Showing papers on "Longitudinal wave published in 1990"

Wakes behind blunt bodies

Abstract: years. These results are based on further research into the existen ce of absolutely unstable regions in the near-wake region and the reformulation of the classical von Karman stability theory on near and far fields in the von Karman vortex street. The existence of absolutely unstable regions at supercritical Reynolds numbers makes effcctivc wake control accessible. Figure I explains the differing instabilities in shear layers. The top diagram shows a classical example of a shear layer that was formed by the velocities uland U2 at the upper and lower sides of a splitter plate. The unstable waves of the shear layer traveling downstream have different characteristic phase velocities C1• In general, the shear layer is convectively unstable. Perturbations that are introduced at specific locations in the shear layer then move downstream. The waves do not, with increasing time, influence the source of the disturbances. A hydroacoustical resonance results when a second body is introduced into the shear layer, producing compression waves that travel upstream (middle diagram), so that self­ sustained oscillations can be achieved. For particular distances between the two objects a resonance can be triggercd, which induccs an acoustical wake tone. The shear flow is still locally convectively unstable, but the

Relationships among compressional wave attenuation, porosity, clay content, and permeability in sandstones

Abstract: Anelastic attenuation is the process by which rocks convert compressional waves into heat and thereby modify the amplitude and phase of the waves. Understanding the causes of compressional wave attenuation is important in the acquisition, processing, and interpretation of high‐resolution seismic data, and in deducing the physical properties of rocks from seismic data. We have measured the attenuation coefficients of compressional waves in 42 sandstones at a confining pressure of 40 MPa (equivalent to a depth of burial of about 1.5 km) in a frequency range from 0.5 to 1.5 MHz. The compressional wave measurements were made using a pulse‐echo method in which the sample (5 cm diameter, 1.8 cm to 3.5 cm long) was sandwiched between perspex (lucite) buffer rods inside the high‐pressure rig. The attenuation of the sample was estimated from the logarithmic spectral ratio of the signals (corrected for beam spreading) reflected from the top and base of the sample. The results show that for these samples, compressio...

Two-dimensional wave number spectra of small-scale water surface waves

Abstract: Two-dimensional wave slope spectra have been measured in the large Delft wind-wave facility using an imaging optical technique and digital image processing. The data cover wavelengths from 0.4 to 24cm and wind speeds (U10) from 2.7 to 17.2 ms−1. The spectral densities of small gravity waves at higher wind speeds are proportional to k−3.5 and u*. Capillary-gravity and capillary waves show features which clearly manifest that the energy balance for these waves is much different from that for gravity waves. The degree of saturation is approximately constant at a given wind speed, but strongly increases with friction velocity (∝ u*2.5). A sharp cutoff, which is almost independent of the wind speed, occurs at a wavelength of about 7 mm.

Global anisotropy in the upper mantle inferred from the regionalization of phase velocities

Abstract: A data set of 2600 paths for Rayleigh waves and 2170 paths for Love waves was selected in order to resolve azimuthal anisotropy of surface waves in the period range 70–250 s. The epicenters were chosen so that the paths provide uniform spatial and azimuthal coverage of Earth. A synthetic seismogram is computed for each path and compared to the observed seismogram in order to infer the phase velocity along each path. To process such a large data set, a new tomographic technique is designed. A good correlation is found with surface tectonics in the whole period range for Love waves and at shorter periods for Rayleigh waves. The directions of maximum velocities are also well correlated with plate tectonics motions for the 2ψ azimuthal term of Rayleigh waves. When the power spectrum of heterogeneities is computed, it is found that for Love waves the even orders are usually larger than the odd orders. For Rayleigh waves the degrees 2 and 6 dominate only at long periods, suggesting a deep origin for these components.

Electrostatic lower hybrid waves excited by electromagnetic whistler mode waves scattering from planar magnetic‐field‐aligned plasma density irregularities

Abstract: This paper presents a theoretical model for electrostatic lower hybrid waves excited by electromagnetic whistler mode waves propagating in regions of the magnetosphere and the topside ionosphere, where small-scale magnetic-field-aligned plasma density irregularities are thought to exist. In this model, the electrostatic waves are excited by linear mode coupling as the incident electromagnetic whistler mode waves scatter from the magnetic-field-aligned plasma density irregularities. Results indicate that high-amplitude short-wavelength (5 to 100 m) quasi-electrostatic whistler mode waves can be excited when electromagnetic whistler mode waves scatter from small-scale planar magnetic-field-aligned plasma density irregularities in the topside ionosphere and magnetosphere.

Steepening of kinetic magnetosonic waves into shocklets: Simulations and consequences for planetary shocks and comets

Abstract: The generation and the nonlinear evolution of oblique low-frequency electromagnetic (kinetic magnetosonic) waves which were observed upstream of planetary bow shocks and at the Giacobini-Zinner comet, and referred to as shocklets, were investigated using an electromagnetic hybrid code. The observations show that the waves, which have a sinusoidal form when their amplitude is small, become steepened and linearly polarized as they grow in amplitude. The results of simulations show the original small-amplitude elliptically polarized wave grows and steepens, so that its polarization changes and becomes somewhat linear. The steepening process is associated with the coherent generation of a broad spectrum of waves on the magnetosonic whistler branch, which propagate at various phase and group velocities. It is shown that the presence of shocklets upstream of a planetary bow shock can modify its local structure by changing the solar wind Mach number and temperature, or by colliding with the shock.

The influence of wave breaking on the surface pressure distribution in wind-wave interactions

Abstract: In reviewing the current status of our understanding of the mechanisms underlying wind-wave generation, it is apparent that existing theories and models are not applicable to situations where the sea surface is disturbed by breaking waves, and that the available experimental data on this question are sparse. In this context, this paper presents the results of a detailed study of the effects of wave breaking on the aerodynamic surface pressure distribution and consequent wave-coherent momentum flux, as well as its influence on the total wind stress. Two complementary experimental configurations were used to focus on the details and consequences of the pressure distribution over breaking waves under wind forcing. The first utilized a stationary breaking wave configuration and confirmed the presence of significant phase shifting, due to air flow separation effects, between the surface pressure and surface elevation (and slope) distributions over a range of wind speeds. The second configuration examined the pressure distribution, recorded at a fixed height above the mean water surface just above the crest level, over short mechanically triggered waves which were induced to break almost continuously under wind forcing. This allowed a very detailed comparison of the form drag for actively breaking waves and for waves of comparable steepness just prior to breaking (‘incipiently’ breaking waves). For these propagating steep-wave experiments, the pressure phase shifts and distributions closely paralleled the stationary configuration findings. Moreover, a large increase (typically 100%) in the total windstress was observed for the breaking waves, with the increase corresponding closely to the comparably enhanced form drag associated with the actively breaking waves. In addition to further elucidating some fundamental features of wind-wave interactions for very steep wind waves, this paper provides a useful data set for future model calculations of wind flow over breaking waves. The results also provide the basis for a parameterization of the wind input source function applicable for a wave field undergoing active breaking, an important result for numerical modelling of short wind waves.

Measurements of acoustic wave velocities and attenuation in marine sediments

Abstract: Propagation and attenuation of acoustic waves in fluid‐saturated sediments have been studied theoretically and experimentally. In situ acoustic transmission tests in saturated beach sand show that compressional waves are dispersive within a certain frequency band where the intrinsic attenuation is maximum. This indicates that low‐frequency wave velocities in marine sediments are at least 5% to 10% less than the velocities obtained from high‐frequency measurements, and viscous damping, due to the relative motion between solid skeleton and fluid, is the main damping mechanism in the frequency range of 1–30 kHz. The agreement between the experimental results and Biot’s theory enables the remote determination of porosity and permeability of marine sediments by using measured compressional and shear wave characteristics. Approximate relations are used to determine the porosity and permeability of the marine sediments using the measured acoustic wave velocities and attenuation.

Polarization and coherence of 5 to 30 Hz seismic wave fields at a hard-rock site and their relevance to velocity heterogeneities in the crust

Abstract: Except for its very onset, the P wave of earthquakes and chemical explosions observed at two narrow-aperture arrays on hard-rock sites in the Adirondack Mountains have a nearly random polarization. The amount of energy on the vertical, radial, and transverse components is about equal over the frequency range 5 to 30 Hz, for the entire seismogram. The spatial coherence of the seismograms is approximately exp(− cf Δ x ), where c is in the range 0.4 to 0.7 km −1 Hz −1 , f is frequency and Δ x is the distance between array elements. Vertical, radial, and transverse components were quite coherent over the aperture of the array, indicating that the transverse motion of the compressional wave is a property of relatively large (10 6 m 3 ) volumes of rock, and not just an anomaly caused by a malfunctioning instrument, poor instrument-rock coupling, or out-crop-scale effects. The spatial coherence is approximately independent of component, epicentral azimuth and range, and whether P - or S -wave coda is being considered, at least for propagation distances between 5 and 170 km. These results imply a strongly and three-dimensionally heterogeneous crust, with near-receiver scattering in the uppermost crust controlling the coherence properties of the waves.

Magnetosonic waves above fc (H+) at geostationary orbit: GEOS 2 results

Abstract: The fast magnetosonic waves in the frequency range 1–11 Hz (i.e., above the proton gyrofrequency Ωp) are considered. The electric wave field δE (mostly less than 0.5 mV/m) has an elliptic polarization in the plane perpendicular to B. While the magnetic wave field δB is strictly polarized along the ambient magnetic field, the ellipticity and the sense of rotation of the electric field polarization ellipses are crucial parameters for the identification of the wave mode. The waves are right-hand polarized, and the ellipticity is usually about 0.2. The main axis of the ellipse is close to the azimuthal direction. The wave vector k is almost parallel to δE, and thus the fast magnetosonic waves propagate at small angles to the azimuthal direction. The wavelengths are usually between 150 and 300 km. The δE/δB ratio of the waves is between νA and υA(1 + ω²/Ωp²)1/2, where υA is the Alfven velocity. In one case a burst of pure electrostatic modes near the second harmonic of the proton gyrofrequency was observed.

Optical and thermal parameter effects on laser‐generated ultrasound

Abstract: The use of a pulsed laser source for the generation of elastic waves in materials is investigated, taking into account optical penetration into the material. Under appropriate conditions, a significant feature of the laser‐generated elastic waveform is a precursor (sharp spike) signaling the arrival of the longitudinal wave. The shape of this precursor signal is strongly dependent on the optical and thermal properties of the material. This paper shows that the observed precursor can be understood through the use of models that account for optical penetration and thermal diffusion into the material.

Effects of azimuthal asymmetry on ULF waves in the dipole magnetosphere

Abstract: The properties of the coupling of compressional and transverse ULF waves strongly depend on the azimuthal wavenumber m. The authors investigate these effects in a numerical model of ULF wave propagation in a dipolar magnetosphere. As the azimuthal wave number m becomes larger, the frequencies of the global modes are increased, each coupling location is shifted toward the plasmapause, and the wave energy of global compressional modes in the magnetosphere is confined to a smaller region near the magnetopause. These conclusions are qualitatively consistent with previous analytical and numerical models. It is suggested that the radial dependence of the azimuthal wavelength in the dipole geometry is important to the propagation of compressional waves. This effect is not present in either box or cylindrical models, in which the azimuthal wavelength does not depend on the radial distance, and can be distinguished from effects arising from the inhomogeneity of the Alfven speed. On the other hand, the Alfven shear modes are found to have periods independent of m.

Harbour excitations by incident wave groups

Abstract: By using the multiple-scales perturbation method, analytical solutions are obtained for the second-order low-frequency oscillations inside a rectangular harbour excited by incident wave groups. The water depth is a constant. The width of the harbour entrance is of the same order of magnitude as the wavelength of incident carrier (short) waves, but small in comparison with the wavelength of the wave envelope. Because of the modulations in the wave envelope, a second-order long wave is locked in with the wave envelope and propagates with the speed of the group velocity. Outside the harbour, locked long waves also exist in the reflected wave groups, but not in the radiated wave groups. Inside the harbour, the analytical expressions for the locked long waves are obtained. Owing to the discontinuity of the locked long waves across the harbour mouth, second-order free long waves are generated. The free long waves propagate with a speed of (gh)½ inside and outside the harbour. The free long waves inside the harbour may be resonated in a low-frequency range which is relevant to the harbour resonance.

Slow wave propagation in air‐filled porous materials and natural rocks

Abstract: Slow compressional waves in fluid‐saturated porous solids offer a unique acoustical means to study certain material properties, such as tortuosity and permeability. We present a novel experimental technique based on the transmission of airborne ultrasound through air‐filled porous samples. The suggested method can be used to measure the velocity and attenuation of the slow compressional wave in a wide frequency range from 30 to 500 kHz. More important, the technique is so sensitive that it provides irrefutable evidence of slow wave propagation in air‐saturated natural rocks and lends itself quite easily to tortuosity measurements in such materials, too.

Observation and theory of Pc 5 waves with harmonically related transverse and compressional components

Abstract: The properties of 23 magnetic pulsation events observed by the AMPTE CCE spacecraft are studied. These events are selected on the basis of the field magnitude which oscillated at the second harmonic of a simultaneously present transverse oscillation. The events have a second harmonic period of 80-600 s (roughly the Pc 5 range), are observed in cluster in the dawn (0300-0800 magnetic local time, MLT) and dusk (1600-2100 MLT) sectors, and are localized near the magnetic equator. Although the azimuthal wave number estimated from an ion finite Larmor radius effect, is generally large (about 50), there is a marked difference between the events observed in the dawn and dusk sectors. In the dawn sector the waves have low frequencies (1-5 mHz), indicate left-hand polarization with respect to the ambient magnetic field, and propagate eastward with respect to the spacecraft. In the dusk sector the waves have high frequencies (5-15 mHz), indicate right-hand polarization, and propagate westward. It is suggested that the waves are all westward propagating in the plasma rest frame and that local-time-dependent Doppler shift is the reason for the local time dependence of the wave properties.

A Lagrangian model for wave-induced harbour oscillations

Abstract: A set of equations in the Lagrangian description are derived for the propagation of long gravity waves in two horizontal directions for the purpose of determining the response of harbours with sloping boundaries to long waves. The equations include terms to account for weakly nonlinear and dispersive processes. A finite element formulation for these equations is developed which treats the propagation of transient waves in regions of arbitrary shape with vertical or sloping boundaries. Open boundaries are treated by specifying the wave elevation along the boundary or by applying a radiation boundary condition to absorb the waves leaving the computational domain. Nonlinear aspects of the interaction of long gravity waves with sloping boundaries and frequency dispersion due to non-hydrostatic effects are investigated. Results from the model are then compared with laboratory experiments of the response to long-wave excitation of a narrow rectangular harbour with a depth that decreases linearly from the entrance to the shore line.

On the Propagation of Maximally Dissipative Phase Boundaries in Solids

Abstract: This paper is concerned with the kinetics of propagating phase boundaries in a bar made of a special nonlinearly elastic material. First, it is shown that there is a kinetic law of the form f = φ(s) relating the driving traction f at a phase boundary to the phase boundary velocity s that corresponds to a notion of maximum dissipation analogous to the concept of maximum plastic work. Second, it is shown that a modified version of the entropy rate admissibility criterion can be described by a kinetic relation of the above form, but with a different φ. Both kinetic relations are applied to the Riemann problem for longitudinal waves in the bar.

On the nature of the so-called subsurface longitudinal wave and/or the surface longitudinal ``creeping'' wave

Abstract: The elastic wave field of certain angle beam probes used for nondestructive testing of solid materials, like steel, has been shown to exhibit a so-called subsurface longitudinal wave, i.e., a wavefront traveling with the pressure wave speed having a beam angle of approximate 74° in steel. In addition, this wavefront is supposed to be connected to the stress-free surface via a headwave, which radiates a nearly plane wave with shear velocity into the bulk material under an angle of 33°, approximately, and giving rise to a strongly attenuated longitudinal “creeping” wave on the surface. In the present paper we utilize a new numerical scheme for the computation of elastodynamic wave fields in nearly arbitrary environments, called elastodynamic finite integration technique (EFIT), to predict the above-mentioned wave features quantitatively. Furthermore, we employ several analytical and analytical-numerical integration procedures to evaluate the angle beam probe plane wave spectrum in terms of an inverse spatial Fourier transform. This gives rise to a theoretical interpretation of the physical origin of the numerically computed EFIT wavefronts. Essential results are as follows: the particular wavefronts of angle beam probes, as referred to in this paper, are exclusively associated with afinite aperture radiating into an elastic half-space; they cannot be explained in terms ofsingle homogeneous and inhomogeneousplane waves. The subsurface longitudinal wave emerges from the superposition of the edge pressure waves of the transducer, resulting in a propagation with pressure wave speed, but, in the near-field, where it is often employed, it is not longitudinally polarized. On the surface, and very close to it, the superposition of the subsurface longitudinal wave and the head waves associated with the probe edges gives rise to a strongly attenuated wavefront exhibiting longitudinal as well as transverse particle displacement components, but neither a surface wave nor a creeping wave is really involved. The bulk shear wavefront is not an appendix of the head wave but the “geometric optical” shear wave radiation pattern of the finite probe.

Transverse modulational instability of collinear waves

Abstract: The transverse modulational instability, or filamentation, of two collinear waves is investigated, using a coupled nonlinear Schrodinger-equation model. For infinite media it is shown that the presence of the second laser field increases the growth rate of the instability and decreases the scale length of the most unstable filaments. Systems of two copropagating waves are shown to be convectively unstable and systems of two counterpropagating waves are shown to be absolutely unstable, even when the ratio of backward- to forward-wave intensity is small. For two counterpropagating waves in finite media, the threshold intensities for the absolute instability depend only weakly on the ratio of wave intensities. The general theory is applied to the pondermotive filamentation of two light waves in homogeneous plasma.

Nondestructive characterization of texture and plastic strain ratio of metal sheets with electromagnetic acoustic transducers

Abstract: All the lowest‐order independent CODF (crystallite orientation distribution function) coefficients W400, W420, and W440 of rolled steel sheets, with thickness less than 1 mm, have been obtained nondestructively by using the known single‐crystal elastic constants and the relative ultrasonic velocities measured with EMATs (electromagnetic acoustic transducers). The ultrasonic velocities of all the waves, longitudinal waves, shear waves propagating in the through thickness direction, and SH0 (shear horizontal) plate waves, were measured by the EMATs. No acoustic coupling medium was necessary, making possible quick, accurate, and reproducible measurements. It is shown that the CODF coefficients can be obtained as the solutions of three linear equations in which the measured relative ultrasonic velocities are included. There was an overall correspondence between the ultrasonic pole figures drawn using the obtained CODF coefficients and x‐ray pole figures. All nine elastic constants of a steel sheet were also c...

Laboratory observation of elastic waves in solids

Abstract: Compressional, torsional, and bending waves in bars and plates can be studied with simple apparatus in the laboratory. Although compressional and torsional waves show little or no dispersion, bending waves propagate at a speed proportional to (f)1/2. Reflections at boundaries lead to standing waves that determine the vibrational mode shapes and mode frequencies. Boundary conditions include free edges, simply supported edges, and clamped edges. Typical mode shapes and mode frequencies for rectangular bars, circular plates, and square plates are described.

Solitary waves on conduits of buoyant fluid in a more viscous fluid

Abstract: Fluid of a lower density and viscosity can buoyantly rise through a viscous fluid through conduits that support simple pipe flows. The conduits also support solitary waves which exhibit near soliton behavior. Laboratory experiments on the characteristics of the solitary waves and their interactions have been conducted and compared with theory. The observations of shape and phase speed of individual waves show good agreement with the theoretical predictions. Large amplitude waves traveled slightly faster than the theoretical predictions. The discrepancy is probably due to higher order effects associated with wave slope not accounted for in the theory. Individual wave characteristics (shape, amplitude and speed) were very nearly preserved after collision with another wave. A phase jump of each wave was the main consequence of an interaction. The larger (faster) waves increased in amplitude by an average of 5 percent after collision and their phase speeds decreased by an average of 4 percent. The sm...

A comprehensive investigation of compressional ULF waves observed in the ring current

Abstract: Eighteen months of data provided by the magnetometer and energetic particle spectrometer on board the geosynchronous satellite GEOS 2 were used to investigate compressional ULF waves with frequencies of a few megahertz associated with large anticorrelated modulations of the ion pressure. The events are classified into two groups according to the behavior of the background magnetic field/plasma configuration at the onset of the oscillations. For one group the oscillation onset is preceded by a sharp increase of the plasma energy density due to the arrival of drifting ion bunches at the satellite and a corresponding diamagnetic decrease of the magnetic field strength. The other group is observed in a steady configuration in the presence of an enhanced ring current. Besides striking differences between the two groups as regards the average event duration and wave frequency, as well as the phase relation between electron and ion flux modulations, we present evidence that both groups of events are of antisymmetric structure with respect to the geomagnetic equator (where symmetry is defined according to the field line displacement) and have a small field-aligned wavelength. Furthermore, for both groups the frequency variation with local time and the azimuthal propagation are closely connected with the ion magnetic gradient curvature drifts, and the waves are associated with a plasma distributed anisotropically in velocity space. Therefore the waves most likely represent the excitation of a single wave mode generated via wave-particle interactions. Using plasma parameters measured in situ we calculated the growth rate of different hydromagnetic wave modes. It was found that the plasma is able to support a wave mode similar to the drift mirror mode with a large parallel wave number, if the effects of a strongly curved magnetic field are taken into account.

Highly nonlinear magnetic pulses at Comet Giacobini-Zinner

Abstract: Nonlinear solitary magnetic pulses have been detected near the outbound bow shock/wave of Comet Giacobini-Zinner. The pulses have peak field-to-background compression ratios ranging from 2.3 to 7.0 and full-width half-maximum durations from 12 to 72s, comparable to the H2O group ion gyroperiod. Because all of the solitary waves have the same spacecraft-frame polarizations, it is suggested that the waves may have phase speeds greater than the solar wind speed. The role that the waves may play with the bow shock is discussed briefly.

Low‐frequency current drive and helicity injection

Abstract: For ω≪Ωi, where Ωi is the ion cyclotron frequency, circularly polarized waves can drive current far exceeding the current resulting from linearly polarized waves. Further, the efficiency can be independent of plasma density. In some cases, this circular polarization may be interpreted in terms of helicity injection. For tokamak applications, where the wavenumber in the toroidal direction is a real quantity, wave helicity is injected only with finite Ez waves, where z is the direction of the static magnetic field. The Alfven waves are possible current drive candidates but, in the cylindrical model considered, the compressional wave is weakly damped because Ez =0, while the shear Alfven wave is totally absorbed at the surface because of finite Ez. A mixture of the two modes is shown to drive an oscillatory surface current even though the efficiency is high and independent of density. A more promising current drive candidate is a fast wave that propagates to the plasma interior and is damped by the minority ...

The first direct measurements of upper oceanic crustal compressional wave attenuation

Abstract: The first direct measurement of compressional wave attenuation of the uppermost 650 m of oceanic crust was performed using data recorded by seafloor hydrophones and large (56–116 kg), deep, explosive sources. The site was 13 km east of the southernmost Juan de Fuca Ridge on crust 0.4 m.y. old Spectral ratios were performed between bottom refracting waves and direct water waves, adjusted for spreading losses and transmission coefficient losses. Several tests of the data were performed, demonstrating that attenuation is linearly related to frequency between 15 and 140 Hz, but frequency-independent components of attenuation are also evident. Values of compressional wave Q cluster between 20 and 50 and do not show any systematic variation with depth over 650 m. The attenuation results also indicate the presence of heterogeneities within the crust, as the solutions for each receiver's data set are significantly different. No evidence for azimuthal variations of attenuation are supported by the data, although the data do not optimally sample a wide variation of azimuths. Our attenuation values are judged to be normal to higher than expected for the whole oceanic crust, based upon comparisons to results from synthetic seismogram modeling by others and by modeling signal to noise ratios of typical seismic refraction profiles. The results are consistent with recent laboratory measurements at ultrasonic frequencies for dry and saturated basalts at seafloor pressures and temperatures.