Showing papers on "Longitudinal wave published in 1982"

The interaction between waves and a turbulent current: waves propagating with the current

Abstract: This paper describes an experimental programme carried out in a laboratory channel with rough and smooth beds, to investigate the interaction between gravity waves and a turbulent current. In particular, changes induced in the mean-velocity profiles, turbulent fluctuations, bed shear stresses and wave attenuation rates are considered for a range of wave heights, keeping the wave period constant. The smooth-boundary tests were carried out as a necessary preliminary to the more-realistic rough-boundary condition. A directionally sensitive laser anemometer was used to measure horizontal, vertical, and 45° velocity components in the oscillating fluid, and an on-line minicomputer was programmed to produce ensemble averages of velocities, Reynolds stresses and wave-elevation data. The cycle was sampled at 200 separate phase positions, with 180 observations at each position. Measurements were made at up to 30 points in the vertical. Preliminary tests were carried out on the unidirectional current and on the waves alone. These show that mean-velocity profiles and turbulence parameters of the current agree satisfactorily with previous experiments, and that the waves are approximated closely by Stokes’ second-order theory. For combined wave and current tests, mean-velocity profiles are generally found to differ from those suggested by a linear superposition of wave and current velocities, a change in boundary-layer thickness being indicated. However, shear stresses at the smooth boundary are found to be described by such a linear addition.

Propagation Speeds and Acoustic Damping of Waves in Magnetic Flux Tubes

Abstract: Propagation speeds are derived for the wave modes of a thin magnetic tube in an otherwise homogeneous magnetized or unmagnetized fluid. These results generalize results obtained by previous authors. There are three types of wave, a (torsional) Alfven wave and two waves which are specific for the thin tube. These are named the longitudinal and transversal tube waves, according to their polarization properties. They can be camped by radiating an MHD or acoustic wave into the surroundings of the tube. Conditions for occurrence of this acoustic damping, and the damping rates, are derived. The behavior of the waves in the solar convection zone and corona is discussed.

Bars, bumps, and holes: Models for the generation of complex beach topography

Abstract: In shallow water, any two waves of the same frequency are shown to produce complex patterns of drift velocity above the sea bed. If the longshore components hi, h: of the wave numbers of the two waves are different, these steady flow patterns exhibit a longshore periodicity of wave number (hi h:) irrespective of whether the waves propagate in the same direction (say hi, he positive) or in opposite directions' (he negative). The interaction of two edge wave modes is examined in detail. The drift velocities are Calculated and a simple sediment transport model is used to predict the beach topography that would be in equilibrium with these flow patterns. As expected, crescentic sand bars are produced by the special case of standing edge waves (hi = --h:). Intriguingly, for all other cases a combination of complex transverse bars plus meandering or straight offshore bars result, patterns that are surprisingly reminiscent of many published descriptions of complex, rhythmic topography. The extension of the model to three or more waves produces topography that appears to be very irregular. Although the pattern should repeat over sufficiently long distances along the beach, even with only three waves these distances may be very large compared to the scale of the bars.

Acoustic slow waves and the consolidation transition

Abstract: We have investigated the ultrasonic properties of unconsolidated (loose) glass beads and of lightly fused (consolidated) glass beads when the pore space is saturated with water. At a frequency of 500 kHz we have observed a single compressional wave in the former whose speed is 1.79 km/s and two distinct compressional waves with speeds 2.81 km/s and 0.96 km/s in the latter. The Biot theory is shown to give an accurate description of this phenomenon. We also analyze the acoustics of low temperature He ii in packed powder superleaks; either the fast wave for unconsolidated systems or the slow wave in a highly consolidated (fused) frame may be considered to be the 4th sound mode. In all such systems, the acoustic properties can be very simply understood by considering the velocities of propagation as continuous functions of the elastic moduli of the solid skeletal frames.

Tortuosity and Acoustic Slow Waves

Abstract: The experimental measurements of tortuosity of porous structures using either the acoustic index of refraction of superfluid $^{4}\mathrm{He}$ or the electrical conductivity are shown to agree with each other. This and other measured parameters are used to calculate directly the acoustic speeds of water-saturated, fused-glass-bead samples; there are no adjustable parameters and agreement with experiment is excellent. The dependence of tortuosity on pore volume fraction, $\ensuremath{\phi}$, is discussed.

Effect of surface topography on the diffraction of P, SV, and Rayleigh waves

Abstract: A generalized inverse method for approximate boundary conditions is adapted for boundary value problems in elastic wave propagation. The diffraction of P, SV , and Rayleigh waves at the vicinity of a semi-elliptical canyon is considered. The effects of mode conversion from compressional to shear waves, or vice versa, are examined in detail. The maximum amplification for each plane wave is also studied.

The scattering of ultrasonic waves by polycrystals

Abstract: An ultrasonic scattering theory is presented which allows one to calculate the scattering coefficients and velocities of plane longitudinal and transverse waves in polycrystals as a function of the wavenumber k times grain radius a without limitation to the Rayleigh region. The theory includes mode conversion and multiple scattering and can be used to describe ultrasonic propagation in polycrystals with randomly orientated grains as well as in those with preferred grain orientation. The calculation was done for compressional waves in polycrystals of cubic symmetry with randomly orientated grains in second‐order perturbation theory using the assumption that the changes in the elastic constants and in the density of the materials from grain to grain are small. The asymptotic values at low ka (Rayleigh scattering) are exactly the same as the well‐known results from Bhatia and Moore. Numerical calculations are carried out for some examples.

Upper mantle anisotropy - Evidence from free oscillations

Abstract: Isotropic earth models are unable to provide uniform fits to the gross Earth normal mode data set or, in many cases, to regional Love-and Rayleigh-wave data. Anisotropic inversion provides a good fit to the data and indicates that the upper 200km of the mantle is anisotropic. The nature and magnitude of the required anisotropy, moreover, is similar to that found in body wave studies and in studies of ultramafic samples from the upper mantle. Pronounced upper mantle low-velocity zones are characteristic of models resulting from isotropic inversion of global or regional data sets. Anisotropic models have more nearly constant velocities in the upper mantle. Normal mode partial (Frediet) derivatives are calculated for a transversely isotropic earth model with a radial axis of symmetry. For this type of anisotropy there are five elastic constant. The two shear-type moduli can be determined from the toroidal modes. Spheroidal and Rayleigh modes are sensitive to all five elastic constants but are mainly controlled by the two compressional-type moduli, one of the shear-type moduli and the remaining, mixed-mode, modulus. The lack of sensitivity of Rayleigh waves to compressional wave velocities is a characteristic only of the isotropic case. The partial derivatives of the horizontal and vertical components of the compressional velocity are nearly equal and opposite in the region of the mantle where the shear velocity sensitivity is the greatest. The net compressional wave partial derivative, at depth, is therefore very small for isotropic perturbations. Compressional wave anisotropy, however, has a significant effect on Rayleigh-wave dispersion. Once it has been established that transverse anisotropy is important it is necessary to invert for all five elastic constants. If the azimuthal effect has not been averaged out a more general anisotropy may have to be allowed for.

Determination of in situ attenuation from full waveform acoustic logs

Abstract: Method for the determination of in situ P and S wave attenuation from full waveform acoustic logs are developed. For P waves, the peak amplitude ratios of the refracted P waves from two different receivers can be used with geometrical spreading taken into account. For S waves, owing to the contamination by the guided waves, its attenuation cannot be determined directly. Instead, S wave attenuation is determined from the attenuation of the guided waves using the partition coefficients (normalized partial derivatives of the phase velocity with respect to the body wave velocities). Analytical forms of these partition coefficients are presented here, along with examples for a number of different rock formations (granite, limestone, sandstone and soft sediments). The results show that in high velocity rocks, the fluid attenuation controls the guided wave attenuation except near the cut-off frequency of the pseudo-Rayleigh wave. For low velocity rock formations, especially in the case where the S wave velocity is lower than the fluid velocity, the S wave attenuation is the main contributor to the guided wave attenuation. Synthetic microseisgmogram calculated with the measured body wave attenuation agrees well with the actual microseismograms.

Strongly nonlinear waves

Abstract: As steep waves have recently come to be described with increasing accuracy, a number of unexpected physical and mathematical phenomena have been revealed. Until ten years ago it had been assumed that accurate solutions for high waves would hold few surprises. Examples of such suppositions are that deep-water solutions would converge for all waves short of the highest, that important integral quantities such as speed, energy, and momentum would increase with wave height until the highest is reached, that the solutions for periodic waves would be unique, and that if one solitary wave overtakes another any change of wave height would be a decrease. It is now known that all these suppositions are false, having been disproved in the last decade. The nonlinearity of the describing equations produces a complexity of solution structure that is only now beginning to be appreciated. This review will deal with effectively exact solutions for nonlinear waves and the phenomena revealed by such solutions. The governing equation within the fluid is taken to be Laplace’s equation, corresponding to irrotational flow of an incompressible fluid. Excluded are the physical effects of viscosity, density gradients, compressibility, and rotation. This model of the flow is the simplest, but one which is an excellent approximation in many cases of wave motion, and is the traditional avenue of approach to most problems of fluid flow. Throughout his review, however, the problems and solutions described are those where the complete nonlinear boundary conditions have been included. It has been the nonlinearity of these conditions which has made the accurate solution of water-wave problems so difficult.

Characteristics of the ULF waves associated with upstream ion beams

Abstract: A new class of upstream wave is reported with relatively high frequencies of about 1 Hz and small amplitudes compared to the more common larger amplitude, low-frequency (0.03 Hz) upstream wave. The waves were first noted in association with beams of ions reflected back upstream at the bowshock, and although beam presence appears to be a necessary condition for the observation of the waves, it is not a sufficient condition for the existence of the waves. Magnetometer measurements are used to determine intrinsic properties of the waves, and simultaneous two point measurements are used to calculate and eliminate Doppler shifting effects. Results indicate that the waves are right-hand elliptically polarized whistler mode waves with plasma rest frame frequencies of about 20-100 times the proton gyrofrequency and wavelengths of about 100 km.

Measurement of velocities in solitary waves

Abstract: The water surface profiles and corresponding water particle velocities of several solitary waves have been obtained. The measurements of the horizontal and vertical velocity components are conducted using a two-dimensional laser-Doppler velocimeter (LDV). Results are presented for three different wave height-to-depth ratios: ϵ = 0.11, 0.19 and 0.29. The experimental results are compared with existing theories which follow different orders of approximation, and the theories are found to agree well with the experiments. It has been convincingly demonstrated that the LDV measurement technique offers an unmatched advantage to determine the water particle velocities under water waves, especially in the region above the still water level.

Amplitude attenuation of impulsive waves in random media based on travel time corrected mean wave formalism

Abstract: Waves gradually collapse with propagation through media with random velocity fluctuation; however, impulsive waves propagate without large attenuation when the wavelength is shorter than the correlation distance. The Q−1 value predicted from the usual mean wave formalism monotonously increases with frequency even in the high‐frequency limit, due to taking a mean over waves with large travel time fluctuations caused by the long scale velocity fluctuation compared with the wavelength studied. We propose a new statistical averaging method appropriate for the amplitude attenuation measurement of impulsive waves, in which the mean wave is defined after the correction of travel time fluctuations. We investigate impulsive scalar waves propagation in three‐dimensional media with homogeneous and isotropic random fractional velocity fluctuation, based on the binary interaction approximation in this improved mean wave formalism. We successfully derive the Q−1 value that has a peak of the order of the mean square fra...

Lattice dynamics of colloidal crystals

Abstract: Photon correlation spectroscopy was performed on a dilute bcc colloidal crystal in a thin-film cell to measure its response to thermal fluctuations with wave vectors along lattice symmetry directions. The phonon dispersion curves show a definite harmonic-lattice behavior for longitudinal and transverse modes. We present a Langevin treatment of the lattice dynamics, based on harmonic potentials and a theory of hydrodynamic interactions which is exact to lowest order in sphere volume fraction and includes important unsteady flow effects. The model takes into consideration the discreteness of the lattice, which is important near the Brillouin-zone boundary, and has the correct behavior for long-wavelength fluctuations as well (underdamped transverse modes, overdamped longitudinal modes). The mass renormalization of propagating transverse lattice modes is discussed, along with the effects of the thin-film configuration on their propagation. The role of backflow in overdamping longitudinal modes is made clear. From the measured dispersion curves for longitudinal wave vectors, we obtained the following elastic constants: ${c}_{11}=6.96$ dyn/${\mathrm{cm}}^{2}$ and ${c}_{12}={c}_{44}=2.43$ dyn/${\mathrm{cm}}^{2}$.

Infinite elements for elastodynamics

Abstract: An axisymmetric infinite element and a three-dimensional infinite element are developed to solve three-dimensional elastic wave propagation problems in unbounded media. The elements are capable of transmitting Rayleigh, shear and compressional waves in the frequency domain. A scheme to integrate numerically the characteristic matrices of the elements is formulated based upon Gauss—Laguerre quadrature. Finally, the axisymmetric infinite element is used to find the compliance functions of a rigid circular plate subjected to harmonic loading on a semi-infinite medium. By using infinite elements, the size of the near field may be kept small. Consequently, the system is characterized by relatively few degrees of freedom, thus providing the analyst with an inexpensive solution.

Direct imaging of travelling Rayleigh waves by stroboscopic X-ray topography

Abstract: We report here the first successful experiments which exploit the time structure and single bunch mode of operation of the Daresbury Synchrotron Radiation Source (SRS). Rayleigh waves travelling on the surface of a piezoelectric crystal have been imaged by stroboscopic X-ray topography, in which the generation of the waves is synchronized with X rays emitted by the orbiting electrons in the storage ring. Interactions between the Rayleigh waves and microscopic crystalline defects have been observed and provide new insights into the factors affecting surface acoustic wave (SAW) device operation. It has been demonstrated that this novel technique has considerable potential for the study of periodic phenomena in crystals.

Ultrasonic aircraft ice detector using flexural waves

Abstract: A system for the detection of wing icing by monitoring variations in flexural waves transmitted through the outer plate material of an aircraft airfoil The flexural waves in the plate of the wing airfoil are more subject to variation from the accumulation of ice on the wing than the compressional waves The flexural waves are detected apart from the compressional waves, which tend to remain relatively constant, to provide an indication of icing Changes in amplitude, phase or dispersion characteristics of the flexural waves are detected to indicate ice buildup, and, in one embodiment, these values are ratioed to the corresponding levels in the compressional wave in order to provide compensation for variations other than ice buildup The ultrasonic waves may be coupled directly from a transducer to the airfoil plate or via an ultrasonic waveguide interposed between the transducer and the plate The receiver for the ultrasonic waves to be detected may be positioned to receive direct flexural waves transmitted over a distance through the plate or flexural waves reflected from reflecting boundaries in the plate

Finite-amplitude steady waves in stratified fluids

Abstract: : An exact theory regarding solitary internal gravity waves in stratified fluids is presented. Two-dimensional, inviscid, incompressible flows confined between plane horizontal rigid boundaries are considered. Variational techniques are used to demonstrate that the Euler equations possess solutions that represent progressing waves of permanent form. These are analogous to the surface, solitary waves so easily generated in a flume. Periodic wave trains of permanent form, the analogue of the classical cnoidal waves, are also found. Moreover, internal solitary-wave solutions are shown to arise as the limit of cnoidal wave trains as the period length grows unboundedly. (Author)

Surface waves on solar wind tangential discontinuities

Abstract: It is demonstrated that (tangential) discontinuities in the magnetic field direction can support MHD surface waves. The surface waves are similar to the usual Alfven wave, but there are seven important differences. The first is that the surface waves exhibit a low-frequency cutoff; the second is that the velocity and magnetic field fluctuations are elliptically, and sometimes circularly, polarized. It is noted that they may account for the solar wind helicity spectrum. The third difference is that the surface waves are compressive, although there are special cases where they are noncompressive. The fourth is that the wave vector k, the local normals to the surfaces of constant phase, and the magnetic minimum variance direction do not all coincide. The fifth is that there is a tendency for the minimum variance direction to align itself with the mean magnetic field direction. The sixth difference is that the waves can be intrinsically nonplanar, and the seventh is that equipartition between magnetic and kinetic energies is not obeyed locally. These properties of the surface waves are interpreted to mean that surface waves may be common in the solar wind.

Reflection and refraction of seismic waves incident obliquely at the boundary of a liquid-saturated porous solid

Abstract: A systematic theory of the propagation of seismic waves in liquid-saturated porous solids was first developed by Biot in 1956. Since then, some theoretical investigations have been carried out on the propagation of body and surface waves in such media. Further studies in this area may be useful in giving greater insight into the propagation of seismic waves in underground layers of porous solids saturated with oil or groundwater. In this connection, the transmission of normally incident seismic waves across the boundary of a liquid-saturated porous solid has been considered earlier. Keeping in view the fact that oblique incidence is more likely than normal incidence for such seismic waves, the authors have investigated the reflection and refraction of P and SV waves, which become obliquely incident at the boundary of a liquid-saturated porous solid, after propagating through an elastic solid. It is found that, corresponding to both P and SV waves obliquely incident at the boundary, there will be two refracted dilatational waves traveling with different velocities, which may be called the Pf and Ps waves, and one refracted SV wave, in the liquid-saturated porous solid, together with reflected P and SV waves in the elastic solid. The amplitude and energy ratios for the different reflected and refracted waves have been calculated theoretically. Numerical values of the amplitude and energy ratios have been computed for different angles of incidence for P and SV waves which propagate through granite, and then become incident at the boundary between the granite and oil-saturated sandstone, using results of laboratory experiments on the elastic behavior of oil-saturated sandstone. It is found that the amplitudes of the reflected and refracted waves depend significantly on the angle of incidence. It is also found that the amplitude of the second refracted P wave is usually much smaller than that of the other reflected and refracted P and SV waves, so that this slower refracted P wave will be difficult to detect. Similar amplitudes and energy ratios are also calculated for P and SV waves incident at the boundary between granite and dry sandstone. Comparison between the cases of dry sandstone and oil-saturated sandstone shows that the presence of oil usually has a significant effect on the amplitudes of the reflected and refracted P and SV waves. It is noted that such theoretical investigations may be useful in utilizing the amplitudes and other characteristics of reflected and refracted seismic waves in the detection and study of underground layers of porous solids saturated with oil or groundwater.

Finite-amplitude interfacial waves in the presence of a current

Abstract: Solutions for interfacial waves of permanent form in the presence of a current wcre obtained for small-to-moderate wave amplitudes. A weakly nonlinear approximation was used to give simple analytical solutions to second order in wave height. Numerical methods were usctl to obtain solutions for larger wave amplitudes, details are reported for a number of selected cases. A special class of finite-amplitude solutions, closely related to the well-known Stokes surface waves, were identified. Factors limiting the existence of steady solutions are examined.

The potential of shear-wave observations*

Abstract: Shear waves can today be generated and observed, though not with the flexibility and the technical standard of compressional waves, and they can be identified in seismograms by various means. Their potential lies not so much in their lower velocity (corresponding—for the same frequency—to shorter wavelength and higher resolution) but in the fact that they probe the earth with stresses and strains that differ from those of compressional waves. Full utilization of the information potential of shear waves, therefore, requires combined use of P-and S-waves. Complications in the combined use of different wave types should be regarded as opportunities to obtain additional information. A typical example is the observation that the depth of one and the same interface estimated on the bases of P- and SH-reflections, respectively, can differ significantly. This discrepancy may be due to the anisotropy of a finely layered medium. Under favorable circumstances some of the parameters describing this anisotropy can be deduced from the different depth estimates and the curvature of the squared-offset/squared-time representation of the different reflections. Since in anisotropic media vertically polarized shear waves are significantly different from horizontally polarized ones, the combined observation of all three waves opens up additional possibilities.

Waves on glaciers

Abstract: This paper is an attempt at a mathematical synopsis of the theory of wave motions on glaciers. These comprise surface waves (analogous to water waves) and seasonal waves (more like compression waves). Surface waves have been often treated and are well understood, but seasonal waves, while observed, do not seem to have attracted any theoretical explanation. Additionally, the spectacular phenomenon of glacier surges, while apparently a dynamic phenomenon, has not been satisfactorily explained. The present thesis is that the two wave motions (and probably also surging, though a discussion of this is not developed here) can both be derived from a rational theory based on conservation laws of mass and momentum, provided that the basal kinematic boundary condition involving boundary slip is taken to have a certain reasonable form. It is the opinion of this author that the form of this ‘sliding law’ is the crux of the difference between seasonal and surface waves, and that a further understanding of these motions must be based on a more satisfactory analysis of basal sliding. Since ice is here treated in the context of a slow, shallow, non-Newtonian fluid flow, the theory that emerges is that of non-Newtonian viscous shallow-water theory; rather than balance inertia terms with gravity in the momentum equation, we balance the shear-stress gradient. The resulting set of equationsis, in essence, a first-order nonlinear hyperbolic (kinematic) wave equation, and susceptible to various kinds of analysis. We show how both surface and seasonal waves are naturally described by such a model when the basal boundary condition is appropriately specified. Shocks can naturally occur, and we identify the (small) diffusive parameters that are present, and give the shock structure: in so doing, we gain a useful understanding of the effects of surface slope and longitudinal stress in these waves.