Showing papers on "Longitudinal wave published in 1976"

Linear and Nonlinear Waves

Abstract: Keywords: ondes ; chocs ; onde de : choc Reference Record created on 2005-11-18, modified on 2016-08-08

Estimation of incident and reflected waves in random wave experiments

Abstract: A technique to resolve the incident and reflected waves from the records of composite waves is presented. It is applicable to both regular and irregular trains of waves. Two simultaneous wave records are taken at adjacent locations, and all the amplitudes of Fourier components are analyzed by the FFT technique. The amplitudes of incident and reflected wave components are estimated from the Fourier components, and the incident and reflected wave spectra are constructed by smoothing the estimated periodograms. The wave resolution is effective in the range outside the condition of the gauge spacing being even integer of half wavelength. The ratio of incident and reflected wave energies in the effective resolution range is employed in estimating the overall reflection coefficient. The incident and reflected wave heights are estimated from the composite wave heights by energy consideration.

Interaction of Water Waves and Currents

Abstract: Publisher Summary This chapter discusses the varied physical circumstances in which interactions among water waves and currents occur. Different mathematical approaches, relevant observations, and experiments that are applicable to all or some of these physical circumstances are described. The emphasis is on waves and their interaction with preexisting currents rather than on wave-generated currents. Common simplifying assumption is that the waves are of sufficiently small amplitude for the free-surface boundary conditions to be linearized and evaluated at, or close to, the mean free surface. Most progress can be made in this subject with such a constraint, but wherever possible, finite-amplitude effects are discussed. Unlike some other common forms of wave motion, water waves involve water motion varying with direction perpendicular to the space in which they propagate. The chapter concludes on the interaction of waves generated by a ship with the flow around it.

Velocities of seismic waves in porous rocks

Abstract: Velocities of seismic compressional and shear waves in porous rocks under different saturation conditions are calculated theoretically and compared with laboratory data. For theoretical formulations, the rocks are represented by a solid matrix and pores of spherical and oblate spheroidal shapes. The effect of confining pressure on velocities is calculated by taking into account pore closing and saturant compressibilities.The theoretical calculations show that with all other parameters fixed, thin pores (small aspect ratios) have much greater effects on elastic moduli and velocities than rounded pores at the same concentration. The properties of the saturating fluid (gas, oil, or water) have greater effects on the compressional velocities than on shear velocities. The velocities of compressional waves are higher when the rock is saturated with water than when it is dry or gas-saturated. For shear waves the behavior is generally opposite, with shear velocities higher in the dry or gas-saturated case than in the water-saturated case.Compressional and shear velocities measured as a function of pressure in laboratory samples of granite, limestone, and sandstone, under dry and water-saturated states, are fitted with theoretical curves and pore shape spectra which fit the data are calculated. A spectrum of pore shapes ranging from spheres to very fine cracks (aspect ratios 1 to 10 (super -5) ) is required to fit the data. Theoretical velocities calculated using these models fit the measured velocities in water-saturated and frozen rocks, as well as the compressional velocities in partially saturated rocks.With the rock models derived on the basis of laboratory data, theoretical seismic velocities are calculated for various pressures and temperatures for reservoir rocks fully or partially saturated with gas, oil, or brine. Compressional velocities are highest for brine saturation and lowest for gas saturation. The difference decreases with increasing pressure. The presence of a small amount (5 percent) of gas in brine as an immiscible mixture reduces the compressional velocities significantly, even below those of fully gas-saturated values at some pressures.The reflection coefficients for compressional waves at a gas-brine interface in a model of a sandstone are high at pressures corresponding to shallow and moderate (less than about 8000 ft) depths. At greater confining pressures, reflection coefficients become small, except when the pore fluid pressure (gas pressure) is very high. Thus, large reflections or 'bright spots' from great depths may indicate overpressured formations. The reflection coefficients from mixed gas-brine interfaces are lower than those of pure gas interfaces. A combination of interval velocities and reflection amplitudes may help identify the mixed gas-brine reservoirs. Poisson's ratios for gas-saturated rocks are lower than those for brine-saturated. This difference persists to great depths.

Banded Convective Activity and Ducted Gravity Waves

Abstract: Convective activity is frequently organized into band-like structures with space and time scales appropriate to internal gravity waves. When the convective activity involves cumulonimbus, then latent heat release can form a significant energy source for the waves which in turn may organize the convection [as described, for example, by wave-CISK (Lindzen, 1974; Raymond, 1975)]. However, in other cases strong forcing is absent and the existence of the waves requires the existence of a duct from which very little wave energy leaks. We show that the energy cannot be contained by an inversion. Instead, we find that a stable duct adjacent to the surface must be capped by an unstable layer wherein the mean flow at some level either equals or comes close to the phase speed of the ducted waves. We also find that the wind amplitudes associated with the observed pressure amplitudes in these waves are consistent with observed squall winds. Finally, we find that the horizontal scales of mesoscale waves are cl...

Wave propagation along a magnetic tube

Abstract: Motivated by the filamentary structure of solar magnetic fields, this paper considers the propagation of quasi-longitudinal waves along a slender magnetic tube in pressure equilibrium with the ambient medium. The velocity of such waves is expressed in terms of the Alven speed and the sound speed inside the tube. The divergence of a vertical magnetic tube in a stratified atmosphere introduces a critical frequency below which propagation is impossible.

Parametric decay of electromagnetic waves into two plasmons and its consequences

Abstract: The parametric decay of the laser radiation into two plasma waves at the quarter critical density of an inhomogeneous plasma is analyzed. The growth rate and threshold of the absolute instability are derived. The bound on the saturation level of the plasma waves is obtained from the consideration of the pump depletion. The scattered radiation at 3/2 ω0 due to the beating of the incident wave with the backward plasma wave is calculated and compared with observations.

Relativistic nonlinear plasma waves in a magnetic field

Abstract: Five relativistic plane nonlinear waves were investigated: circularly polarized waves and electrostatic plasma oscillations propagating parallel to the magnetic field, relativistic Alfven waves, linearly polarized transverse waves propagating in zero magnetic field, and the relativistic analog of the extraordinary mode propagating at an arbitrary angle to the magnetic field. When the ions are driven relativistic, they behave like electrons, and the assumption of an 'electron-positron' plasma leads to equations which have the form of a one-dimensional potential well. The solutions indicate that a large-amplitude superluminous wave determines the average plasma properties.

The effects of pressure, temperature, and pore water on velocities in westerly granite

Abstract: A description is presented of an experimental assembly which has been developed to conduct concurrent measurements of compressional and shear wave velocities in rocks at high temperatures and confining pressures and with independent control of the pore pressure. The apparatus was used in studies of the joint effects of temperature, external confining pressure, and internal pore water on sonic velocities in Westerly granite. It was found that at a given temperature, confining pressure has a larger accelerating effect on compressional waves in dry rock, whereas at a given confining pressure, temperature has a larger retarding effect on shear waves.

Resonant interactions for waves breaking.on a beach

Abstract: A laboratory and theoretical study of the transition from strongly reflected surging to dissipative plunging breakers on a relatively steep plane beach (1:8) has revealed the following: (1) The run-up and offshore variation of sea surface elevation of surging waves are well predicted by linear theory. (2) The fluctuating part of the run-up (related to the amplitude of the reflected incident wave) reaches a maximum value; a further increase in incident progressive wave energy results in increased dissipation. (3) Subharmonic edge waves (the growing instabilities of surging waves) are driven primarily by the swash motion, which does not increase with increasing incident breaking wave height. However, the turbulence accompanying incident wave breaking, and the effective eddy viscosity, rapidly increases with increasing breaker height. As a result, subharmonic resonances do not occur with spilling or steep plunging waves; very strong viscous effects suppress the nonlinear instabilities. (4) edge waves generated by a surging incident wave can be suppressed by superimposing an additional breaking wave of different frequency on the incident wave field. Thus, any excited edge waves are likely to have length scales at least the order of a surf zone width.

Bow Shock and magnetosheath waves at Mercury

Abstract: Mariner 10 measurements at the Mercury bow shock provide examples where the magnetic field is approximately parallel or perpendicular to the bow shock normal. Upstream of a broad irregular parallel shock, left hand circularly polarized waves are observed which cut off very sharply at approximately 4 Hz. Upstream of a perpendicular shock, right hand circularly polarized waves are observed which persist up to the Nyquist frequency of 12 Ha. Determination of the wave propagation vector as a function of frequency helps conclusively identify the waves as whistler mode waves propagating from the shock. The magnetosheath downstream of the parallel shock is disturbed more than that downstream of the perpendicular shock particularly below 1 Hz. In the latter case regular left hand polarized waves observed slightly above the proton gyrofrequency are identified as ion cyclotron waves with wavelength approximately 300 km which are Doppler shifted up to their observed frequency.

Nonlinear theory of acoustic-gravity waves 1. Saturation and enhanced diffusion

Abstract: A method is presented for calculating the nonlinear properties and effects of internal acoustic-gravity waves. This method is referred to as perturbed orbits or modified orbits and has been widely used in theories of plasma waves. The basis of this method is to express nonlinear wave oscillation in terms of the orbits of the particles of the medium. The task of calculating nonlinear wave effects is thus transformed to calculating particle orbits. The latter task is simplified by the use of elementary statistical techniques such as cumulant expansions. The method of perturbed orbits is also closely related to the direct interaction approximation, which has been so useful in theories of fluid turbulence. This method is applied to calculate the nonlinear saturation (self-limited) amplitude of atmospheric gravity waves. Here, saturation amplitude refers to the amplitude of gravity waves above which nonlinearities are strong enough to stop the wave from growing with height. The saturation amplitude is the largest amplitude a gravity wave spectrum can attain. The present results for the saturation amplitude are compared with gravity wave amplitudes observed in the mesosphere. A calculation is also made of the enhancement of atmospheric diffusion by gravity waves. The enhanced diffusion coefficient plays an important role in the present theory, and its predicted value is consistent with observations of enhanced transport in the mesosphere.

On the Speed and Profile of Steep Solitary Waves

Abstract: Previous estimates of the speed of solitary waves in shallow water unexpectedly showed that the speed and energy were greatest for waves of less than the maximum possible height. These calculations were based on Pade approximants. In the present paper we present some quite independent calculations based on an integral equation for the wave profile (Byatt-Smith 1970), now modified so that the wave speed appears as a dependent variable. There is remarkably good agreement with the previous method. In particular the existence of a maximum speed and energy are verified. The method also yields a more accurate profile for the free surface of steep solitary waves. As the wave amplitude increases, it is found that the point of intersection of neighbouring profiles moves up towards the crest. Hence the highest wave lies mostly beneath its neighbours, which helps to explain why its speed is less. Tables are given not only of the wave speed but also of the maximum surface slope as a function of wave amplitude. In no case does the slope exceed 30 degrees, but for still higher waves this possibility is not excluded.

Reflection, Transmission and Attenuation of Elastic Waves at a Loosely-Bonded Interface of Two Half Spaces

Abstract: Summary The problem of reflection and transmission of a longitudinal plane periodic wave incident on the interface between loosely-bonded half spaces is investigated by assuming that the interface behaves like a dislocation which preserves the continuity of traction while allowing a finite amount of slip. The wave equations are solved by imposing further the interface conditions that the normal displacement is continuous and that the shearing stress is proportional to velocity of slip. The results of numerical calculations are given in the form of graphs for different degrees of bonding, ranging from no bonding (zero shear stress) to full bonding (welded contact) between the half spaces. It is found that the elastic wave energy is attenuated at a loosely-bonded interface except at normal incidence, grazing incidence and at (approximately) critical incidence of the longitudinal wave at the interface.

Instability as a source for traveling ion waves

Abstract: Low‐frequency instability is excited by passing a dc electron current in a collisionless Q‐machine plasma. The current is driven by applying a positive bias to a grid situated between the hot plate and the cold end plate. The instability shows a standing‐wave pattern between the hot plate and the grid. The frequency can be controlled by varying the hot plate‐grid separation. This instability is used as a source for excitation of traveling waves behind the grid. The excited waves have the same dispersion relation as ion waves excited by applying external signals to the grid.

Observation of Transverse Zero Sound in Normal He 3

Abstract: The direct transmission of transverse zero sound between two $\mathrm{AC}$-cut quartz transducers is observed in the vicinity of 3 mK; at higher temperatures the transition to classical viscous shear-wave behavior is observed through the effect on the damping of a single transducer.

Breaking of Large-Amplitude Waves as a Result of Relativistic Electron-Mass Variation

Abstract: The role of the relativistic electron-mass variation in the evolution of large-amplitude electromagnetic waves near cutoff and in the generation of plasma waves by linear mode conversion is investigated. Shock formation and subsequent wave breaking along the electric field of the wave will enhance the absorption of the wave by the plasma.

Interaction of waves and a turbulent current

Abstract: An experimental investigation was made to study wave-current interaction. Wave amplitude attenuation was measured along a laboratory wave channel to compare wave dissipation with and without flow. Mean, wave, and turbulent velocities were also measured to determine the modifications of the flow imposed by the gravity waves propogating with the current. The process of energy transfer in the wave current system was studied. Energy was found to be extracted from the waves, diffused downward and dissipated by an increase in bottom shear stress.

Electromagnetic wave ring resonator

Abstract: An electromagnetic wave ring resonator is disclosed including means to spatially rotate the electromagnetic field distribution of waves resonant therein about the direction of propagation of such waves to enable such waves to resonate with opposite senses of circular polarization, and means, including a laser amplifier medium, to provide different indices of refraction to resonant waves of the same sense of circular polarization as they pass through such laser amplifier medium in different directions. With such arrangement the two mentioned means enable the waves to resonate with four different frequencies. In a laser gyroscope using such ring resonator the electromagnetic field distribution rotating means includes a catoptric arrangement which, together with the last-mentioned means, reduces the loss, scatter and linear birefringence associated with the ring resonator included in such gyroscope. The last-mentioned means produces the Zeeman effect in the laser medium and efficiently provides different optical pathlengths for waves passing through such medium because the magnetic field vector of such waves interacts with the processing atomic magnetic dipoles of the amplifier medium at the emission frequency of such amplifier medium.

On the Interaction Between Long and Short Surface Waves

Abstract: Short, dissipative, surface waves superposed on longer waves cause a growth of the long wave momentum Ml at a ratewhere kl, al are the amplitude and wavenumber of the long waves, so that klal is their steepness; Sa is the radiation stress of the short waves and τs, the rate of transfer of momentum to the short waves by the wind; and the angle braces denote an average over the long-wave phase θ = klx−ωlt. The first term in the above equation is the radiation stress interaction (Phillips, 1963; Hasselmann, 1971) and is generally negligible compared with the second term, neglected by Hasselmann (1971), which shows that long waves can grow if short wave generation (rather than dissipation) is correlated with the long wave orbital velocity. Even if the modulation of τs is only O(klal) times 〈τs〉, this mechanism can contribute a significant fraction of long wave momentum. However, even a substantially greater modulation of τs, perhaps due to varying exposure of short waves to the wind, is unlikely to a...

Nonlinear coupling of polarized plasma waves

Abstract: Weak nonlinear coupling between two polarized transverse waves in a weakly relativistic plasma is studied including the effect of dispersion. The frequency of the coupled waves is of the same order of magnitude as the electron plasma frequency. By using the multiple scale method it is shown that the slow modulation of the complex amplitudes is described by simultaneous nonlinear Schrodinger equations. Travelling wave solutions are then obtained for this system of equations by the analytical and the numerical methods. As the result of the wave-wave interaction, two envelope waves are, in general, composed of dispersive shock waves or non-periodic nonlinear wave-trains, while the usual solitary waves or periodic nonlinear wave-trains can exist as a special case. case. The results of analysis can readily be applied to other coupled waves with different polarizations in a nonlinear dispersive medium.

Electromagnetic generation of electronically steered ultrasonic bulk waves

Abstract: The frequency dependence of the propagation direction of ultrasonic shear and longitudinal waves generated by a meander‐line electromagnetic transducer (EMAT) at MHz frequencies has been determined. The results are found to agree well with theory and demonstrate that electronic beam steering is possible using EMAT’s. The relative efficiency of generation in aluminum was also studied and, for a specific meander‐line geometry with a permanent magnet providing the necessary static magnetic field, it was found to be relatively flat versus frequency. Efficiency for shear‐wave generation (frequency range, 5–9 MHz) was about 4 dB per conversion less than the Rayleigh‐wave generation efficiency at 4.6 MHz, and for longitudinal waves (frequency range, 10–24 MHz) about 10 dB less.

Short-wave asymptotics for weak shock waves and solitons in mechanics

Abstract: Some recent applications of the theory of non-linear waves in smoothly inhomogeneous and weakly dissipative media are discussed in the paper. The possibilities of “linear-ray” approximation when the non-linear self-refraction effects may be neglected in comparison with the non-linear wave distortion along the rays are demonstrated for weak acoustic shocks in stratified atmospheres and ocean, the solitary waves in shallow water of variable depth and the solitons in elastic rods.

Leakage and response of waves trapped by round islands

Abstract: A study of surface wave trapping by typical islands of small seabed slope is reported. A new formulation is proposed which includes all the established approximations, but also permits treatment of trapping with energy leakage and complex eigenfrequencies. On this basis, we prove existence of eigenvalues with very small leakage and correspondingly large response to excitation by incident waves. Indeed, certain types of trapped wave modes have exponentially small leakage and therefore, a violently resonant character. Two physical effects are found to promote such resonance: It is typical of waves that bear a close local resemblance to coastal edge waves. It also occurs for waves of large radial wavenumber component. Both effects can combine to produce especially strong resonance. The strongly resonant wave modes have a structure more complicated than is commonly considered important, but still clear‐cut enough to permit characterization by an eigenvalue problem for an ordinary differential equation. It has...

Strong transverse electromagnetic waves in overdense plasmas

Abstract: I present a new class of exact solutions for strong transverse electromagnetic waves in a cold overdense plasma, which incorporates both the exact traveling-wave and standing-wave solutions. The waves are circularly polarized, and the dielectric constant of the plasma is a function of z. (AIP)

The Possibility of Assigning a Signature to Rough Surfaces Using Ultrasonic Backscattering Diagrams

Abstract: Summary It is suggested that ultrasonic waves can be used in NDE as a reliable tool for quantitative flaw characterization. A model is developed in which a flaw in a metal diffracts (scatters) incident ultrasonic waves. An electromagnetic type of diffraction theory was used, and expressions for the diffracted fields were obtained for circular and elliptical crack-like flaws. Corresponding broadband scattering experiments were carried out using as targets metal shims in water, flat-bottomed holes in metals, and cavities embedded in diffusion-bonded samples. The scattered shear and longitudinal waves could be separated due to their differing velocities and were separately analyzed. Experiments agree well with theoretical predictions for the case of crack-like flaws. Significant information can be obtained concerning the shape of the cavities using both shear and longitudinal waves. With further experimental and theoretical developments, these model studies might develop into quantitative characterization of real flaws.

Characteristics of flow in run-up of periodic waves

Abstract: The run-up of waves is an important factor in the design of shore structures. It has been investigated in many studies, both theoretical and experimental. The experimental studies have mostly been confined to the maximum run-up (the greatest height above still water level, reached by the periodic waves on the slope). A simple and reliable formula for the maximum run-up is given by Hunt (I), based on measurements with periodic waves breaking on smooth plane slopes. However, virtually no data are available regarding the characteristics of the flow in the up-rush and the down-rush on a smooth slope, such as layer thickness, particle velocity, wave front velocity, and so on. Such information can be of use in developing or adjusting schemes for numerical calculation of run-up and overtopping, as well as in problems of stability of cover layer material or of seepage of water into the core material of a dike. The purpose of this report is to present empirical results concerning the above-mentioned flow parameters, obtained from experiments with periodic waves breaking on smooth plane slopes. In the analysis of the data considerable attention is given to similarities in the run-up process; the existence of such similarities had previously been inferred from Hunt's formula for the maximum run-up height.

Phase Memory and Additional Memory in W.K.B. Solutions for Wave Propagation in Stratified Media

Abstract: For a wave travelling obliquely in a stratified inhomogeneous medium the W. K. B. solution contains a phase memory term that expresses the cumulative change of complex phase as the wave propagates. This memory may have two parts. One is the familiar phase memory displayed in all cases. The other is an additional memory that has recently been shown to be important for radio waves in an anisotropic ionosphere, but it is not present for an isotropic ionosphere. The subject is examined here for some other types of wave in geophysics and atmospheric physics. It is shown that there can be an important additional memory for atmospheric acoustic gravity waves, and a small additional memory in some other cases including seismic waves when Coriolis force is allowed for, and electromagnetic waves in a stratified optically active but isotropic medium. For magnetohydrodynamic waves there is additional memory if a gravitational field is present, but not otherwise.