Showing papers on "Longitudinal wave published in 1981"

Reflection of acoustic waves at a water–sediment interface

Abstract: Reflection and refraction of plane acoustic waves are studied for the case where the sediment is modeled as a porous viscoelastic medium. The model is based on the classical work of Biot which predicts that three different kinds of attenuating body waves may propagate in the sediment. As a consequence when homogeneous plane waves in water are incident to a water‐sediment interface, three nonhomogeneous waves are generated in the sediment. In these waves the direction of phase propagation and the direction of maximum attenuation are not the same and particle motion follows an elliptic path. Moreover, the velocity and attenuation of the refracted waves become dependent on the angle of incidence and no “critical” angle occurs. Numerical examples show that the reflectivity of a porous viscoelastic model differs significantly from the case where the sediment is modeled as a viscoelastic solid with constant complex modulus. Finally, because of the frequency dependence of reflectivity in the porous model, it is ...

Gravity waves on water with non-uniform depth and current

Abstract: A mathematical model for the combined refraction-diffraction of linear periodic gravity waves on water is developed, in which the influence of inhomogeneities of depth and current is taken into account. The model is used to compute partial reflection of waves a gully or an undersea slope, with influence of a current. The model is also applied to prismatic wave channels with reflecting side-walls. For a gully bounded by shallows the model predicts the decay of wave height due to radiation of energy in lateral direction. For practical application in regions with arbitrary bottom and current topography a parabolic approximation of the model is derived. This is used as a basis for numerical calculation of waves in a sea region near the coast.

Near-limiting gravity waves in water of finite depth

Abstract: Progressive, irrotational gravity waves of constant form exist as a two-parameter family. The first parameter, the ratio of mean depth to wavelength, varies from zero (the solitary wave) to infinity (the deep-water wave). The second parameter, the wave height or amplitude, varies from zero (the infinitesimal wave) to a limiting value dependent on the first parameter. For limiting waves the wave crest ceases to be rounded and becomes angled, with an included angle of 120°. Most methods of calculating finite-amplitude waves use either a form of series expansion or the solution of an integral equation. For waves nearing the limiting amplitude many terms (or nodal points) are needed to describe the wave form accurately. Consequently the accuracy even of recent solutions on modern computers can be improved upon, except at the deep-water end of the range. The present work extends an integral equation technique used previously in which the angled crest of the limiting wave is included as a specific term, derived from the well known Stokes corner flow. This term is now supplemented by a second term, proposed by Grant in a study of the flow near the crest. Solutions comprising 80 terms at the shallow-water end of the range, reducing to 20 at the deep-water end, have defined many field and integral properties of the flow to within 1 to 2 parts in 106. It is shown that without the new crest term this level of accuracy would have demanded some hundreds of terms while without either crest term many thousands of terms would have been needed. The practical limits of the computing range are shown to correspond, to working accuracy, with the theoretical extremes of the solitary wave and the deep-water wave. In each case the results agree well with several previous accurate solutions and it is considered that the accuracy has been improved. For example, the height: depth ratio of the solitary wave is now estimated to be 0.833 197 and the height: wavelength ratio of the deep-water wave to be 0.141063. The results are presented in detail to facilitate further theoretical study and early practical application. The coefficients defining the wave motion are given for 22 cases, five of which, including the two extremes, are fully documented with tables of displacement, velocity, acceleration, pressure and time. Examples of particle orbits and drift profiles are presented graphically and are shown for the extreme waves to agree very closely with simplified calculations by Longuet-Higgins. Finally, the opportunity has been taken to calculate to greater accuracy the long-term Lagrangian-mean angular momentum of the maximum deep-water wave, according to the recent method proposed by Longuet-Higgins, with the conclusion that the level of action is slightly above the crest.

Three-Dimensional Instability of Finite-Amplitude Water Waves

Abstract: Computations based on the full water-wave equations reveal that there are two distinct types of instabilities for gravity waves of finite amplitude on deep water. One is predominantly two dimensional and is related to all the known results for special cases. The other is predominantly three dimensional and becomes dominant when the wave steepness is sufficiently large.

Rarefaction Ion Acoustic Solitons in Two-Electron-Temperature Plasma

Abstract: This paper shows that rarefaction ion acoustic solitons appear in a two-electron-temperature plasma. And also it presents general conditions and physical mechanism for existence of the rarefaction solitons. It is found that finite amplitude rarefaction and compression solitons coexist in a plasma within a certain parameter region.

Solar cycle Lorentz force waves and the torsional oscillations of the sun

Abstract: A hypothesis is proposed and analyzed that the longitudinal component of the Lorentz force of the dynamo waves which well simulate the observed solar cycle can drive the recently observed torsional oscillations by Howard and LaBonte. The force component, which is reduced to a correlation between the toroidal and poloidal magnetic fields, consists of a nonwave part and a wave part. Only the nonwave part remains in the deep regions of the convection zone where the dynamo waves can propagate freely. The wave part, called here the Lorentz force waves, emerges only near the surface where the propagating dynamo waves are piled up and their wave profiles are deformed. Thus, the force waves are confined near the surface where the density is low and the moment of inertial is small. Hence, the oscillations are likely to be a phenomenon of rather shallow regions of the solar convection zone. Amplitude of force waves is estimated for typical values of the magnetic fields in the convection zone. It is concluded that driving the torsional oscillations by the force waves is possible in the solar convection zone. If this hypothesis is correct, the torsional oscillations can be the first concrete evidence that themore » magnetic force is indeed working on the global dynamics of the Sun.« less

Shear wave measurements of the elasticity of the ground

Abstract: Shear waves provide a direct way of determining the dynamic shear modulus of the ground that is independent of Poisson's ratio. Two shear wave methods have been applied to determine in situ properties as a function of depth on three clay sites. The first method was that of shear wave refraction using a strong shear wave source and an enhancement seismograph. The second method measured the velocity of Rayleigh or surface waves generated by vibrators on the surface of the ground. In addition compression wave velocities were measured enabling the dynamic Poisson's ratio to be calculated. On all three sites the moduli were found to increase with depth. They were compared with semi-static values from plate tests and pressuremeter measurements. The comparisons were made by means of a generalized viscoelastic model based on published values of damping for clays as a function of strain. Les ondes de cisaillement permettent de determiner directement le module de cisaillement dynamique du sol qui est independant du...

Pressure and velocity detectors for seismic exploration

Abstract: Pressure and velocity detectors produce outputs which are combined to substantially cancel ghost reflections. The pressure detector produces a positive output in response to upwardly travelling compressional waves and a negative output in response to downwardly travelling rarefaction waves. The velocity detector for this is a positive output in response to upwardly travelling compressional waves and a positive output in response to downwardly travelling rarefaction waves. These outputs are filtered so that the impulse response of the rarefaction waves cancels. The filtered outputs are combined to produce an output in which the ghost reflection is substantially suppressed.

Internal gravity waves in the solar atmosphere. I - Adiabatic waves in the chromosphere

Abstract: The properties of adiabatic and linear internal gravity waves propagating in a solar wind model are discussed, using nonlinearity criteria unique to gravity waves to estimate wave-breaking heights. The results are used to deduce information on the possible role of gravity waves in the chromospheric energy balance. Maximum vertical velocity amplitudes for gravity waves are estimated to be on the order of 2 km/sec or less, and maximum horizontal velocity amplitudes are less than 6 km/sec, with temperature perturbations as large as 1000-2000 K. It is also estimated that gravity waves with an incident energy flux of one million ergs/sq cm-sec can propagate upward to a maximum height of 900-1000 km above the visible surface before nonlinearities lead to wave breaking, while those with an energy flux of 100,000 ergs/sq cm-sec can reach maximum heights of 1400-1600 km.

Cylindrical waves in transversely isotropic media

Abstract: Because of fine layering, many sedimentary rocks can be characterized as transversely isotropic, possessing an axis of symmetry perpendicular to the layering. The many kinds of measurements made in fluid‐filled holes drilled parallel to this axis prompted this study of axisymmetric cylindrical waves. The literature shows how such waves in an isotropic solid can be expressed in terms of a compressional potential or a shear potential. This paper shows that in a transversely isotropic medium, particular combinations of these potentials are needed simultaneously, yielding either a quasi‐compressional wave or a quasi‐shear wave. The expressions are used to compute the transient response of an acoustic logging tool. The speeds of refracted compressional and shear waves agree with the speeds of plane waves traveling along the axis of symmetry. Dispersive waves in the fluid annulus yield further information about the elastic constants of the solid. The potentials also portray the radiation of elastic waves from a point force or from a transducer on the surface.

The instability of atmospheric gravity waves through wave‐wave interactions

Abstract: We investigate the possibility of a propagating primary wave decaying into secondary waves through three-wave interactions. Such a possibility exists in an inviscid isothermal atmosphere when the vertical wavelength is small compared to the scale height. Initially, the amplitude of the secondary waves grows exponentially, and this growth time decreases exponentially with height. This means that as the primary wave propagates upward its energy is continuously transfered to the secondary waves. This transfer becomes increasingly rapid with increasing height. It is shown that this process can take place even when the local Richardson number is more than 100, indicating dynamic stability.

Ultrasonic Attenuation Measurement by Spectral Ratios Utilizing Signal Processing Techniques

Abstract: A new approach using signal averaging and signal processing is described for measuring ultrasonic attenuation of compressional (P) and shear (S) waves in highly attenuative (low Q) materials. Broadband ultrasonic pulses in the frequency range of 0.7-1.1 MHz are transmitted through a specimen to be characterized for comparison to a reference with low dissipation. Attenuation is calculated from the ratio of spectral amplitudes which are corrected for diffraction effects. An experimental example is given based upon measurements made on dry polycrystalline sodium chloride (halite or rock salt) from Avery Island, LA. The measured QP of compressional waves is 46 ± 5.5 and QS of shear waves is 12 ± 0.3. This is a through transmission technique which gives results for materials so lossy that multiple echoes cannot be detected.

Wave scattering from a step change in surface topography

Abstract: Scattering of body waves to surface waves is a means for converting energy with essentially infinite horizontal wavelength to motion with short wavelengths. This process, of interest to engineers designing structures with large horizontal dimensions such as pipelines, tunnels, and bridges, has received little attention from seismologists. Finite-difference calculations have been performed for the simple case of vertically incident SV and P waves impinging on a step change in surface elevation. These calculations predict scattered Rayleigh waves with amplitudes as large as 0.4 times the amplitude of the surface motion of the incident waves in the absence of any topographic relief, even for incident wavelengths several times the height of the step. Both vertical and inclined steps are examined.

Propagation of simple non-linear waves in gas filled tubes with friction

Abstract: The propagation of simple nonlinear waves in tubes is investigated. It is seen that both continuous and discontinuous asymptotic waves exist for which the nonlinear distortion and the viscous effect owing to the boundary layer just balance. Both types of solutions can be collapsed into one normalized asymptotic solution. A numerical method is given to compute time-dependent solutions. The evolution of continuous and discontinuous waves is illustrated with two examples.

Linear waves and instabilities on magnetically insulated gaps

Abstract: A linear, fully relativistic and electromagnetic analysis of waves perturbing the Brillouin flow state on planar, magnetically insulated gaps is presented. Three independent classes of waves are treated individually; transverse‐magnetic waves propagating normal to the insulating magnetic field, transverse‐electric waves propagating in the same direction, and a set of waves propagating along the magnetic field. Dispersion relations governing discrete modes of oscillation for each class are found and solved for some cases of interest. Only the transverse‐magnetic waves are found to be unstable due to the existence of a Doppler‐shifted plasma reasonance layer at frequencies above the plasma frequency. The scaling of the growth rate for this instability with respect to parameters characterizing the equilibrium state is examined. In addition to these discrete modes, spectral continua associated with localized resonance phenomena in the electron sheath bounding the cathode are described and explained.

Ultrasonic multiple-beam technique for detecting cracks in bimetallic or coarse-grained materials

Abstract: A reliable ultrasonic method for testing inner diameter cladded pipe adjacent to welds comprising use of multiple beams, bands and pulses in addition to pulseshaping and beamforming, spectral and directional averaging, as well as spatial filtering and pattern recognition. An automated inspection mode aims short shear-wave pulses from different source locations and different beam orientations to detect signals characteristic of defects. A manual confirmation mode aims both longitudinal waves and shear waves at the suspected defect and analyzes the detected returned pulses by an associated pulse pattern recognition method.

Response of buried structures to traveling waves

Abstract: The response of buried long structures to waves traveling in the longitudinal direction of the structures was studied. The structures and the surrounding soils were represented by three-dimensional finite elements. The three-dimensional models, however, were reduced to two-dimensional models by using a special type of wave-transmitting element which faithfully accounts for the effects of wave propagation. The results obtained for a linear system indicate that, for large structures, soil-structure interaction effects on the computed stresses and strains are indeed significant; therefore, it will be overly conservative to use free field strains in the design. Also, the assumption of vertically propagating waves is not adequate in predicting response; therefore, appropriate considerations should be given to traveling waves.

Ultrasonic thickness measuring apparatus and method

Abstract: In a method for ultrasonically measuring the thickness between opposed surfaces of a workpiece from one surface, a velocity parameter of ultrasonic longitudinal waves through the material of a workpiece is measured at a location along a first surface of the workpiece. Ultrasonic longitudinal waves are transmitted from one surface to the opposite surface, and the ultrasonic waves reflected from the opposite surface are received and a time parameter between transmission of the longitudinal waves and reception of the reflected waves is measured. The thickness between the opposed surfaces is determined from the measured velocity parameter and the measured time parameter. A device for measuring the thickness of a workpiece from one surface includes a transducer assembly with a pair of spaced apart transducer units each having a coupling member and a piezoelectric element mounted thereon. A third coupling member has a pair of piezoelectrics elements mounted thereon, and an electrical circuit connected to the piezoelectric elements for control and measurement. The piezoelectric element is mounted on the first coupling member of one of the pair of transducer units at a predetermined angle relative to the bottom surface to generate a subsurface longitudinal ultrasonic wave through the workpiece to be tested and to be received by the other piezoelectric element of the pair of units. The measuring device further includes apparatus for supplying couplant medium to the interface between the bottom surface of the coupling members and on the workpiece, and means for supporting and moving the transducer assembly along the workpiece.

Diffuse wave fields in solid media

Abstract: The diffuse‐field concept is applied to develop the power balance equations relating the time‐averaged energy densities associated with longitudinal and transverse waves to the diffuse‐field mode conversion coefficients and the power generated by sources in the medium. A solution for an impulsive source in a solid with stress‐free surfaces shows that, regardless of the initial partition of energy, the transverse‐wave energy density quickly increases to become the dominant energy form in the medium.

Nonlinear Waves in Rods

Abstract: Rods are simple structures that are often regarded as one-dimensional continua, but because of finite transverse dimensions, propagating waves are subject to dispersion, which may mask other effects. A one-dimensional continuum theory with one internal, scalar variable can be used to model a solid rod with longitudinal waves. In this paper the material is assumed to be homogeneous, isotropic, and hyperelastic. First, the linear theory is reviewed to exhibit clearly the multiple wave hierarchy that exists in a rod. Next, expansion and scaling techniques are used in the fully nonlinear case to examine the main pulse. Finally, steady nonlinear waves are examined and both solitary waves and periodic waves are found to exist. Results are compared to the simple wave solutions available from the most elementary one-dimensional nonlinear theory for rods.

Stimulated and spontaneous emission of acoustic waves from shock fronts

Abstract: In certain materials, shock waves of sufficient intensity spontaneously emit transverse rarefaction waves and are therefore unstable. A criterion is derived by calculating the relative amplitudes of reflected acoustic waves incident on the shock from behind. This criterion is found to delimit the conditions under which both acoustic amplification and acoustic emission can occur; it agrees with earlier results by Kontorovich.

Dispersion curves for waves in a cubic micropolar medium with reference to estimations of the material constants for diamond

Abstract: The authors start with an analytical study on the propagation of plane harmonic waves in an infinitely extended, cubi-anisotropic, elastic, and micropolar medium. It is possible to have six fundamental waves. Of these, a longitudinal uncoupled displacement wave and two coupled transverse waves of displacement and microrotation which become uncoupled with become uncoupled displacement waves at the limit of long wavelength are compared with the acoustical waves in the classical theory. The micropolar elastic constants of diamond, as well as its local moment of inertia, are estimated under the requirement that the theoretical dispersion curves for these waves fit the experimental data. Numerical computations are carried out and the results are made into a table.

Conditions of excitation of new waves (LITW) at nonlinear interface and diagram of wave states in the system

Abstract: We have found the conditions for the excitation of all of the possible waves in a nonlinear medium with a "negative" nonlinearity, in the case when a plane wave is incident from a linear medium upon a plane surface of the nonlinear mediums. We show that these conditions depend on only two independent parameters so that all possible states of the interface can be represented in a two-dimensional diagram. This diagram consists of regions of surface waves (SW), plane waves (PW), and so-called longitudinally inhomogeneous traveling waves (LITW) which were studied recently. The diagram includes two triple points: the first one corresponds to the intersection of boundaries between regions of SW, PW, and LITW states, while the other corresponds to the formation of the hysteresis (i.e., bistable) region between PW and LITW states.

Spatial and temporal variations of monthly mean total columnar ozone derived from 7 years of BUV data

Abstract: Ninth-degree spherical harmonic models are used to represent monthly mean total columnar ozone fields, with spatial spectra defined in terms of simple analytic expressions representing the rms value of each spherical harmonic coefficient. The spectra are combined with estimation theory techniques to develop a realistic error analysis accounting for errors due to nonglobal coverage. Amplitude and phase variations for longitudinal waves one, two and three are presented, and it is shown that these waves reinforce in space and time in the period of high poleward ozone transport in the northern hemisphere. In the southern hemisphere, the wave two and three components are much smaller, with wave one maximum amplitude occurring in September and October.

Geophone apparatus and a seismic exploration method

Abstract: A geophone apparatus capable of detecting both horizontal shear and compressional seismic waves has a pair of geophones mounted such that, when in use, said geophones will be inclined at an angle of about 45° in opposite directions from vertical. The output signals generated by the two geophones are summed to yield a compressional wave trace and/or are subtracted one from the other to yield a horizontal shear wave trace.