Showing papers on "Longitudinal wave published in 1997"

Solitary waves in a chain of beads under Hertz contact

Abstract: We study experimentally the propagation of high-amplitude compressional waves in a chain of beads in contact, submitted or not to a small static force. In such a system, solitary waves have been theoretically predicted by Nesterenko J. Appl. Mech. Tech. Phys. USSR 5, 733 1984. We have built an impact generator in order to create high-amplitude waves in the chain. We observe the propagation of isolated nonlinear pulses, measure their velocity as a function of their maximum amplitude, for different applied static forces, and record their shape. In all experiments, we find good agreement between our observations and the theoretical predictions of the above reference, without using any adjustable parameter in the data analysis. We also show that the velocity measurements taken at three different nonzero applied static forces all lie on a single curve, when expressed in rescaled variables. The size of the pulses is typically one-tenth the total length of the chain. All the measurements support the identification of these isolated nonlinear pulses with the solitary waves predicted by Nesterenko. S1063-651X9704211-6

Wave Propagation in Structures: Spectral Analysis Using Fast Discrete Fourier Transforms

Abstract: 1 Spectral Analysis of Wave Motion.- 1.1 Continuous Fourier Transforms.- 1.2 Discrete Fourier Transform.- 1.3 Examples Using the FFT Algorithm.- 1.4 Experimental Aspects of Wave Signals.- 1.5 Spectral Analysis of Wave Motion.- 1.6 Propagating and Reconstructing Waves.- Problems.- 2 Longitudinal Waves in Rods.- 2.1 Elementary Rod Theory.- 2.2 Basic Solution for Waves in Rods.- 2.3 Dissipation in Rods.- 2.4 Coupled Thermoelastic Waves.- 2.5 Reflections and Transmissions.- 2.6 Distributed Loading.- Problems.- 3 Flexural Waves in Beams.- 3.1 Bernoulli-Euler Beam Theory.- 3.2 Basic Solution for Waves in Beams.- 3.3 Bernoulli-Euler Beam with Constraints.- 3.4 Reflection of Flexural Waves.- 3.5 Curved Beams and Rings.- 3.6 Coupled Beam Structure.- Problems.- 4 Higher-Order Waveguides.- 4.1 Waves in Infinite Media.- 4.2 Semi-Infinite Media.- 4.3 Doubly Bounded Media.- 4.4 Doubly Bounded Media: Lamb Waves.- 4.5 Hamilton's Principle.- 4.6 Modified Beam Theories.- 4.7 Modified Rod Theories.- Problems.- 5 The Spectral Element Method.- 5.1 Structures as Connected Waveguides.- 5.2 Spectral Element for Rods.- 5.3 Spectral Element for Beams.- 5.4 General Frame Structures.- 5.5 Structural Applications.- 5.6 Waveguides with Varying Cross Section.- 5.7 Spectral Super-Elements.- 5.8 Impact Force Identification.- Problems.- 6 Waves in Thin Plates.- 6.1 Plate Theory.- 6.2 Point Impact of a Plate.- 6.3 Wavenumber Transform Solution.- 6.4 Waves Reflected from a Straight Edge.- 6.5 Scattering of Flexural Waves.- 6.6 Lateral Boundary Conditions.- 6.7 Curved Plates and Shells.- Problems.- 7 Structure-Fluid Interaction.- 7.1 Acoustic Wave Motion.- 7.2 Plate-Fluid Interaction.- 7.3 Double Panel Systems.- 7.4 Waveguide Modeling.- 7.5 Radiation from Finite Plates.- 7.6 Cylindrical Cavity.- Problems.- 8 Thin-Walled Structures.- 8.1 Membrane Spectral Elements.- 8.2 Spectral Elements for Flexure.- 8.3 Folded Plate Structures.- 8.4 Structural Applications.- 8.5 Segmented Cylindrical Shells.- 8.6 Future of Spectral Elements.- Problems.- Afterword.- Appendix: Bessel Functions.- References.

Ultrasonic wave propagation in bovine cancellous bone

Abstract: The acoustic properties of bovine cancellous (spongy) bone have been experimentally studied in vitro by the pulse transmission technique Fast and slow longitudinal waves have been clearly identified when the acoustic wave propagates parallel to the direction of the trabeculae Propagation speeds and attenuation of the fast and slow waves were observed in the frequency range of 05–5 MHz Theoretical discussion is given to Biot’s theory and the propagation of sound waves in fluid-saturated porous media

Ultraviolet Coronagraph Spectrometer Observations of Density Fluctuations in the Solar Wind

Abstract: Recent Ultraviolet Coronagraph Spectrometer (UVCS) white-light channel (WLC) observations on board the Solar and Heliospheric Observatory (SOHO) indicate quasi-periodic variations in the polarized brightness (pB) in the polar coronal holes. This is the first observation of possible signatures of compressional waves high above the limb (at heliocentric distances in the range 1.9-2.45 R☉). The Fourier power spectrum of the pB time series at 1.9 R☉ shows significant peak at about 6 minutes and possible fluctuations on longer timescales (20-50 minutes). The observation at 1.9 R☉ is the only currently available WLC data set with sufficient cadence to resolve the 6 minute period. These preliminary observations may result from density fluctuations caused by compressional waves propagating in polar coronal holes. We stress that our results are preliminary, and we plan future high-cadence observations in both plume and interplume regions of coronal holes. Recently, Ofman & Davila used a 2.5 D MHD model and found that Alfven waves with an amplitude of 20-70 km s-1 at the base of the coronal hole can generate nonlinear, high-amplitude compressional waves that can contribute significantly to the acceleration of the fast solar wind. The nonlinear solitary-like waves appear as fluctuations in the density and the radial outflow velocity and contribute significantly to solar wind acceleration in open magnetic field structures. The motivation for the reported observations is the MHD model prediction.

The measurement of velocity dispersion and frequency-dependent intrinsic attenuation in sedimentary rocks

Abstract: A series of experiments to determine the elastic properties of a sequence of saturated sedimentary rocks over as wide a frequency range as possible was carried out at the Imperial College borehole test site. These experiments fall into four categories: vertical seismic profiles (VSPs) within the frequency range 30-280 Hz, crosshole surveys (0.2-2.3 kHz), sonic logging (8-24 kHz), and laboratory measurements (300-900 kHz). The intrinsic attenuation and velocity of compressional and shear waves were measured whenever possible. Velocity dispersion is observed for both compressional and shear waves. The intrinsic attenuation of compressional waves is frequency dependent with a peak in the attenuation in the sonic frequency band. The data were modeled assuming the attenuation is caused by local fluid flow in pores of small aspect ratio. The modeling indicates that the intrinsic attenuation may be dominated by cracks with aspect ratios of around 10 (super -3) to 10 (super -4) .

P-SH conversions in a flat-layered medium with anisotropy of arbitrary orientation

Abstract: SUMMARY P-SH conversion is commonly observed in teleseismic P waves, and is often attributed to dipping interfaces beneath the receiver. Our modelling suggests an alternative explanation in terms of flat-layered anisotropy. We use reflectivity techniques to compute three-component synthetic seismograms in a 1-D anisotropic layered medium. For each layer of the medium, we prescribe values of seismic velocities and hexagonally symmetric anisotropy about a common symmetry axis of arbitrary orientation. A compressional wave in an anisotropic velocity structure suffers conversion to both SV-and SH-polarized shear waves, unless the axis of symmetry is everywhere vertical or the wave travels parallel to all symmetry axes. The P-SV conversion forms the basis of the widely used ‘receiver function’ technique. The P-SH conversion occurs at interfaces where one or both layers are anisotropic. A tilted axis of symmetry and a dipping interface in isotropic media produce similar amplitudes of both direct (P) and converted (Ps) phases, leaving the backazimuth variation of the P-Ps delay as the main discriminant. Seismic anisotropy with a tilted symmetry axis leads to complex synthetic seismograms in velocity models composed of just a few flat homogeneous layers. It is possible therefore to model observations of P coda with prominent transverse components with relatively simple 1-D velocity structures. Successful retrieval of salient model characteristics appears possible using multiple realizations of a genetic-algorithm (GA) inversion of P coda from several backazimuths. Using GA inversion, we determine that six P coda recorded at station ARU in central Russia are consistent with models that possess strong (> 10 per cent) anisotropy in the top 5 km and between 30 and 43 km depth. The symmetry axes are tilted, and appear aligned with the seismic anisotropy orientation in the mantle under ARU suggested by SKS splitting.

Kinetic Alfvén waves and plasma transport at the magnetopause

Abstract: Large amplitude compressional type ULF waves can propagate from the magnetosheath to the magnetopause where there are large gradients in density, pressure and magnetic field. These gradients efficiently couple compressional waves with shear/kinetic Alfven waves near the Alfven field-line resonance location (ω=k∥υA). We present a solution of the kinetic-MHD wave equations for this process using a realistic equilibrium profile including full ion Larmor radius effects and wave-particle resonance interactions for electrons and ions to model the dissipation. For northward IMF a KAW propagates backward to the magnetosheath. For southward IMF the wave remains in the magnetopause but can propagate through the k∥=0 location. The quasilinear theory predicts that transport due to KAWs at the magnetopause primarily results from the perpendicular electric field coupling with magnetic drift effects with diffusion coefficient D⟂ ∼ 109 m²/s. For southward IMF additional transport can occur because magnetic islands form at the k∥=0 location. Due to the broadband nature of the observed waves these islands can overlap leading to stochastic transport which is larger than that due to quasilinear effects.

Numerical Generation and Absorption of Fully Nonlinear Periodic Waves

Abstract: Permanent form periodic waves with zero-average mass flux are generated in a two-dimensional numerical wave tank solving fully nonlinear potential flow equations. An absorbing beach is modeled at the end of the tank in which (1) an external free-surface pressure absorbs energy from high frequency waves; and (2) a pistonlike condition absorbs energy from low-frequency waves. A feedback mechanism adaptively calibrates the beach parameters to absorb the period-averaged energy of incident waves. Wave generation and absorption are validated over constant depth, for tanks and beaches of various lengths, and optimal parameter values are identified for which reflection from the beach is reduced to a few percent. Shoaling of periodic waves is then modeled over a 1:50 slope, up to very close to the breaking point. A quasi-steady state is reached in the tank for which (not previously calculated) characteristics of fully nonlinear shoaling waves are obtained.

A model for microwave Doppler sea return at high incidence angles: Bragg scattering from bound, tilted waves

Abstract: We show that if ocean surface waves of the order of a few meters long are frequently steep enough to generate bound centimetric waves, then composite surface scattering theory can account for many anomalous properties of microwave backscatter from the sea at high incidence angles. The model proposed here postulates that these intermediate waves are made sufficiently steep to generate bound centimetric waves because of their modulation by longer, dominant ocean surface waves. The bound centimetric waves have a nonzero mean tilt because they are located on the steep forward face of the intermediate waves, and they move at the speed of the intermediate waves. Applying composite surface scattering theory to this sea surface model, we show that much of the apparently anomalous behavior of microwave sea return measured at incidence angles between 50° and 80° during the Synthetic Aperture Radar and X Band Ocean Nonlinarities-Forschungsplatform Nordsee (SAXON-FPN) experiment can be explained using reasonable parameters to characterize the surface waves. In the SAXON-FPN measurements the mean values of the first moments of microwave Doppler spectra for horizontally polarized backscatter differ from those for vertically polarized backscatter by an amount which varies with the incidence angle and with the azimuthal angle between the radar look direction and the direction of the dominant wave. The modulation of this first moment by surface waves tens of meters in length is the same for the two polarizations at low to moderate incidence angles and can be interpreted in terms of the advection of free centimetric waves by the long waves. At higher incidence angles, however, this modulation is different for the two polarizations and cannot be explained by simple advection of free waves. Finally, microwave cross sections measured at high incidence angles using horizontal polarization are much larger than can be explained by a composite surface theory that includes only freely propagating centimetric waves. Most of these effects can be explained by the composite surface model presented here, which includes Bragg scattering from both free and bound, tilted waves.

Alfven Wave Phase Mixing as a Source of Fast Magnetosonic Waves

Abstract: The nonlinear excitation of fast magnetosonic waves by phase mixing Alfven waves in a cold plasma with a smooth inhomogeneity of density across a uniform magnetic field is considered If initially fast waves are absent from the system, then nonlinearity leads to their excitation by transversal gradients in the Alfven wave The efficiency of the nonlinear Alfven–fast magnetosonic wave coupling is strongly increased by the inhomogeneity of the medium The fast waves, permanently generated by Alfven wave phase mixing, are refracted from the region with transversal gradients of the Alfven speed This nonlinear process suggests a mechanism of indirect plasma heating by phase mixing through the excitation of obliquely propagating fast waves

Field dependence of coupling efficiency between electromagnetic field and ultrasonic bulk waves

Abstract: The coupling mechanism of the electromagnetic acoustic transducer (EMAT) for bulk waves has been studied by examining the magnetic-field dependence of the wave amplitudes. A spiral elongated coil placed on a thin plate of low carbon steel excites and receives the longitudinal and the shear waves propagating in the thickness direction in the presence of the bias magnetic field. The field dependences of the bulk-wave amplitudes are measured using the electromagnetic acoustic resonance both for the normal and tangential bias fields, which showed different features, depending on the bias-field direction and the wave mode. A two-dimensional model is presented for the explanation of the observed results. The present analysis emphasizes the inclined total field in the derivation of the magnetostriction constants, which is revealed to play an essential role for the wave generation. Both the measurement and the model analysis conclude that the magnetostrictive effect dominates the EMAT phenomena for the bulk waves...

The modified Korteweg - de Vries equation in the theory of large - amplitude internal waves

Abstract: The propagation of large- amplitude internal waves in the ocean is studied here for the case when the nonlinear effects are of cubic order, leading to the modified Korteweg - de Vries equation. The coefficients of this equation are calculated analytically for several models of the density stratification. It is shown that the coefficient of the cubic nonlinear term may have either sign (previously only cases of a negative cubic nonlinearity were known). Cubic nonlinear effects are more important for the high modes of the internal waves. The nonlinear evolution of long periodic (sine) waves is simulated for a three-layer model of the density stratification. The sign of the cubic nonlinear term influences the character of the solitary wave generation. It is shown that the solitary waves of both polarities can appear for either sign of the cubic nonlinear term; if it is positive the solitary waves have a zero pedestal, and if it is negative the solitary waves are generated on the crest and the trough of the long wave. The case of a localised impulsive initial disturbance is also simulated. Here, if the cubic nonlinear term is negative, there is no solitary wave generation at large times, but if it is positive solitary waves appear as the asymptotic solution of the nonlinear wave evolution.

Reflection of a high-amplitude solitary wave at a vertical wall

Abstract: (Received 29 February 1996 and in revised form 25 October 1996) The collision of a solitary wave, travelling over a horizontal bed, with a vertical wall is investigated using a boundary-integral method to compute the potential fluid flow described by the Euler equations. We concentrate on reporting new results for that part of the motion when the wave is near the wall. The wall residence time, i.e. the time the wave crest remains attached to the wall, is introduced. It is shown that the wall residence time provides an unambiguous characterization of the phase shift incurred during reflection for waves of both small and large amplitude. Numerically computed attachment and detachment times and amplitudes are compared with asymptotic formulae developed using the perturbation results of Su & Mirie (1980). Other features of the flow, including the maximum run-up and the instantaneous wall force, are also presented. The numerically determined residence times are in good agreement with measurements taken from a cine film of solitary wave reflection experiments conducted by Maxworthy (1976). In this paper we consider the reflection at a vertical wall of a solitary wave, using a boundary-integral numerical code, a perturbation method, and re-analysis of cine film taken during the study by Maxworthy (1976). Most attention is given to that part of the motion during which the point of greatest free-surface elevation (the crest) lies close to the wall. The problem of solitary wave reflection has received attention in studies of the interaction between solitary waves, of which the head-on collision of two equal waves is a special case equivalent to that studied here. When weakly nonlinear solitary waves overtake or collide with one another there may be a spatial phase shift but no loss of energy from either wave once sucient time has passed for the two waves to separate; this is the feature by which a soliton is defined (Zabusky & Kruskal 1965). Recent studies have shown that large-amplitude solitary water waves do not behave like solitons. A long time after the collision between two equal waves there is a loss to secondary waves, and a reduction in wave speed. The reduced wave speed necessarily produces a spatial phase shift that increases without bound as t U¢ . It is useful to briefly review certain aspects of the phenomena we wish to study, some of which bear on the interpretation of results to be presented later. In what follows, f(x, t) is the free-surface elevation about the quiescent fluid level and e fl a}h is the dimensionless solitary wave amplitude, a being the amplitude of the incident wave travelling on a fluid of constant still-water depth h. Byatt-Smith (1971) investigated the interaction between two weakly nonlinear solitary waves travelling in opposite

Wave Propagation in Poroelastic Media Saturated by Two Fluids

Abstract: A theory of wave propagation in isotropic poroelastic media saturated by two immiscible Newtonian fluids is presented. The macroscopic constitutive relations, and mass and momentum balance equations are obtained by volume averaging the microscale balance and constitutive equations and assuming small deformations. Momentum transfer terms are expressed in terms of intrinsic and relative permeabilities assuming the validity of Darcy's law. The coefficients of macroscopic constitutive relations are expressed in terms of measurable quantities in a novel way. The theory demonstrates the existence of three compressional and one rotational wave. The third compressional wave is associated with the pressure difference between the fluid phase and dependent on the slope of the capillary pressure-saturation relation.

Acoustic heterodyne device and method

Abstract: The present invention is the emission of new sonic or subsonic compression waves from a resonant cavity (80) as a result of interference of at least two ultrasonic wave trains (30, 32) In one embodiment, two ultrasonic emitters (20) are oriented toward the cavity When the difference in frequency between the two ultrasonic wave trains is in the sonic or subsonic frequency range, a new sonic or subsonic wave train of that frequency is emitted from within the cavity or region of interference in accordance with the principles of acoustical heterodyning The preferred embodiment is a system comprised of a single ultrasonic radiating element oriented toward the cavity emitting multiple waves

Laboratory studies of seismic wave propagation in inhomogeneous media using a laser doppler vibrometer

Abstract: We performed physical model experiments by utilizing a laser doppler vibrometer (LDV). Because LDV converts velocity of vibration to the Doppler shift frequency, it enables very precise measurements of ultrasonic waves without any resonating element that conventional transducers usually include. A piezoelectric transducer (PZT) was used as a source of elastic waves, and the waveform was measured in a very small area of about 400 μ m in diameter by focusing the beam. We can easily perform very precise measurements of wave field in a physical model, and thus physical model experiments of wave propagation can simulate realistic seismic field observations. For models of inhomogeneous material, we used three granitic rocks with different grain sizes: Westerly granite (fine grained), Oshima granite (medium grained), and Inada granite (coarse grained). Large rock prisms, 300 × 300 × 80 to 90 mm, were used to prevent contamination by multiple reflections from the side ends in the earlier portion of waveforms. The direct P and S waves and reflected waves were identified by their travel times. Observations were made by long in-line, circular, and small-aperture arrays. When the rock grain size becomes comparable to the wavelength, transmitted waves are strongly attenuated by backward scattering, and a large amount of wave energy is transferred to the coda portion. Semblance plots in the time-slowness plane obtained from the small-aperture array suggest that incoherent waves become dominant as the grain size becomes large and comparable to the wavelength.

Absorbing-Generating Boundary Condition for Shallow Water Models

Abstract: An absorbing-generating boundary condition is derived for the two-dimensional-horizontal nonlinear shallow equations using the method of characteristics. It assumes local superposition of the incoming and outgoing long waves at the boundary, and uses a relationship between the flux and surface elevation of the waves. This boundary condition allows the outgoing waves to leave the computational domain through the boundaries with a minimum of reflection, while specifying incoming waves at the same boundaries. The boundary condition's absorbing properties are tested for both linear and nonlinear waves for a range of amplitudes and of angles of incidence. Its performance is compared to the classical Sommerfeld radiation condition for the linear case and is shown to cause significantly less reflection errors, especially for oblique angles. Also, a case of simultaneous absorption and generation of waves at the same boundary is analyzed where it is shown that the errors are of the same order as for the case of ab...

Excess attenuation of leaky Lamb waves due to viscous fluid loading

Abstract: In two recent papers [J. Acoust. Soc. Am. 97, 3191–3193 (1995) and 98, 1057–1064 (1995)], Zhu and Wu presented an analytical technique to assess the effect of viscous fluid loading on the propagation properties of Rayleigh and Lamb waves in fluid-loaded solids. They modeled the viscous fluid as a hypothetical isotropic solid having rigidity c55=−iωη, where η denotes the viscosity of the fluid and ω is the angular frequency. In this way, the vorticity mode associated with the viscosity of the fluid is formally described as the shear-mode in the fictitious solid. In this paper this technique is further developed by removing certain inconsistencies that unnecessarily reduce the accuracy and the range of validity of Zhu and Wu’s results. By properly accounting for viscous effects on the bulk compressional wave in the fluid and applying a rigorous treatment of the field equations and boundary conditions, the exact dispersion equations that are not limited to low frequencies and viscosities are derived. Example...

Model equations for waves in stratified fluids

Abstract: Model equations for gravity waves in horizontally stratified fluids are considered. The theories to be addressed focus on stratifications featuring either a single pycnocline or neighbouring pairs of pycnoclines. Particular models investigated include the general version of the intermediate long-wave equation derived by Kubota, Ko and Dobbs to simulate waves in a model system consisting of two homogeneous layers separated by a narrow region of variable density, and the related system of equations derived by Liu, Ko and Pereira for the transfer of energy between waves running along neighbouring pycnoclines. Issues given rigorous mathematical treatment herein include the well-posedness of the initial value problem for these models, the question of existence of solitary wave solutions, and theoretical results about the stability of these solitary waves.

Solar Wind Acceleration by Solitary Waves in Coronal Holes

Abstract: Coronal holes are well-known sources of the high-speed solar wind; however, the exact acceleration mechanism of the fast wind is still unknown. We solve numerically the time-dependent, nonlinear, resistive 2.5-dimensional MHD equations and find that solitary waves are generated in coronal holes nonlinearly by torsional Alfven waves. The solitary wave phase velocity was found to be slightly above the sound speed in the coronal hole; for example, with the driving Alfven wave amplitude vd ≈ 36 km s-1 and plasma β = 5%, the solitary wave phase speed is ~185 km s-1. We show with a more simplified analytical model of the coronal hole that sound waves are generated nonlinearly by Alfven waves. We find numerically that these waves steepen nonlinearly into solitary waves. In addition, ohmic heating takes place in the coronal hole inhomogeneities owing to phase-mixing of the torsional Alfven waves. When solitary waves are present, the solar wind speed and density fluctuate considerably on timescales of ~20-40 minutes in addition to the Alfvenic fluctuations. The solitary wave-driven wind might be in better qualitative agreement with observations than the thermally driven and WKB Alfven wave solar wind models.

Numerical computation of capillary–gravity interfacial solitary waves

Abstract: Two types of capillary–gravity interfacial solitary waves are computed numerically: ‘classical’ solitary waves which bifurcate from a uniform flow at a critical value of the velocity and solitary waves in the form of wave packets which bifurcate from a train of infinitesimal periodic waves with equal phase and group velocities. The effects of finite amplitude are shown to be quite different from the pure gravity case for the classical solitary waves. The solitary waves in the form of wave packets, which are known to exist for small density ratios, are shown to exist even for larger density ratios, but only at finite amplitude. The numerical code is based on an integro-differential formulation of the full Euler equations. The experimental results of Koop & Butler (1981), which have been compared earlier with results from model equations, are compared with the present numerical results.

Reflection and transmission of qP-qS plane waves at a plane boundary between viscoelastic transversely isotropic media

Abstract: SUMMARY We consider the problem of reflection and transmission in two viscoelastic transversely isotropic (VTI) media in contact, with the symmetry axis of each medium perpendicular to the interface. The problem is investigated by means of a plane-wave analysis and a numerical simulation experiment. For an incident homogeneous wave, the reflected wave is of the same type and is also homogeneous, while the other waves are inhomogeneous, that is, equiphase planes do not coincide with equiamplitude planes. If the transmission medium is elastic, the refracted waves are inhomogeneous of the elastic type, that is, the attenuation vectors are perpendicular to the respective UmovPoynting vectors (energy direction). On the other hand, if the incidence medium is elastic and the transmission medium anelastic, the attenuation vectors of the transmitted waves are perpendicular to the interface. The angle between the attenuation and the real slowness vectors may exceed 90°, but the angle between the attenuation and the Umov-Poynting vectors is always less than 90". As in the anisotropic case, energy flow parallel to the interface is the criterion for obtaining a critical angle, which exists only in rare instances in viscoelastic media. In fact, for this particular example, the transmitted flux of the quasi-compressional wave is always greater than zero. To balance energy flux it is necessary to consider the interference fluxes between the different waves (these fluxes vanish in the elastic case). The relevant physical phenomena are related to the energy flow direction (Umov-Poynting vector) rather than to the propagation direction (real slowness vector). The simulation experiment gives the particle velocity fields caused by a mean stress source. The results are in good agreement with the plane-wave analysis, despite the fact that only a qualitative comparison can be performed. The presence of the conical wave, which cannot be explained with a plane analysis, indicates that, in spite of the absence of a critical angle, some of the refracted energy disturbs the interface.

Numerical prediction of breaking waves and currents with a boussinesq model

Abstract: This paper describes the extension of a comprehensive numerical model for simulating the propagation and transformation of ocean waves in coastal regions and harbours to include wave breaking, runup and breaking-induced currents. The numerical model is based on a time-domain solution of a fully nonlinear set of Boussinesq-type equations for wave propagation in intermediate and shallow water depths. The equations are able to describe most of the phenomena of interest in the nearshore zone including shoaling, refraction, diffraction, reflection, wave directionality and nonlinear wave-wave interactions. The Boussinesq model is extended to the surf and swash zones by coupling the mass and momentum equations with a one-equation model for the temporal and spatial evolution of the turbulent kinetic energy produced by wave breaking. The waves are assumed to start breaking when the horizontal component of the orbital velocity at the wave crest exceeds the phase velocity of the waves. Numerical and experimental results are presented for the shoaling and runup of regular and irregular waves on a constant slope beach and wave-induced currents behind a detached breakwater.

Theory of the time-reversal process in solids

Abstract: In this paper, a theoretical formulation is proposed to describe a time-reversal process in a solid medium with two propagation modes, longitudinal and transverse waves. A plane time-reversal mirror (TRM) is used, installed in a fluid which is in contact with the solid through a plane interface parallel to the TRM. The basic approach is similar to the case of a plane fluid–fluid interface [D. Cassereau and M. Fink, J. Acoust. Soc. Am. 96, 3145–3154 (1994)]; it is extended to take into account the different wave types. It is shown that the TRM is able to recreate properly in time and space the reversed fields of the longitudinal wave and the vertical polarization SV of the transverse waves, but not the horizontal polarization SH. The focusing quality of the backpropagating waves is limited by their respective wavelengths, so the slower SV wave can be better focused. Additional, unwanted wavefronts are created in the solid, too, but they are of weak amplitude and they are not focused. Numerical simulations illustrate the dependence of the focal pattern on parameters like distance–source interface, size, and eccentricity of the mirror.

Apparatus and method for determining movements and velocities of moving objects

Abstract: With an apparatus according to the invention it is possible to detect an object's velocity transverse to the direction of propagation of an interacting field. Such transverse movement is detected by applying a field that oscillates spatially in the transverse direction. The method used in the apparatus is applicable where wave energy is used to sense or detect an object by its scattering properties when using either sound waves or electro-magnetic waves. The movement can be detected according to the field properties. The field represented by the sampling pulse must feature a spatial oscillation in the directions, where the velocity components are of interest. Such a transversely oscillating field is e.g. generated by using apodization on individual transducer elements and a special focusing scheme. The apparatus uses waves of either sound or electro-magnetic radiation.