the variable angle basement reflection and the doubly converted lower crustal shear waves even though we may only consider compressional waves incident on and returned from the crust. Thus, at typical seismic source frequencies, a change of only a few metres to a few tens of metres in the shear wave transition zone thickness, although considerably less than the wavelength of an incident compressional wave may greatly alter the resultant compressional wave crustal seismogram.

Interaction of Ocean Waves with a Soft Bottom

Abstract: Soft muddy bottoms have significant effects on properties of water waves which propagate over them. The wave dispersion equation is modified and wave energy is dissipated by the coupling between the waves in water and those induced in the mud layer. These effects are theoretically determined by assuming a viscoelastic mud layer. A boundary-value problem is solved for the water-mud system with sinusoidal waves. The theoretical dissipation rates are compared favorably with field measurements.

System for inspecting welded joints in pipe lines by means of ultrasonic waves

Abstract: An ultrasonic flaw detection system is used for inspecting circumferentially welded joints in a pipeline. The ultrasonic probes include crystals for directing and receiving longitudinal waves reflected from the pipe interior surface in order to measure the pipe thickness. A gating device is timed on the basis of the measured pipe thickness and enables the angled crystals to receive transverse ultrasonic waves from weld defects and avoids recording reflections due to weld geometry. In addition a manipulation device having a guide band positioned around the pipe and an eccentric movable toward and away from the band may be used for clamping the carriage to the band.

Waves in an Ultra-Relativistic Electron-Positron Plasma

Abstract: Basic equations describing a macroscopic behaviour of ultra-relativistic plasma ( T ≫ m c 2 ) are formulated in a covariant form. Waves in an electron-positron plasma are investigated in a frame of two-fluid model equation. Dispersion relations for electrostatic wave, electromagnetic wave and Alfven wave propagating parallel to a constant magnetic field are shown. In the case that both electron and positron gases have same temperature, there does not exist the slow mode which corresponds to the ion acoustic wave. Right and left circular polarized waves propagate with the same dispersion relation which is different from one of the non-relativistic electron-ion plasma.

Erratum: Equivalence between fourth sound in liquid He ii at low temperatures and the Biot slow wave in consolidated porous media

Abstract: The theory of acoustic propagation in porous fluid‐filled media developed by Biot is applied to the case where superfluid 4He is in the pores (T<1.1 K where there is a negligible amount of normal fluid). For a consolidated (fused) matrix Biot’s slow compressional wave is shown to be identical to the phenomenon known as fourth sound; V(slow wave/fourth sound)=V(fluid)/n. The index of refraction of fourth sound is related to the ’’structure factor’’α, of the Biot theory by n=α1/2, and so use of the superfluid provides a direct means of measuring α in a given sample. Predictions for the velocities of the fast wave, the shear wave, and the slow wave/fourth sound are made for fused gass bead samples in which Plona has previously reported seeing these three waves under the condition of water saturation.

The generation of long waves in the laboratory

Abstract: It became evident in the experimental aspects of a recent study of the propagation of nonlinear long waves past a step and up a slope that it was important to be able to generate waves which were initially well defined. The investigation dealt with the reflection and transmission of tsunamis past the continental shelf-break, and as such, two simple waves were used to represent certain characteristics of tsunamis: solitary waves and cnoidal waves. (Both of these permanent waves are solutions to the Korteweg-de Vries equation which to a certain order describe the propagation in two dimensions of nonlinear dispersive shallow water waves (see, e.g. Whitham, 1974).) The solitary wave actually can be generated in the laboratory in a simple manner if the wave tank is long enough and wave groups trailing the main wave are unimportant to the study. An example of the resulting waves obtained in the laboratory using a crude generation, procedure is demonstrated by the oscillograph record presented in Figure 1. Six traces are shown: the one at the bottom of the figure describes the time-displacement history of a vertical bulkhead wave generator which is moved by a hydraulic-servo system, the other five are the time variations of the water surface obtained using resistance wave gages spaced at the indicated number of depths downstream from the generator. (In the example presented, the depth of water was 10 cm and the wave plate was moved linearly with time a distance of 10.33 cm in 0.8 sec.) The wave generated and first shown 10 depths downstream appears to qonsist of a large wave followed by a series of oscillatory waves (termed the tail). As would be expected, as the waves propagate, due to the frequency content and the amplitude of the waves, the system separates into a leading wave followed some distance behind by the tail. The lead wave has the characteristic shape of a solitary wave. However, if the oscillatory tail is unacceptable for the type of experiments being conducted, and if it cannot be eliminated or the method of elimination is unacceptable, then a means of generation must be sought which eliminates the trailing waves initially.

Real Time Synthetic Aperture Imaging System

Abstract: A synthetic-aperture acoustic imaging system has been developed which employs digital electronics to perform real-time imaging with a 32-element acoustic transducer array. This system has also been implemented on a computer (not real-time) so that new concepts can be tested before they are implemented in hardware. A number of real-time and computer-reconstructed images are presented to illustrate the performance of this system, including images obtained using longitudinal waves in a water tank and Rayleigh (surface) waves on aluminum samples. Computer-generated contour plots are shown to illustrate the point response of this system and to demonstrate the resolution and sidelobe levels obtained with this synthetic-aperture technique.

The Excitation and Propagation of Elastic Waves

Abstract: J A Hudson 1980 Cambridge: Cambridge University Press viii + 226 pp price £14 Elastic waves in solids can involve shear strain as well as compression, and the two types are capable of separate existence in a homogeneous, unbounded medium. At interfaces they interact, giving rise to special motions such as Rayleigh waves, Stoneley waves and Love waves.

Determination of the impact response of PMMA using combined compression and shear loading

Abstract: Large amplitude one‐dimensional compression and shear wave measurements have been made in polymethyl methacrylate (PMMA). Measurements of shear and longitudinal wave velocities were used to determine the shear modulus, bulk modulus, and the mean stress‐volume relations under impact loading. The mean stress‐volume relation determined from impact data is considerably stiffer than the static hydrostat often used to interpret shock data and leads to a lower strength in shock wave data. Unlike the quasi‐static‐uniaxial strain results, the shock data show strength reduction at higher stresses. Measurement of shear wave amplitudes, at different compressive stresses, independently support the strength loss determined from wave velocity analysis. Measurement of shear particle velocity at the impact surface shows that the dynamic friction behavior of PMMA depends on the inelastic material response near the surface.

Experimental facility to produce and measure compression and shear waves in impacted solids

Abstract: An impact facility has been designed and constructed to produce and measure large amplitude one‐dimensional compression and shear waves in solids. Design considerations and experimental details to produce the necessary impact configuration and to measure the particle velocity profiles resulting from compression and shear waves are described. Experimental results are presented to show that the impact facility was satisfactorily constructed. After a brief discussion of shear wave measurements, the experimental measurements made under compression and shear loading in polymethyl methacrylate and polycrystalline aluminum oxide are presented. These results are expected to provide new information on material response at high strain rates.

Fluid wave propagation in saturated and nearly saturated sands

Abstract: Impacts at the end of a 4-ft (1.22-m) long test chamber developed compression waves in saturated and nearly saturated sands. The wave velocities depended upon the void ratio, void size, particle compressibility, particle shape, specific gravity, and degree of saturation. Of these variables, degree of saturation was the most important. A decrease from 100% to 99.7% saturation could reduce the wave velocity by a factor of two. The time to reach 100% saturation, from about 99% saturation, was on the order of one month when the fluid pressure was 75 psi (517.5 kN/m²). These results indicate that sand embankments adjacent to tidal zones or reservoir fluctuations are probably not completely saturated. Thus, propagation of compression waves in the pore fluids of such structures will be reduced below the fully saturated values.

Correct reproduction of group-induced long waves

Abstract: In nature short period storm waves generate longer waves with periods corresponding to the wave group periods. The long waves are generally referred to as the wave set-down of water level. The set-down term is of second order in the height of the short waves. With first order reproduction of natural storm waves in the laboratory, the setdown bound to the wave groups is not reproduced. As a result, various free waves are generated, propagate towards the model and reflect from the boundaries. These so-called parasitic waves cause an exaggeration of long wave phenomena, such as harbour resonance and slow drift oscillations of moored ships. The parasitic waves can be eliminated by means of compensating free waves imposed on the system by second-order paddle motion reproducing the natural set-down. The control signal for this motion has been calculated and checked by testing. The agreement between calculated and measured results is found to be good. Further, an alternative method for reducing the parasitic wave problem is presented. Utilizing the shoaling properties of the various waves, the influence of parasitic waves can be diminished by generating the waves in somewhat deeper water before they propagate into the shallower model area.

Resonant scattering of elastic waves from spherical solid inclusions

Abstract: Previous investigation concerning the scattering of elastic waves from solid spherical inclusions have furnished expressions for the scattering cross sections which, upon numerical evaluation, exhibited resonancelike features as a function of frequency. In the present work, we study these resonances in a fashion suggested by the resonance theory of acoustic scattering due to Flax, Dragonette, and Uberall [J. Acoust. Soc. Am. 63, 723 (1978)]. The resonances of the solid inclusions, exemplified by iron or lucite spheres imbedded in an aluminum matrix, are found numerically in the individual normal‐mode scattering amplitudes, and are interpreted in terms of phase‐matched circumferential waves. Dispersion curves for the phase velocities of the latter are obtained, exhibiting two families of waves of different type. Finally, the connection of these waves with the Stonely waves on the boundary between two flat half‐spaces is noted in high‐frequency limit.

Theoretical analysis of observed second bulk compressional wave in a fluid-saturated porous solid at ultrasonic frequencies

Abstract: We show that the second bulk compressional wave observed recently in an experiment by Plona is consistent with the ’’slow’’ compressional wave as predicted by Biot’s theory. We present dispersion and attenuation curves for all of the body waves for Plona’s samples computed as a function of frequency and Biot’s structure factor S. At high frequencies the velocity of the slow compressional wave is approximately equal to Vf/ S1/2, where Vf is the normal compressional‐wave velocity in the pore fluid. Thus, from the measured velocities of slow compressional waves one can obtain S. For Plona’s three samples, the predicted structure factors are 2.1, 2.2, and 3.3.