Showing papers on "Longitudinal wave published in 1979"

Attenuation of seismic waves in dry and saturated rocks; I, Laboratory measurements

Abstract: The attenuation of compressional (P) and shear (S) waves in dry, saturated, and frozen rocks is measured in the laboratory at ultrasonic frequencies. A pulse transmission technique and spectral ratios are used to determine attenuation coefficients and quality factor (Q) values relative to a reference sample with very low attenuation. In the frequency range of about 0.1–1.0 MHz, the attenuation coefficient is linearly proportional to frequency (constant Q) both for P‐ and S‐waves. In dry rocks, Qp of compressional waves is slightly smaller than Qs of shear waves. In brine and water‐saturated rocks, Qp is larger than Qs. Attenuation decreases substantially (Q values increase) with increasing differential pressure for both P‐ and S‐waves.

Attenuation and dispersion of compressional waves in fluid-filled porous rocks with partial gas saturation (White model); Part I, Biot theory

Abstract: An exact theory of attenuation and dispersion of seismic waves in porous rocks containing spherical gas pockets (White model) is presented using the coupled equations of motion given by Biot. Assumptions made are (1) the acoustic wavelength is long with respect to the distance between gas pockets and their size, and (2) the gas pockets do not interact. Thus, the present theory essentially is quite similar to that proposed by White (1975), but the problem of the radially oscillating gas pocket is solved in a more rigorous manner by means of Biot’s theory (1962). The solid‐fluid coupling is automatically included, and the model is solved as a boundary value problem requiring all radial stresses and displacements to be continuous at the gas‐brine interface. Thus, we do not require any assumed fluid‐pressure discontinuity at the gas‐water contact, such as the one employed by White (1975). We have also presented an analysis of all of the field variables in terms of Biot’s type I (the classical compressional) w...

Long-wave elastic anisotropy in transversely isotropic media

Abstract: Compressional waves in horizontally layered media exhibit very weak long‐wave anisotropy for short offset seismic data within the physically relevant range of parameters. Shear waves have much stronger anisotropic behavior. Our results generalize the analogous results of Krey and Helbig (1956) in several respects: (1) The inequality (c11-c44)(c33-c44)⩾(c13+c44)2 derived by Postma (1955) for periodic isotropic, two‐layered media is shown to be valid for any homogeneous, transversely isotropic medium; (2) a general perturbation scheme for analyzing the angular dependence of the phase velocity is formulated and readily yields Krey and Helbig’s results in limiting cases; and (3) the effects of relaxing the assumption of constant Poisson’s ratio σ are considered. The phase and group velocities for all three modes of elastic wave propagation are illustrated for typical layered media with (1) one‐quarter limestone and three‐quarters sandstone, (2) half‐limestone and half‐sandstone, and (3) three‐quarters limesto...

Compressional and shear waves in saturated rock during water-steam transition

Abstract: Compressional and shear wave velocities were measured in water-filled Berea sandstone as a function of pore pressure, with a constant confining pressure of 300 bars. The measurements were made at room temperature, 145°C, and 198°C. At 145°C, compressional velocity increased from vapor-saturated (low pore pressure) to liquid-saturated (high pore pressure) conditions, whereas shear wave velocity decreased. For Compressional waves there was a velocity minimum and increased attenuation near the liquid-vapor transition. The results at 198°C show decreases of both compressional and shear velocities and a small velocity minimum for compressional velocity without marked attenuation. At both temperatures, Vp/Vs and Poisson's ratios increased from steam- to water-saturated rock. The results are compatible with the mechanical effects of mixing steam and water in the pore space near the phase transition and may be applicable to in situ geothermal field evaluation.

Generation of horizontally polarized shear waves in ferromagnetic materials using magnetostrictively coupled meander‐coil electromagnetic transducers

Abstract: A new electromagnetic transducer configuration is described for generating horizontally polarized shear (SH) waves in ferromagnetic materials. The transducer consists of a meander coil and static bias magnetic field parallel to the coil elements. This configuration generates no ultrasonic waves in a nonmagnetic metal since the induced eddy currents are parallel to the bias field and the driving Lorentz forces vanish. However, the configuration provides coupling to SH waves in ferromagnetic materials through magnetostrictive effects. Experimental measurements of the variation of transduction efficiency with bias field in nickel and 4130 steel plate are presented and compared to the efficiency obtained with the same meander coils when the bias is rotated 90° in the plane of the plate so that antisymmetric Lamb waves are generated. Peak efficiencies occur at considerably different bias fields for the two configurations. This result, as well as other features in the data, are interpreted in terms of a simple ...

Hydromagnetic surface waves

Abstract: Plane and filamentary structures aligned with a magnetic field abound on the Sun and in both interplanetary and interstellar space. When the Alfven speed changes across such boundaries, hydromagnetic surface waves can travel along them, carry energy, and provide heating. This paper surveys the nature of such surface waves, with emphasis on the dispersion relations, the spatial extent of the waves, the degree of gas compression, and the possibility of coupling to ordinary hydromagnetic waves. Explicit results are provided for the cases when the gas pressure is either much smaller or much larger than the magnetic pressure on either side of the surface. The waves are shear waves wherever p< or =B/sup 2//8..pi... All surface waves involve finite gas compression, but this compression is negligible when kxBvery-much-less-thankB.

Third-order approximation to short-crested waves

Abstract: Short-crested wave systems, as produced by two progressive waves propagating at an oblique angle to each other, have an extremely important effect on a sedimentary bed. The complex water-particle motions are conducive to lifting material into suspension and sustaining it in motion. In order to study this phenomenon rigorously, the variables of this wave system are derived to a third-order approximation by a perturbation method. The case of waves reflecting obliquely from a vertical wall is examined under the assumptions of full reflexion, uniform finite depth and an inviscid incompressible fluid. The new formulation reduces to standing or Stokes waves at the limiting angles of approach. Expressions for kinematic quantities are also presented.

A Theory of Stationary Long Waves. Part II: Resonant Rossby Waves in the Presence of Realistic Vertical Shears

Abstract: In Part I a simple theory of resonant Rossby waves in a uniform zonal flow was developed. The present paper extends the previous results to the case of an atmosphere with winds varying with height. The wave responses to a large number of physically possible wind configurations are studied to help determine whether the observed wind fields in the winter atmosphere permit resonance of the large-scale waves and, in cases where resonance is possible, to search for the most favorable conditions for resonance. It is found that an increase in stratospheric jet strength and the descent of the stratospheric jet are both capable of exciting the resonant waves of zonal wavenumbers 1 and 2, with the latter (the descent of the stratospheric jet) being most effective in resonating the large-scale waves. The shorter waves (with zonal wavenumbers 3, 4 and up) are found to be insensitive to changes in wind conditions in the stratosphere as they are mostly trapped in the troposphere. These waves are easier to exci...

Nonlinear effects upon waves near caustics

Abstract: According to linear theory the wave intensity of a slowly varying wave train becomes particularly large near caustics. In this paper it is shown how the waves are modified when the wave intensity is sufficient for nonlinear effects to begin to be important. Two types of near-linear caustics can arise in which nonlinearity either tends to advance or to retard the reflexion of waves from the caustic. General examples are given in terms of one-dimensional wave propagation, and of propagation in a uniform medium. Detailed consideration is given to a particular example: small-amplitude water waves on deep currents. This helps to provide an interpretative framework for the large-amplitude results presented in the companion paper (Peregrine & Thomas 1979). For the more exceptional case of triple roots, or cusped caustics, the increase in wave intensity is even more dramatic. In three appendices the analysis for caustics is extended to some higher-order cases.

Laser‐induced Rayleigh waves in aluminum

Abstract: A bulk aluminum‐alloy irradiated with a Q‐switched Nd‐glass laser shows three distinct elastic waves: longitudinal, transverse, and Rayleigh (surface) waves. The elastic‐wave velocities agree with those measured by more familiar methods.

Mass transfer, marangoni effect, and instability of interfacial longitudinal waves: I. Diffusional exchanges

Abstract: A general formalism is developed to study interfacial instability of two immiscible incompressible fluids. Mass diffusion fluxes across the interface are the determining step. The surface mass balance equation depends upon the surface diffusion and convection and on the net flux. Discussion is restricted to longitudinal perturbations. Using the concept of surface elasticity, necessary and sufficient instability conditions for oscillating and non oscillating regimes are given for long wavelengths. The obtained criteria are extensions of the Sternling and Scriven ones.

A Theory of Stationary Long Waves. Part III: Quasi-Normal Modes in a Singular Waveguide

Abstract: The present paper deals with the fundamental issue of whether one can treat waves as normal modes when critical surface, where the phase speed of the wave matches the zonal wind speed, are present. In particular the question of whether a Rossby critical level (such as the zero-wind line for stationary waves) is absorbing or reflecting is raised and subsequently addressed. It is found that the critical level is never totally absorbing; Rossby waves are partially reflected even if the critical layer is dominated by dissipative processes. The relevance of nonlinearity in planetary-scale Rossby wave critical layers is also discussed and it is found to be the dominant mechanism. With the relative magnitudes of nonlinearity versus viscosity relevant to the earth's atmosphere it is found that the steady-state critical level should be almost perfectly reflecting to incident Rossby waves. Consequently, normal-mode solutions can be found; the quantization condition for these waves is also derived.

HF radar studies of two‐stream instability during an equatorial counter‐electrojet

Abstract: A very strong daytime counter-electrojet was observed on January 21, 1977, near the magnetic equator in Africa. This phenomenon was investigated for the first time using simultaneous magnetic and radar measurements. As predicted by the linear theory, irregularities associated with the two-stream instability were detected in the absence of the usual turbulence related to the cross-field effect (or type 2 irregularities). In addition, taking advantage of the refraction of the HF radio waves in the E layer, horizontal or quasi-horizontal plasma waves were detected for the first time together with the usual oblique waves. Two kinds of spectra were then distinguished from the radar observations: (1) Spectra associated with oblique waves which do not have the usual behavior of type 1 (their phase velocity is dependent on time and angle of incidence) and (2) type H spectra associated with horizontal or quasi-horizontal waves which have a smaller phase velocity (constant with time and range) and a larger amplitude than oblique waves. Among different hypotheses we presume that the quasi-linear reduction of the polarization electric field at the bottom of the instability layer explains the constant value of the phase velocity of the horizontal waves. The absence of turbulence (or type 2) would be the source of the difference observed beween oblique waves and usual type 1.

Surface waves in a pre-stressed elastic body

Abstract: The bearing of the Barnett–Lothe formulation of the theory of elastic surface waves in a crystalline medium on surface motions of a pre-stressed elastic body is examined in this paper. The main results are a general uniqueness theorem and the notion of a neutral set, bounding the domain of existence of surface waves and interpretable as the totality of standing wave solutions. As an application of these ideas a full account is given of the existence of surface waves in a homogeneously deformed elastic body possessing a restricted form of the Hadamard strain-energy function. In conclusion, the difficulties involved in treating an analysis of surface waves as a test of the stability of a loaded semi-infinite elastic body are briefly discussed.

Ion-acoustic solutions and shock waves in multicomponent plasmas

Abstract: The present investigation of ion-acoustic waves is based on the study of the nonlinearity of plasma waves in a dispersive medium. Here the authors study ion-acoustic solitary waves in a warm ion plasma with non-isothermal electrons and then the results for solitary waves in a plasma with isothermal electrons are obtained. Incorporating the previous results obtained from the solitary wave solutions, the authors generalize the effect of negative ions on ion-acoustic waves in plasmas consisting of either a warm or cold ion species. A reflection phenomenon of ions in these waves is also studied. These results can be generalized, but the discussion is limited to a particular model of the plasma.

The dissipation of hydromagnetic surface waves.

Abstract: When hydromagnetic surface waves travel along a surface with a thin but finite boundary layer, velocities within this layer become singular when computed according to the ideal MHD equations. I compute the corresponding rate of wave damping. Sufficiently weak surface waves are dissipated either by a resonant conversion into kinetic Alfven waves or by viscosity. Astrophysically important surface waves may involve such large velocity amplitudes outside the narrow zone of linear dissipation that nonlinear phenomena limit the singularity and the method of dissipation. Even these, however, are confined to extremely narrow layers.

Breaking waves in deep water and resulting wave forces

Abstract: The aim of this study is to try to establish new criteria for the design of offshore structures against extreme forces caused by breaking waves. The objective is to study shock forces and drag and inertia wave forces by means of several series of laboratory experiments and extensive field measurements. In a series of laboratory experiments dispersion properties of water waves are used to generate a non-steady situation where one wave train overtakes another resulting in the generation of an extreme wave. Collisions between wave solitons are studied in detail qualitatively and quantitatively, and results are obtained for characteristic wave properties: form, attenuation, dispersion, initiation and type of breaking, total pressure head and shock pressures. Results are also included for cases where currents are superimposed upon the mechanism for the generation of extreme waves. This deterministic approach in the laboratory will later be followed by extensive field measurements on a concrete gravity platform in the North Sea. Shock pressures near mean water level together with spectral and directional wave properties will be recoreded in the field. The laboratory experiments showed that three distinct types of breaking waves could be generated by wave-wave interaction in deep water, namely plunging breakers, deep water bores and spilling breakers. Field data on extreme waves obtained from wave rider buoys was analysed with the zero-downcross method which provided a wave height parameter relevant to the evaluation both of shock pressures and of the operation and stability of smaller vessels. Crest front steepness epsilon of the waves was used in the analysis as the total wave stepness s = H/L is not sufficient for asymmetric waves. The magnitude of shock pressures depends on the type and the wave form of the breaking waves.

Reflection and transmission of discontinuity waves through a shock wave. General theory including also the case of characteristic shocks

Abstract: An incident wave creates a discontinuity in the acceleration of the shock front. The amplitudes of the reflected and transmitted waves are also determined. Special attention is given to the case of the weak shocks and the characteristic shocks.

Finite-Amplitude Deep-Water Waves on Currents

Abstract: Accurate integral properties of plane periodic deep-water waves of amplitudes up to the steepest are tabulated by Longuet-Higgins (1975). These are used to define an averaged Lagrangian which, following Whitham, is used to describe the properties of slowly varying wave trains. Two examples of waves on large-scale currents are examined in detail. One flow is that of a shearing current, V ( x ) j , which causes waves to be refracted. The other flow, U ( x ) i , varies in the direction of wave propagation and causes waves to either steepen or become more gentle. Some surprising features are found.

Second-Order Directional Seas and Associated Wave Forces

Abstract: Most available methods for wave force computation incorporate either the nonlinearities of the ocean surface for a single fundamental component or the random and/or directional characteristics using the superposition of linear wave components. An exception is the intuitive "hybrid" method 1 which combines elements of linear and nonlinear waves. The present paper describes and applies a method, which is correct to second order in wave height, for calculating waves and wave forces on an offshore structure due to a directional wave spectrum. Starting with a prescribed linear spectrum of directional waves, a set of random phases is generated and the second-order spectrum computered with phases defined by all contributing pairs of first-order components. With one realization of the spectrum thus complete up to the second order, the wave profile and water particle kinematics can be simulated in the time domain. The wave forces are also computed in the time domain taking full account of their nonlinear and directional properties. The resulting wave forces at any level vary in direction and magnitude. The total wave forces summed over all piling of a structure are less than those for a unidirectional train of waves with the same one-dimensional spectrum. Several examples are presented to illustrate reductions in maximum wave forces due to the directional distribution of the waves. It is found that for a single piling the maximum force decreases by a factor ranging from 1.0 to 0.61 as the directional spread increases from unidirectional to omnidirectional. For a four-pile group on a square array of 300 ft. spacing, the corresponding decrease in the factor is from 1.0 to 0.51 for a Bretschneider spectrum with a peak period of approximately 12 seconds. The results of this complete model are compared with the more intuitive and approximate hybrid method and are found to agree quite well. Force spectra are presented and discussed for the inline and transverse directions.

The spectral energy transfer from surface waves to internal waves

Abstract: The generation of internal waves by resonantly interacting surface waves is examined in the framework of spectral scattering theory in the random-phase approximation. Coupling coefficients are derived from Euler's equation of motion for arbitrary stratification. The spectral energy transfer is discussed for deep-water surface waves and a simple three-layer model of the stability frequency. Analytical and numerical evaluation of the transfer integral leads to a parametrization in terms of the basic model parameters. These are the depth, thickness and stability frequency of the thermocline and the scale parameters and bandwidth of the surface wave spectrum. Strong dependence on some of these parameters, in particular the surface wave energy and the ratio of surface and internal wave frequencies, indicates a large spatial and temporal variability of the transfer rate. The transfer to the internal wave field in the oceanic main thermocline is found to be negligible compared with the effect of other processes. High frequency waves in the seasonal thermocline may be generated very efficiently.

Rayleigh Waves in Linear Elasticity as a Propagation of Singularities Phenomenon

Abstract: We examine the propagation of surface waves known as Rayleigh waves from the perspective of microlocal analysis. This paper is a TeXed version of Taylor (1979).