Showing papers on "Phase velocity published in 1992"

Multidimensional modeling of turbulent two‐phase flows in stirred vessels

Abstract: This article outlines a computational procedure for the prediction of dispersed two-phase, solid-liquid and gas-liquid, turbulent flows in baffled, impeller-stirred vessles common in the chemical industries. A two-flow Eulerian model is employed, based on the main assumption of interpenetrating coexisting continua. Mean momentum and mass conservation equations are solved for each phase and turbulent closure is effected by extending the single phase k- epsilon turbulence model to two-phase flows. The resulting set of highly coupled equations is solved by a two-phase implicit algorithm, PISO-2P, which allows calculation for a wide range of phase fraction, particle size and phase density ratios. Predictions are presented for solid-liquid and gas-liquid (bubbly) flows. Comparisons are made with experimental data for the mean phase velocities and volume fraction, mean slip velocity and turbulence quantities. (from Authors)

Capillary rollers and bores

Abstract: A very intriguing phenomenon, which throws much light on the small-scale structure of the sea surface, is the occurrence of “parasitic capillaries” on the forward face of moderately short gravity waves, especially those with wavelengths 5 to 50 cm; see Figure la. These capillary waves were first studied experimentally by Cox (1958). Evidently their existence depends on the fact that a gravity wave and a much shorter capillary wave may have the same phase speed. The dynamical theory of the generation of parasitic capillaries has been developed by Longuet-Higgins (1963), Crapper (1970) and Ruvinsky et al. (1981, 1985, 1991). This so far takes into account only the first-order effects of viscous damping.

Instabilities of shallow dynamic thermocapillary liquid layers

Abstract: Results of experiments with thermocapillary flow in shallow liquid layers heated from the side are presented. The fluid has Prandtl number 17 and the main configuration investigated is an annular gap to avoid side‐wall effects. The liquid depth d was d≤3.00 mm to have negligible buoyancy effects. Various instabilities have been observed. At a Marangoni number M≂6⋅102, a transition to steady multicellular flow occurred. The convection cells are longitudinal rolls embedded in the main flow all rotating in the same direction. At M≂3⋅103, a transition of the steady multicellular flow to time‐dependent flow states (t) was observed. Two different t‐flow states have been identified by thermocouple measurements and by visualization of the dynamic‐free surface deformations of oscillatory flow. Both t states can be described by disturbances in the form of traveling waves. A short‐wavelength t state with small surface deformations and with waves traveling in azimuthal direction is the preferred mode for d≤1.4 mm. A long‐wavelength t state with larger surface deformations and with waves traveling in radial and in azimuthal directions is preferred for d≥1.4 mm. The stability diagram, wavelength, frequency, and phase speed of both t states are presented and the findings in comparison to an already existing theory by Smith and Davis [J. Fluid Mech. 132, 119, 145 (1983)] are discussed.

Laser generation and detection of surface acoustic waves: Elastic properties of surface layers

Abstract: A noncontact all‐optical method for surface photoacoustics is described. The surface acoustic waves (SAWs) were excited employing a KrF laser and detected with a Michelson interferometer using a 633‐nm HeNe laser. Due to an active stabilization scheme developed for the interferometer a surface displacement of 0.2 A could be detected. The materials investigated included pure materials such as polycrystalline aluminum, and crystalline silicon; films of gold, silver, aluminum, iron, and nickel on fused silica; and a‐Si:H on Si(100). In the case of pure materials the shape of the acoustic pulse and the phase velocity were determined. The dispersion of the SAW phase velocity observed for the film systems was used to extract information on the film thickness, density, and transverse and longitudinal sound velocity. Models for the theoretical treatment of film systems and the calculation of dispersion curves are presented.

A Seismic Model for the Source of Long-Period Events and Harmonic Tremor

Abstract: The sharply peaked spectra of long-period events and harmonic tremor can be explained by the resonance of a three-dimensional, fluid-driven crack induced by a pressure transient applied over a small area ΔS of the crack wall. The crack resonance is sustained by a very slow dispersive wave called the crack wave, the phase velocity of which decreases rapidly with increasing wavelength and with increasing values of the crack stiffness, C = (b/μ)(L/d), a dimensionless parameter where b is the bulk modulus of the fluid, μ is the rigidity of the solid, L is the crack length and d the crack thickness. The excitation of modes depends on the position of the pressure transient, the extent of crack surface affected by the transient, the time history of the transient, and the boundary conditions in effect at the crack perimeter. The far-field spectrum depends critically on the crack stiffness and on the impedance contrast between the fluid and solid, Z = (ρ s α)/(ρ f α), in which ρ s , ρ f are the densities of the solid and fluid, and α and a represent the velocity of the compressional wave in the solid and acoustic wavespeed of the liquid, respectively. Lowering the ratio b/μ, or increasing the ratios α/a and ρ s /ρ f increases Z, which increases the signal duration. The duration of resonance is measured by the quality factor Q describing the damping of oscillations of the dominant mode observed in the far field. Values of Q ≃ 10 - 20 that are consistent with those observed for shallow tremor and long-period events can be obtained with Z ≃ 3 - 40, b/μ ≃ 0.5 - 0.01, α/a ≃ 2 - 8, and ρ s /ρ f ≃1.5 - 5. A high impedance contrast Z and sustained oscillatory source within the fluid are required to explain Q > 20 observed in some events. The low ratio b/μ associated with the large values of Z can be achieved with void fractions of gas in the liquid ranging up to a few percent. The presence of these bubbles drastically reduces the acoustic wavespeed of the fluid so that resonance at a long period is possible in a crack of small dimensions. The far-field signature is strongly dependent on the spatio-temporal characteristics of the transient driving the crack. These features of the model suggest that the dynamics of the gas phase may play a critical role in the excitation mechanism of both long-period events and tremor.

Double through‐transmission bulk wave method for ultrasonic phase velocity measurement and determination of elastic constants of composite materials

Abstract: This paper describes a modification of a nondestructive ultrasonic method for measurements of the phase velocity of bulk waves in arbitrary directions in generally anisotropic materials. In the conventional method the through‐transmission technique is used for velocity measurements at a specified angle of incidence. When this angle is changed by rotation of the sample, the transmitted beam changes position, and so the position of the receiving transducer must be changed. This leads to experimental difficulties and loss of precision. In the double‐transmission technique, the ultrasonic wave is reflected from reflector plates behind the sample and returns via the same path to the same position on the transmitter/receiver working in pulse‐echo mode, which eliminates the necessity of readjusting the receiver position. It is also shown that for arbitrary direction of measurement in anisotropic materials, time‐delay measurements give phase velocity regardless of the angle of deviation between phase and group ve...

Harmonic excitation of mantle Rayleigh waves by the 1991 eruption of Mount Pinatubo, Philippines

Abstract: An unusually long (at least two hours) seismic wave train having periods of about 230 sec was recorded at many worldwide seismic stations during the major eruption of Mount Pinatubo in the Philippines on June 15, 1991. This wave train exhibits two sharp spectral peaks at 228 and 270 sec. The group velocity, phase velocity, and the particle motion of this wave train indicate that it is a Rayleigh wave. The most probable excitation mechanism is acoustic coupling of atmospheric oscillations that were set off by continuous thermal energy flux from the volcano. The two spectral peaks correspond to the characteristic periods of acoustic and gravity modes of the Earth's atmosphere. The magnitude of the vertical single force equivalent to the acoustic coupling is 1.6×10^(17) dynes over a frequency band of 0.003 to 0.01 Hz. The results suggest the possibility of using acoustically coupled Rayleigh waves for detection, characterization and quantification of volcanic eruptions. Acoustic coupling of the atmosphere and the solid Earth provides a unique seismic source with long duration.

Neural basis for eye velocity generation in the vestibular nuclei of alert monkeys during off-vertical axis rotation

Abstract: Activity of “vestibular only” (VO) and “vestibular plus saccade” (VPS) units was recorded in the rostral part of the medial vestibular nucleus and caudal part of the superior vestibular nucleus of alert rhesus monkeys. By estimating the “null axes” of recorded units (n = 79), the optimal plane of activation was approximately the mean plane of reciprocal semicircular canals, i.e., lateral canals, left anterior-right posterior (LARP) canals or right anterior-left posterior (RALP) canals. All units were excited by rotation in a direction that excited a corresponding ipsilateral semicircular canal. Thus, they all displayed a “type I” response. With the animal upright, there were rapid changes in firing rates of both VO and VPS units in response to steps of angular velocity about a vertical axis. The units were bidirectionally activated during vestibular nystagmus (VN), horizontal optokinetic nystagmus (OKN), optokinetic afternystagmus (OKAN) and off-vertical axis rotation (OVAR). The rising and falling time constants of the responses to rotation indicated that they were closely linked to velocity storage. There were differences between VPS and VO neurons in that activity of VO units followed the expected time course in response to a stimulus even during periods of drowsiness, when eye volocity was reduced. Firing rates of VPS units, on the other hand, were significantly reduced in the drowsy state. Lateral canal-related units had average firing rates that were linearly related to the bias or steady state level of horizontal eye velocity during OVAR over a range of ±60 deg/s. These units could be further divided into two classes according to whether they were modulated during OVAR. Non-modulated units (n = 5) were VO types and all modulated units (n = 5) were VPS types. There was no significant difference between the bias level sensitivities relative to eye velocity of the units with and without modulation (P>0.05). The modulated units had no sustained change in firing rate in response to static head tilts and their phases relative to head position varied from unit to unit. The phase did not appear to be linked to the modulation of horizontal eye velocity during OVAR. The sensitivities of unit activity to eye velocity were similar during all stimulus modalities despite the different gains of eye velocity vs stimulus velocity during VN, OKN and OVAR. Therefore, VO and VPS units are likely to carry an eye velocity signal related to velocity storage. For example, when unit sensitivities were related to head or surround velocity, sensitivity relative to OVAR was less than for VN or OKN. Firing rates of both vertical canal-related VO and VPS units (n= 19) were strongly modulated during OVAR, although they did not show changes in discharge rate during static head tilts relative to the spatial vertical up to a maximal 25 deg. In some cases the amplitude of the modulation increased with increases in head velocity and eye velocity. Average activity of vertical canal-related units was linearly related to steady state horizontal eye velocity in the ipsilateral direction during OVAR. The mean sensitivities of RALP units were not significantly different from those of LARP neurons (P>0.05). Together, their mean sensitivity during OVAR about a subject yaw axis was 0.34 (imp/s)/(deg/s) relative to horizontal eye velocity. This could be explained as a contribution of the vertical canals to horizontal eye velocity due to their orientation in the head. During OVAR to the ipsilateral side, the bias level of neuronal activity decreased and saturated. For steps of rotation about a vertical axis with the animal upright, the firing rates of RALP and LARP units were linearly related to stimulus velocity and eye velocity. Contralateral rotation excited the units reflecting the orientation of the semicircular canals relative to the yaw axis of rotation. RALP and LARP units also responded during horizontal optokinetic stimulation producing both OKN and OKAN. All the “vertical canal” units had dynamic characteristics closely related to velocity storage. Their response characteristics were consistent with the model that they contribute to horizontal slow phase velocity as part of a three-dimensional system based on a semicircular canal frame of reference. Otolith-related units (n= 5) in the vestibular nuclei showed no evidence of velocity storage and were modulated in accordance with head position during OVAR. Mean amplitude of the modulation of activity during OVAR at a 20 deg tilt and 60 deg/s rotational velocity was 24 imp/s. The data indicate that the vestibular nuclei contain the requisite signals to generate horizontal eye velocity during OVAR. VO and VPS units probably contribute to the “bias” or velocity storage component while otolith units mainly contribute to the oscillations in eye velocity by generating gravity dependent eye position changes during OVAR. In addition to the velocity storage component of horizontal eye velocity, the vertical VO neurons also have oscillations in their discharge patterns probably related to the vertical component of eye movements generated by the velocity storage integrator.

The propagation of Lamb waves in a plate bordered with layers of a liquid

Abstract: The influence of liquid layers on the propagation of Lamb waves in a plate of finite thickness is studied theoretically. The dispersion equations of Lamb waves in a plate bordered with layers of liquids are derived. Numerical solutions of the equations show that the phase velocity of Lamb waves changes with the thickness of the liquid layers. For the lowest antisymmetrical mode of very thin plates, the numerical results calculated from the dispersion equations are compared with those derived from the bending wave acoustic impedance approach. The limitation of the latter is discussed. Applications of Lamb waves pertinent to biosensing are also presented.

Observation of modulational instability in Nd-laser beat-wave experiments.

Abstract: The modulational instability of the high-phase-velocity plasma wave generated by a Nd-laser beat wave has been observed for the first time Both ion and electron waves are detected when the electron density is close to the resonant density for which the plasma frequency is equal to the difference frequency between the two pump lasers We also detect the presence of harmonics of the beat frequency which are a signature of high-amplitude density perturbations

Third-harmonic generation with ultrahigh-intensity laser pulses.

Abstract: When an intense, plane-polarized, laser pulse interacts with a plasma, the relativistic nonlinearities induce a third-harmonic polarization. A phase-locked growth of a third-harmonic wave can take place, but the difference between the nonlinear dispersion of the pump and driven waves leads to a rapid unlocking, resulting in a saturation. What become third-harmonic amplitude oscillations are identified here, and the nonlinear phase velocity and the renormalized electron mass due to plasmon screening are calculated. A simple phase-matching scheme, based on a resonant density modulation, is then proposed and analyzed.

Scattering of elastic waves by a fracture zone containing randomly distributed cracks

Abstract: We theoretically study the scattering ofP, SV andSH waves by a zonal distribution of cracks, which simulates a fault fracture zone. An investigation is conducted how the geometrical properties of the crack distribution and the frictional characteristics of the crack surface are reflected in the attenuation and dispersion of incident waves, as well as in the amplitudes of the transmitted and reflected waves from the zone. If the crack distribution within the fault zone changes temporally during the preparation process of the expected earthquake, it will be important for earthquake prediction to monitor it, utilizing the scattering-induced wave phenomena. We consider the two-dimensional problem. Aligned cracks with the same length are assumed to be randomly distributed in a zone with a finite width, on which elastic waves are assumed to be incident. The distribution of cracks is assumed to be homogeneous and sparse. The crack surface is assumed to be stress-free, or to undergo viscous friction; the latter case simulates fluid-filled cracks. The opening displacement of the crack is assumed to be negligibly small. The idea of the mean wave formalism is employed in the analysis, and Foldy's approximation is assumed. When the crack surface is stress-free, it is commonly observed for every wave mode (P, SV andSH) that the attenuation coefficientQ −1 peaks aroundka∼1, the phase velocity is almost independent ofk in the rangeka 1, wherek is the intrinsicS wavenumber anda is the half length of the crack. The effect of the friction is to shift the peak ofQ −1 and the corner of the phase velocity curve to the low wavenumber range. The high wavenumber asymptote ofQ −1 is proportional tok −1 independently of model parameters and the wave modes. If the seismological observation thatQ −1 ofS waves has a peak at around 0.5 Hz in the earth's crust is combined with our results, the upper limit of crack size within the crust is estimated about 4 km. The information regarding the transmitted and reflected waves, such as the high wavenumber limit of the amplitude of the transmitted wave etc., allows estimation of the strength of the friction.

Self-consistent field theory of a helix traveling wave tube amplifier

Abstract: A self-consistent relativistic field theory of a helix traveling wave tube (TWT) is presented for a configuration in which a thin annular beam propagates through a sheath helix enclosed within a loss-free wall. A linear analysis of the interaction is carried out, subject to the boundary conditions imposed by the beam, helix, and wall. A detrimental dispersion equation is obtained which implicitly includes beam space-charge effects without recourse to a heuristic model of the space-charge field. The equation is valid for arbitrary azimuthal mode number and is solved numerically for the azimuthally symmetric case. The coupled-wave Pierce theory is recovered in the near-resonant limit. Numerical comparisons between the complete dispersion equation and the Pierce model are described. A discrepancy is found between the Pierce and the field theory even for low currents in the nominally ballistic regime, owing to the dielectric effect of the beam on the helix modes. >

Effects of acceleration on the accuracy of MR phase velocity measurements.

Abstract: Acceleration in blood flow can affect the accuracy of phase velocity measurements. Convective acceleration is due to changes in flow geometry and is independent of the time-varying acceleration caused by flow pulsatility. To analyze the effects of convective acceleration on flow velocity measurements, phase velocity measurements were obtained in steady laminar flow in the convergent segment of a 90%, hourglass-shaped stenosis phantom at a Reynolds number of 1,500. Measurements at the stenosis indicated that convective acceleration caused the measured values of average cross-sectional velocity to deviate as much as 37% from the theoretical values. The magnitude of the error could be accounted for by including the convective acceleration term in the phase shift equation. Convective acceleration effects should not be ignored in flow velocity measurements through stenoses, even when time-dependent acceleration due to flow pulsatility can be neglected.

Nonlinear evolutions of surface gravity waves on fluid of finite depth.

Abstract: t appended to p and ri denote partial differentiations. This notation will be used throughout the paper. ri is assumed to be negative without loss of generality. The dimensional quantities, with tildes, are related to the corresponding dimensionless ones by the relations x = lx, y =hpy, t =(l/cp)t, ri art, and p =(gla/cp)p, where l, a, and cp are characteristic scales of length, amplitude, and velocity of the wave, respectively, — hp is the vertical coordinate of the flat bottom, and g is the acceleration due to gravity. The dimensionless parameters a, a, and b are then defined by a a/l, a=a/hp, and b=hp/I. Note the relation e=ab. e is called the steepness parameter. cp is given by cp dgl/x where x is assumed to be b ' in the shallow-water limit 8 0 and I in the deep-water limit b ~ in accordance with the phase velocity of linear surface gravity waves. The effect of the surface tension has been neglected in (3) to simplify the discussion. It can be included without any difficulty. Let us proceed to derive the time evolutions of the free surface and the horizontal component of the surface velocity. We first take the solution of (1) of the form i [f+(x ib— y, t ) f — (x+ iby— , t )],

Gravity‐Wave Observations Using an Array of Microbarographs In the Alearic Islands

Abstract: Time series of surface pressure from an array of microbarographs in the Balearic Islands (western Mediterranean) are used to obtain wavelength, phase speed and direction of propagation of gravity waves on the Balearic Islands. These pressure waves are commonly found during the summer and they force the large seal-level oscillations observed in the inlet of Ciutadella; a phenomenon locally known as ‘rissaga’. Four events are described here, each of which has a duration of between 30 and 48 hours. Radiosonde data from Palma de Mallorca are used to relate the waves to the vertical structure of the atmosphere. the various source mechanisms of these waves and also the possibility of the existence of a duct layer trapping the wave energy near the surface are discussed. the waves are found to have no significant variation of phase speed with frequency and so they are basically non-dispersive. This is an indicator pointing either to a local generation of gravity waves by wind-shear instability or to the existence of neutral trapped waves, in the lower troposphere.

Observation of the dispersion behavior of surface acoustic waves in a wedge waveguide by laser ultrasonics

Abstract: Wedge (or line) acoustic waves, propagating along the tip of an elastic wedge waveguide, are generated by pulsed YAG laser impact and detected by a wideband optical interferometer. In an ideal infinitely sharp and tall wedge guide, the antisymmetrical flexural (ASF) modes are nondispersive and their energies are mostly confined near the wedge tip. The displacement measurements with the optical probe on metallic wedges show broadband pulsed wave forms of ASF modes. Dispersive behavior of these wave forms, which are not predicted by the theoretical models, are clearly demonstrated. The dispersion curves of the phase velocity are quantitatively deduced by a phase analysis method.

Surface acoustic wave gas sensors

Abstract: Surface acoustic wave (SAW) delay line (DL) oscillators offer many advantages as gas sensors. Such devices are fabricated on a piezoelectric (PE) substrate, whose propagation path is coated with a selectively sorbing film. The sorption produces a change in the SAW phase velocity, which can be detected as a frequency shift of the SAW oscillator frequency. Very often these sensors consist of a double DL oscillator circuitry which cancels the undesirable influences of the environment, e.g., temperature, pressure and so on. In practice one of the DLs serves as a reference. In this work we present the theoretical and experimental results obtained by many authors, concerning the SAW gas sensor response determination for three types of overlying thin films: insulating, conducting and semiconducting. The theoretical and experimental results are compared and discussed.

Aspect angle variations in intensity, phase velocity, and altitude for high-latitude 34-cm E region irregularities

Abstract: The sensitivity of the Millstone 440-MHz radar system is such that coherent echoes from E region irregularities can be observed over a 90-dB dynamic range above the incoherent scatter background. At antenna elevation angles between 4° and 20°, aspect angles between 0° and 10° (from perpendicularity with the magnetic field) are viewed at E region heights at invariant latitudes between 61°Λ and 57°Λ. During disturbed conditions, when convection electric fields in excess of 15 mV/m and E region irregularities span this range of latitudes, antenna scanning experiments have been performed to determine the aspect angle sensitivity with high precision. Our measurements are unique in that they provide a clear high-frequency description of the variation in both power and Doppler shift as functions of aspect angle, all the way from a region where the waves are known to be linearly unstable, in a direction perpendicular to the geomagnetic field, to as much as 10° away from perpendicularity. We find that the 440-MHz aspect sensitivity is about −15 dB deg−1 for aspect angles between 0° and 3°, −10 dB deg−1 for aspect angles between 3° and 6°, and −7 dB deg−1 for aspect angles between 6° and 9°. The magnitude of the phase velocity is at an approximate ion acoustic level (350 m/s) for aspect angles 3°. For highly disturbed conditions the magnitude of the velocity can increase to >700 m/s for aspect angles <2°. The tendency for the altitude of the most intense return to decrease by ∼5 km as the aspect angle increases beyond 2° can be explained as a consequence of the variation of aspect angle with height.

Acoustic streaming in the ear itself

Abstract: Just as mean motions, usually described as acoustic streaming, can be generated by sound waves, so also those cochlear travelling waves into which incident sound waves are converted in the liquid-filled mammalian inner ear are capable of generating mean motions. These predominate, for acoustic components of each frequency ω, near the characteristic place where the wave energy E per unit length rises rather steeply to a maximum Emax before dropping precipitously to zero.Even though the nature of cochlear travelling waves, as determined (above all) by the sharply and continuously falling distribution of stiffness for the basilar membrane vibrating within the cochlear fluids, is very different from that of ordinary sound waves (see §§2, 3 and 4 respectively for energy distribution along the length of the cochlea, over a cochlear cross-section and within boundary layers), nevertheless a comprehensive analysis of mean streaming motions in the cochlea shows them to be governed by remarkably similar laws. The expression \[ {\textstyle\frac{1}{4}}V^2c^{-1}-{\textstyle\frac{3}{4}}V({\rm d}V/{\rm d}x)\,\omega^{-1} \] (equation (1)) appropriate to a wave travelling in the x-direction with velocity amplitude V(x), as obtained by Rayleigh (1896) for the mean acoustic-streaming velocity just outside a boundary layer due to wave dissipation therein, remains a good approximation (see §§5 and 6 – with some modest corrections, at low or at high wavenumbers respectively, analysed in §§7 and 8) for travelling waves in the cochlea; where, however, the decrease of their phase velocity c to low values near the characteristic place conspires with the increase of V to enhance streaming there.Farther from the boundary layer attached to the basilar membrane, the mean streaming is derived (§9) as a low-Reynolds-number motion compatible with the distribution (1) of ‘effective slip velocity’ at the boundary. This velocity's precipitous fall to zero at the characteristic place is shown (§§9 and 10) to produce there a mean volume outflow \[ q = \frac{0.15 E^{\max}}{\rho(\omega u)^{\frac{1}{2}}L} \] (equation (160)) per unit length of the basilar membrane into the scala media; here, ρ and ν are the endolymph's density and kinematic viscosity (essentially, those of water) and L is the e-folding distance for basilar-membrane stiffness.Equation (160), derived here for a freely propagating wave (and so not allowing for enhancements from any travelling-wave amplification – discussed qualitatively in §3 – due to forcing by vibrations of outer hair cells) is the main conclusion of this paper. Physiological questions of whether this flow q may be channelled through the space between the tectorial membrane and inner hair cells, whose stereocilia may therefore be stimulated by a mean deflecting force, are noted here but postponed for detailed consideration in a later paper.

Love-Rayleigh wave incompatibility and possible deep upper mantle anisotropy in the Iberian peninsula

Abstract: Love and Rayleigh wave phase velocities are analyzed with the goal of retrieving information about the anisotropic structure of the Iberian lithosphere. The cross-correlation method is used to measure the interstation phase velocities between diverse stations of the ILIHA network at periods between 20 and 120 s. Despite the 2-D structure of the network, the Love wave data are too few to enable an analysis of phase velocity azimuthal variations. Azimuthal averages of Love and Rayleigh wave phase velocities are calculated and inverted both in terms of isotropic and anisotropic structures. Realistic isotropic models explain the Rayleigh wave and short-period Love wave phase velocities. Therefore no significant anisotropy needs to be introduced in the crust and down to 100 km depth in the upper mantle to explain our data. A discrepancy is observed only at long periods, where the data are less reliable. Love wave data at periods between 80 and 120 s remain 0.15 km/s faster than predicted by isotropic models explaining the long-period Rayleigh wave data. Possibilities of biases in the measurements due to interferences with higher modes are examined but seem unlikely. A transversely isotropic model with 8% of S-wave velocity anisotropy in the upper mantle at depths larger than 100 km can explain the whole set of data. In terms of a classical model of mantle anisotropy, this corresponds to 100% of the crystals perfectly oriented in the horizontal plane in a pyrolitic mantle. This is a rather extreme model, which predicts at time delay between 0 and 2 seconds for split SKS.

Deep structure of the Iberian Peninsula determined by Rayleigh wave velocity inversion

Abstract: SUMMARY A rigorous study of velocity dispersion of surface waves generated by teleseismic events propagating across the Iberian Peninsula and traversing main geological units, has been carried out from a set of selected analogue data, as digital records have only become available recently. Dispersed seismic signals have been obtained over a period of 16 years, between 1967 and 1982, at the five Iberian stations having long-period instruments. In our study, we have considered many earthquakes thus obtaining a fairly good path coverage of most of the peninsula for two-station Rayleigh wave velocity measurements. In all cases, the approach azimuths of the wavefronts were carefully checked. Several digital filtering techniques have been employed to remove the effects of multipathing and modal contamination, and to isolate the fundamental mode from Rayleigh wavetrains. Thus, we have obtained good estimates for both phase and group velocities. A time-variable filter has reduced the influence of noise and removed higher mode interference. Multiple filtering is then used to compute group velocity. Frequency-domain Wiener deconvolution is used to compute the interstation phase velocity. The determined average Rayleigh wave velocities reveal differences in the propagation conditions of the seismic energy across the peninsula. A mapping of velocities for various periods of reference, together with a mapping of errors in velocity, are the basis for obtaining the Rayleigh wave velocity distribution in the peninsula. Theoretical 2-D layered earth models are obtained by joint inversion of phase and group velocity dispersion curves using the stochastic inverse operator. In our inversion scheme, we use velocities corrected for anelastic effects. Finally, a 3-D mapping of S velocity is performed. This study shows important regional features of the deep structure of Iberia; we see small lateral inhomogeneities and also two low-velocity layers: one with shear velocities usually ranging from 4.23 to 4.31 km s-1 directly under the Moho, and another, the asthenosphere, with a negative velocity gradient for depths between 81 and 181 km, terminated at the bottom by a sharp discontinuity.

Excitation of solitons by an external resonant wave with a slowly varying phase velocity

Abstract: A novel mechanism is proposed for the excitation of solitons in nonlinear dispersive media. The mechanism employs an external pumping wave with a varying phase velocity, which provides a continuous resonant excitation of a nonlinear wave in the medium. Two different schemes of a continuous resonant growth (continuous phase-locking) of the induced nonlinear wave are suggested. The first of them requires a definite time dependence of the pumping wave phase velocity and is relatively sensitive to the initial wave phase. The second employs the dynamic autoresonance effect and is insensitive to the exact time dependence of the pumping wave phase velocity. It is demonstrated analytically and numerically, for a particular example of a driven Korteweg-de Vries (KdV) equation with periodic boundary conditions, that as the nonlinear wave grows, it transforms into a soliton, which continues growing and accelerating adiabatically. A fully nonlinear perturbation theory is developed for the driven KdV equation to follow the growing wave into the strongly nonlinear regime and describe the soliton formation.

A class of high‐m pulsations and its auroral radar signature

Abstract: Bistatic Auroral Radar System radar events showing a repetitive equatorward (or radarward) traveling band signature in the range-time-intensity plots have been analyzed. The associated pulsations have many features in common with previously reported high-m storm time Pc 5 pulsations. The periods, azimuthal wave numbers (m), Dst dependence, and polarization ellipses are similar. One difference is also seen. The pulsation phase velocity of our events often has a significant equatorward component in the ionosphere. However, of the three cases for which the phase velocity direction in the magnetospheric equatorial plane was determined, one had phase velocities close to azimuthal at both locations, one had an azimuthal phase velocity in the magnetosphere but an equatorward component of the phase velocity in the ionosphere, and the final event had equatorward or inward components of phase velocity at both locations. These events are very similar to the equatorward traveling bands events observed by the Sweden and Britain Auroral Radar Experiment system (Tian et al., 1991; Yeoman et al., 1992) except that our m values are distinctly larger. If coupling to energetic protons is involved in exciting these pulsations, this difference implies that the energy of the protons involved decreases with increasing L of the interaction location. Finally, our data do not lend themselves to the plasmapause field line resonance interpretation of Tian et al. (1991).

Absolute measurements of elastic-wave phase and group velocities in lossy materials

Abstract: Traditional methods of determining phase and group velocities are often inadequate for many thick‐section materials that exhibit greater than 30 dB, frequency‐dependent propagation losses across the passband of the transducer. This article describes a measurement method that addresses this problem. Our method is mechanized as a pulsed, swept‐frequency interferometer. The method’s accuracy and reliability are enhanced by a combination of circuit‐design improvements, which increase the signal‐to‐noise ratio and linearity, and signal‐processing methods, which remove circuit‐related measurement errors and compensate for diffraction. First we describe the foundations of our measurement method and its mechanization. Then we describe the signal‐processing procedures, used to calibrate the instrumentation and to determine the absolute phase and group velocities. To illustrate the method, we determine the phase velocities in a very lossy, 50‐mm‐thick, glass/epoxy specimen in the 0.3–1.2‐MHz region.

Acoustic wave propagation through periodic bubbly liquids

Abstract: A three‐dimensional finite‐element analysis is used to determine the acoustic behavior of plane waves propagating through bubbly liquids having periodic bubble distributions. The results obtained from the model include the effective phase speed and attenuation of the medium, the acoustic field in the region of each bubble, and the virtual mass for both the monopole and dipole modes of bubble oscillation. The results are in agreement with both experimental data and previous analytical results.

Analytic and Numerical Models of Wave-CISK with Conditional Heating

Abstract: Wave-CISK with conditional heating is investigated in the equatorial zonal-height plane by analytic and numerical techniques. For two- and three-level models, previous results are extended to give additional evidence that the most unstable mode has a single wet region of infinitesimal width. A three-level model has qualitatively similar behavior as the two-level model except that propagating solutions are possible due to coalescence of internal vertical modes. Phase speeds with conditional heating are found to be slightly greater than those for unconditional heating. The structure has one circulation cell in the vertical and is asymmetric in longitude with stronger motion on the leading edge. Growth rate is inversely proportional to the width of the single wet region. That width can be limited by second-order diffusion. A general integral relationship between growth rate, viscosity, phase speed, and heating is derived. The main conclusion is that the linear wave-CISK catastrophe is modified by conditional heating but not eliminated. The preferred mode of instability has one wet region, but it occurs on the smallest possible scale. It is likely that numerical models that use conditional heating are sensitive to resolution, especially for the commonly used spectral truncations, unless there is sufficiently strong damping at the smallest scales.