Showing papers on "Phase velocity published in 1988"

Polymers on disordered trees, spin glasses, and traveling waves

Abstract: We show that the problem of a directed polymer on a tree with disorder can be reduced to the study of nonlinear equations of reaction-diffusion type. These equations admit traveling wave solutions that move at all possible speeds above a certain minimal speed. The speed of the wavefront is the free energy of the polymer problem and the minimal speed corresponds to a phase transition to a glassy phase similar to the spin-glass phase. Several properties of the polymer problem can be extracted from the correspondence with the traveling wave: probability distribution of the free energy, overlaps, etc.

Resonance of a fluid-driven crack: Radiation properties and implications for the source of long-period events and harmonic tremor

Abstract: A dynamic source model is presented, in which a three-dimensional crack containing a viscous compressible fluid is excited into resonance by an impulsive pressure transient applied over a small area ΔS of the crack surface. The crack excitation depends critically on two dimensionless parameters called the crack stiffness, C = (b/μ)(L/d), and viscous damping loss, F = (12ηL)/(ρƒd2α), where b is the bulk modulus, η is the viscosity, ρƒ is the density of the fluid, μ is the rigidity, α is the compressional velocity of the solid, L is the crack length, and d is the crack thickness. The first parameter characterizes the ability of the crack to vibrate and shapes the spectral signature of the source, and the second quantifies the effect of fluid viscosity on the duration of resonance. Resonance is sustained by a very slow wave trapped in the fluid-filled crack. This guided wave, called the crack wave, is similar to the tube wave propagating in a fluid-filled borehole; it is inversely dispersive, showing a phase velocity that decreases with increasing wavelength, and its wave speed is always lower than the acoustic velocity of the fluid, decreasing rapidly as the crack stiffness increases. The source spectrum shows many sharp peaks characterizing the individual modes of vibration of the crack; the variation of spectral shape, both in the number and width of peaks, is surprisingly complex, reflecting the interference between the lateral and longitudinal modes of resonance, as well as nodes for these modes. The far-field spectrum is marked by narrow-band dominant and subdominant peaks that reflect the interaction of the various source modes. The frequency of the dominant spectral peak radiated by the source is independent of the radiation direction. The frequency, bandwidth, and spacing of the resonant peaks are strongly dependent on the crack stiffness, larger values of the stiffness factor shifting these peaks to lower frequencies and decreasing their bandwidth. The excitation of a particular mode depends on the position of the trigger and on the extent of the crack surface affected by the pressure transient. Fluid viscosity decreases the amplitudes of the main spectral peaks, smears out the finer structure of the spectrum, and greatly reduces the duration of the radiated signal. The energy loss by radiation is stronger for high frequencies, producing a seismic signature that is marked by a high-frequency content near the onset of the signal and dominated by a longer-period component of much longer duration in the signal coda. Such signature is in harmony with those displayed by long-period events observed on active volcanoes and in hydrofracture experiments. The very low velocity which is possible in a crack with high stiffness (C ≥ 100) also provides an attractive explanation for very long period tremor, such as type 2 tremor at Aso volcano, Japan, without the requirement of an unrealistically large magma container. The standing wave pattern set up on the crack surface by the sustained resonance in the fluid is observable in the near field of the crack, suggesting that the location and extent of the source may be estimated from the mapping of the pattern of nodes and antinodes seen in its vicinity. According to the model, the long-period event and harmonic tremor share the same source but differ in the boundary conditions for fluid flow and in the triggering mechanism setting up the resonance of the source, the former being viewed as the impulse response of the tremor generating system and the latter representing the excitation due to more complex forcing functions.

Velocity and attenuation of ultrasound in suspensions of particles in fluids

Abstract: The theory of the scattering of compression waves in viscous fluids is examined. The effects of fluid viscosity, of differences in density and in elastic modulus between the particles and the fluid, of heat transfer and of concentration are considered. Ultrasonic phase velocity and attenuation are derived. Results for the phase velocity are compared with several other formulations. The feasibility of using ultrasound to characterise suspensions is discussed.

Large‐Scale waveform inversions of surface waves for lateral heterogeneity: 2. Application to surface waves in Europe and the Mediterranean

Abstract: Linear surface wave scattering theory is used to reconstruct the lateral heterogeneity under Europe and the Mediterranean using surface wave data recorded with the Network of Autonomously Recording Seismographs (NARS). The waveform inversion of the phase and the amplitude of the direct surface wave leads to a variance reduction of approximately 40% and results in phase velocity maps in the period ranges 30–40 s, 40–60 s and 60–100 s. A resolution analysis is performed in order to establish the lateral resolution of these inversions. Using the phase velocity perturbations of the three period bands, a two-layer model for the S velocity under Europe and the Mediterranean is constructed. The S′ velocity perturbations in the deepest layer (100–200 km) are much more pronounced than in the top layer (0–100 km), which confirms that the low-velocity zone exhibits pronounced lateral variations. In both layers the S velocity is low under the western Mediterranean, while the S velocity is high under the Scandinavian shield. In the deepest layer a high S velocity region extends from Greece under the Adriatic to northern Italy. Several interesting smaller features, such as the Massif Central, are reconstructed. One of the spectacular features of the reconstructed models is a sharp transition in the layer between 100 and 200 km near the Tornquist-Tesseyre zone. This would indicate that there is a sharp transition at depth between Central Europe and the East European platform. The waveform inversion of the surface wave coda leads to good waveform fits, but the reconstructed models are chaotic. This is due both to a lack of sufficient data for a good imaging of the surface wave energy on the heterogeneities and to an appreciable noise component in the surface wave coda.

Principal oscillation pattern analysis of the 30- to 60-day oscillation in general circulation model equatorial troposphere

Abstract: A new technique is described for identifying time-dependent patterns (i.e., “principal oscillation patterns,” or POPs) in a set of geophysical time series. POPs are defined as the normal modes of a linear dynamical representation of the data in terms of a first-order autoregressive vector process with residual noise forcing. POPs associated with real eigenvalues represent nonpropagating, nonoscillatory patterns which decay exponentially. POPs associated with complex eigenvalues occur in complex conjugate pairs and can represent standing wave structures (if one pattern is much stronger than the other), propagating waves (if both patterns are periodic and have the same structure except for a quarter-wavelength shift) or, in general, an arbitrary amphidromal oscillation. After the POPs have been defined for a selected set of primary variables, associated correlation or composite patterns may be derived for additional secondary fields to gain further insight into the structure of the interaction mechanisms. The method is illustrated by analyzing the tropical variability structure of a 10-year numerical simulation with the T21 general circulation model (GCM) of the European Centre for Medium Range Weather Forecasts, Reading, England. The POP analysis is applied to the 200-hPa horizontal divergence field along the equator for time scales shorter than 10 weeks. The associated patterns are determined for a number of additional fields in the tropical belt between 30°S and 30°N. One dominant POP pair is found. Its spatial scale corresponds to zonal wave number 1. The patterns travel eastward, with an average period of 24 days and an e-folding decay time of 10 days. The maximum variance occurs in the area with maximum tropical precipitation, between 100°E and the dateline. These features correspond rather closely to the characteristics of the observed tropical “30- to 60-day wave,” except for the smaller period. A frequency–wave number analysis confirms that this 30- to 60-day wave is the most dominant regular oscillation in the tropical GCM troposphere. The associated patterns of sea level pressure, precipitation, and other quantities exhibit a number of intriguing aspects, namely, (1) the phase velocity of the 30- to 60-day wave varies with longitude from 6 m s−1 in the Indonesian area to more than 30 m s−1 over the eastern Pacific, small phase speeds being associated with large amplitudes and high phase speeds with small amplitudes; (2) in the high-amplitude regions, rainfall and upper air velocity potential are in phase, while in the low-amplitude regions, rainfall and velocity potential appear uncorrelated; (3) at the surface a pattern strongly resembling Gill's theoretical response to an equatorial heating source is found, with a trough to the east and two off-equatorial cyclones to the west of the heating. The lack of meridional winds is probably related to the disregard of the seasonal asymmetries.

Rayleigh wave phase velocities in the Pacific with implications for azimuthal anisotropy and lateral heterogeneities

Abstract: SUMMARY The lateral distribution of fundamental-mode Rayleigh wave phase velocities in the Pacific has been calculated in order to determine the variation in velocity as a function of the age of the oceanic plate, the importance of azimuthal anisotropy, and the presence of secondary lateral heterogeneities. The data set used in this study consists of phase velocity measurements in the period range 20-125 s for 178 paths traversing the Pacific. Both the pure-path and spherical harmonic inversion techniques are used in this investigation with an emphasis placed on determining the effectiveness and resolving power of these methods in calculating the velocity distribution in an oceanic regime. The first-order velocity-age relation which dominantly characterizes surface wave dispersion in an oceanic environment can be adequately modelled by either the pure-path or spherical harmonic techniques. Azimuthal anisotropy is the dominant second-order effect and is best developed in regions less than 80 Myr in age. In this age zone, the faster direction of wave propagation is either in the direction of fossil seafloor spreading or in the direction of present-day absolute plate motion. In the western Pacific, there is a correlation with paleo-relative motion (fossil seafloor spreading) for periods less than 50 s. Lateral velocity heterogeneities which are not related to the age of the oceanic plate are found by pure-path inversions and are correlated with regions associated with shallow residual depth anomalies. This effect (slow velocities with respect to the velocity-age model) monotonically decreases as a function of period and is indicative of a shallow origin. Age independent anomalies were also modelled by the application of the pure-path and spherical harmonic methods in a sequential inversion.

Propagation model for ultrafast signals on superconducting dispersive striplines

Abstract: The algorithm suitable for the computer-aided design of transmission lines is used to model the propagation of picosecond and subpicosecond electrical signals on superconducting planar transmission lines. Included in the computation of a complex propagation factor are geometry-dependent modal dispersion and the frequency-dependent attenuation and phase velocity which arise as a result of the presence of a superconductor in the structure. The results of calculations are presented along with a comparison to experimental data. The effects of modal dispersion and the complex surface conductivity of the superconductor are demonstrated, with the conclusion that it is necessary to incorporate both phenomena for accurate modeling of transient propagation in strip transmission lines. >

Spatial variation and stochastic modelling of seismic differential ground movement

Abstract: Specially designed arrays of strong motion seismographs located near earthquake sources are required for engineering studies of near-source earthquake properties as well as spatial variation of seismic waves. The SMART-1 array in Tath provides good records for this type of study. Based on the SMART-1 array data, the analysis of the principal direction wave propagation and the space-time correlation of some events recorded by SMART-1 have been studied. A stoce model for predicting the differential ground movement was also developed. This stochastic model includes the effect of source characteristics, attenuation of wave passage and spatial correlation characteristics. The performance of this more discussed and compared with the ground movement recorded by the SMART-1 array. From the present study, it is that spatial correlations do exist as seismic waves propagate across the array site. Generally, the loss of coherence is direction of propagation can be explained by energy at the same frequency exhibiting a slightly different velocity with the measurement intervals. It is also concluded that the phase velocity of seismic waves and the corner frequency of the grep displacement spectrum are controlling factors in the prediction of the root mean square of differential grep displacement.

Full-wave synthetic acoustic logs in radially semiinfinite saturated porous media

Abstract: The wave field generated by a point source in an axisymmetric fluid‐filled borehole embedded in a saturated porous formation is studied in both the spectral domain and time domain. The formation is modeled following Biot theory modified in accordance with homogenization theory. When the borehole wall is permeable, guided waves can be significantly affected by the permeability of the formation. Whatever the formation, fast or slow, Stoneley‐wave phase velocity and energy decrease and attenuation (in the sense of Q-1) increases with increasing permeability. These effects are more important in the very low‐frequency range, where Darcy’s law governs the fluid motion and the wave energy at the interface is maximum, than at higher frequencies. The effects increase and persist over a larger frequency range with decreasing viscosity and increasing compressibility of the saturant fluid, with increasing pore‐fluid volume, and with decreasing borehole radius. In contrast, the effects decrease with decreasing stiffne...

Implications of frequency-domain inversion of earthquake ground motions for resolving the space-time dependence of slip on an extended fault

Abstract: SUMMARY A frequency-domain method is presented in which the Fourier spectral amplitudes of observed earthquake ground motions are used as data to constrain the space-time dependence of slip on the fault. Performing the temporal deconvolution in the frequency domain allows the spatial dependence of slip at each frequency to be computed independently. This greatly reduces the computational effort and allows the grid spacing to be chosen sufficiently fine enough to form an accurate numerical approximation to the continuous problem, thereby eliminating spatial and temporal discretization effects. Time-domain methods require the specification of rupture time as a function of position on the fault in order to reduce the number of parameters in inversion. Some non-linear inversion methods iterate on the rupture time in order to find a set of rupture times which provides the best fit to the data. This non-linear restriction, and the potential bias it may introduce, is eliminated in the frequency-domain formulation. The method is applied to synthetic test data calculated using Haskell's model of a uniform rupture in a homogeneous full-space. Three different recording geometries with characteristics comparable to current strong motion arrays are considered. Inversion for the slip function is demonstrated to be non-unique and a particular solution is found which minimizes the square of the slip velocity averaged over the fault surface. The minimum norm solutions have systematically lower peak slip velocities and spectra which fall off much faster than the input model (fP3 vs. f-'). This discrepancy is shown to result from a trade-off between the spectral amplitude of slip at a point on the fault and the local phase velocity of slip propagation. The trade-off is quite large for the arrays considered, a factor of 10 to 100 at frequencies between 1.0 Hz and 2.5 Hz.

Synthetic Aperture Radar imaging of ocean waves from an airborne platform: Focus and tracking issues

Abstract: There has been a controversial issue of many years standing in airborne Synthetic Aperture Radar (SAR) ocean imaging which this paper addresses and resolves. Investigators have been strongly divided on the reasons for apparent improvement in wave contrast in response to processor focus adjustment. The dispute has centered on two parameters of wave dynamics: orbital velocity and phase velocity. This paper shows that both orbital velocity and phase velocity are of fundamental importance in the SAR wave imaging problem. The first affects the phase of the received signal, leads to velocity bunching, and is scaled by the ratio of sensor altitude to sensor velocity. The second affects the magnitude of the received signal, leads to translation of wave features during image formation (observed as blurring in the image), and is scaled by the ratio of wave phase velocity to sensor velocity, thus becoming significant for airborne radars. This treatment of the phase velocity parameter is new. It is shown that focus adjustment, as a side effect, shifts image position. This explains why experiments have appeared to “prove” that focus adjustment may be optimised for wave movement. The paper shows that better performance is obtained by compensating individual looks for wave movement before look summation, while using nominal perfect focus just as for static scatterers. The work is applicable to a full ocean wave spectrum and does not depend on the details of the scattering mechanism itself.

Ordered motion in the turbulent boundary layer over wind waves

Abstract: The turbulent boundary layer over young wind waves (C/u* ∼ 1, where C is the phase speed of wind waves and u* is the friction velocity) has been investigated in a laboratory tank. Ordered motions have been found, and their structures studied in detail. Visualization of the outer boundary layer (0.4δ–1δ, where δ is the boundary-layer thickness) by paraffin mist has demonstrated the existence of a train of large-scale ordered motions having a horizontal lengthscale that corresponds to the wavelength of the underlying wind waves. Hot-wire measurements combined with the visualization have shown that the passage of the outer boundary-layer bulge is related to the occurrence of a low-speed air mass, usually accompanied by an upward velocity to produce large Reynolds stress. In the vicinity of the wave surface (0–0.15δ), flow separation occurs over these wind waves. Instantaneous velocity shear measurements, using two hot wires 0.15 cm apart vertically, have detected a high-shear layer at the edge of the separation bubbles. This high-shear layer, the potential site for generating much turbulence, reattaches on the windward side of the preceding wind waves. A pressure rise and a shear-stress spike, expected near the reattachment region, could be the mechanisms for supplying energy to the wind waves.The bursting phenomena over wind waves have been examined in detail in the logarithmic boundary layer (0.15δ–0.3δ). The bursting phenomena are a major mechanism for producing Reynolds stress and have a specific relationship with the phase of the wind wave. To explain the bursting phenomena, two mechanisms (not present in the boundary layer over a flat plate) are proposed, involving air-flow separation and the large-scale ordered motions, respectively. The two mechanisms are a ‘big burst’ related to the discharge of a whole separation bubble, and a ‘small burst’ which is the upward bursting of a low-speed air mass from the unstable separated shear layer into the ordered motions passing over a separation bubble.

Gravity Wave Propagation Characteristics (60–120 km) as Determined by the Saskatoon MF Radar (Gravnet) System: 1983–85 at 52°N, 107°W

Abstract: Gravity waves (GW) have been detected and their characteristics measured by observations with the Saskatoon multiple bistatic system, Gravnet. Data are available from 50 days for two height ranges 64–97 km, ∼100–115 km, and for the four seasons of 1983–85. Wave characteristics include horizontal wavelength, phase velocity, period, and amplitude. Background wind data allows the corresponding intrinsic parameters to be calculated; many waves are Doppler shifted to near their critical levels. Altitude and seasonal variations in the GW characteristics are shown. The strongest variation is in the horizontal direction of wave propagation, with southward directions dominating, but significant eastward(westward) fluxes in summer(winter) below 100 km.

Large-scale waveform inversions of surface waves for lateral heterogeneity: 1. Theory and numerical examples

Abstract: Surface wave scattering theory is presented as a new method for analyzing teleseismic surface wave data. Using surface wave scattering integrals the effect of lateral heterogeneity both on the surface wave coda generation and on the direct surface wave is described. Since the employed scattering theory for the forward problem is linear, the inverse problem can conveniently be solved in the least squares sense using an iterative matrix solver. For waveform inversions of the direct surface wave, only near forward scattering contributes. For this case the isotropic approximation is introduced, which makes it possible to retrieve phase velocity information from scattering theory. It is shown that for practical waveform inversions the resulting system of linear equations is extremely large and how row action methods can be used conveniently for carrying out the inversion on moderate size computers. The performance of the inversions is illustrated with two numerical examples. In the first example the surface wave coda generated by one point scatterer is inverted. It is shown that the reconstruction in this case is similar to Kirchhoff migration methods as used in exploration seismics. In the second example, ray geometrical effects (focusing and phase shifting) are obtained from the linear inversion with scattering theory. It follows from this example that linear waveform inversion can simultaneously fit the amplitude and the phase of surface wave data.

A new technique for ultrasonic-nondestructive evaluation of thin specimens

Abstract: Combining standard FFT methods with conventional ultrasonics, a method has been developed for measuring the phase velocity, the group velocity and the attenuation in ultrathin specimens (submillimeter or subwavelength in thickness). A detailed description of this technique is given. The technique was used on four disparate materials: aluminum, an epoxy, a particulate composite and a graphite-fiber/epoxy composite. The method works equally well for thin or thick specimens, and for dispersive as well as nondispersive media.

Modeling Slow Phase Velocity Generation during Off‐Vertical Axis Rotationa

Abstract: 1. Rotation about an off-vertical axis (OVAR) causes continuous unidirectional nystagmus in darkness. An analysis of the dynamics of the nystagmus suggests that the continuous slow-phase velocity is generated by a signal that is an estimate of the velocity of a traveling wave pattern associated with the excitation and inhibition of the cells of the otolith maculae. The estimated velocity signal then excites the velocity storage integrator. 2. A mathematical model has been developed that shows how the velocity of the traveling wave might be estimated from patterns of otolith activation related to head position. The estimation of velocity is based on a "template matching" algorithm. It is assumed that the signal arising in each cell of the macula is delayed by a certain time (T). As the head rotates in the gravitational field, a delayed pattern representing a previous position of the head is available as a "template" that can be compared to the pattern associated with the present position of the head. 3. The delayed signal level for each cell is approximated from the present pattern by a spatial extrapolation in pattern space using information from the given cell and an adjacent one. The value of the displacement that minimizes the mean square error between the extrapolated and the delayed signal values over all cells gives a best estimate of head rotation (d) in time T. The estimated head velocity is proportional to the estimated head displacement (d) and inversely proportional to the delay time (T). 4. By using a linear spatial extrapolation function and assuming a uniformly spaced distribution of polarization vectors over 360 degrees, sinusoidal spatial patterns are obtained. The formula for the estimated head velocity (ŵ) reduces to a sinusoidal function of angular head velocity (w) and delay time (T). For T = 0.85 seconds, the model predicts that the steady state estimate of head velocity will rise as a function of stimulus velocity (w) to a peak value at w = 50 deg/sec. The estimate then declines for larger values of stimulus velocity (w). This type of behavior is observed in the slow-phase velocity characteristics of OVAR in monkeys. 5. The model predicts that when animals are tilted after prolonged rotation about a vertical axis, the estimate of head velocity is delayed relative to actual head velocity. This accounts for the delay in the buildup of slow-phase velocity during the initial second.(ABSTRACT TRUNCATED AT 400 WORDS)

Investigation of Lamb waves having a negative group velocity

Abstract: The propagation characteristics of Lamb waves in a solid plate are typically represented by a set of dispersion curves, which describe the Lamb‐wave phase velocity as a function of the product fd, where f is the acoustic frequency and d is the plate thickness. For certain modes, within a range of phase velocity and fd, it has been theoretically predicted that the associated group velocity could be negative, i.e., the energy transport is in the opposite direction to the phase velocity. In the present study, Lamb waves are generated via mode conversion from a water‐borne sound beam incident onto a flat brass plate. Measurement of the phase and group velocities of the Lamb waves of the S1 mode is performed for the fd range of 2.0–2.3 MHz‐mm. Comparison of the measured and computed values of phase and group velocities shows good agreement and clearly demonstrates that S1‐mode Lamb waves have a negative group velocity for fd=2.08–2.24 MHz‐mm.

A mesoscale gravity wave event observed during CCOPE. II: Interactions between mesoscale convective systems and the antecedent waves

Abstract: The interactions between preexisting gravity waves and convective systems were investigated using data obtained by the Cooperative Convection Precipitation Experiment observational network in Montana on July 11-12, 1981. The results indicate that strong convection substantially affects gravity waves locally by augmenting the wave amplitude, reducing its wavelength, distorting the wave shape, altering the wave phase velocity, and greatly weakening the in-phase covariance between the perturbation wind and pressure fields. These convective effects upon gravity waves are explained in terms of hydrostatic and nonhydrostatic pressure forces and gust front processes associated with thunderstorms.

Relativistic focusing and beat wave phase velocity control in the plasma beat wave accelerator

Abstract: Relativistic focusing allows two collinear short pulse radiation beams, provided they are of sufficiently high power, to propagate through a plasma without diffracting. By further accounting for finite radial beam geometry, it is possible for the phase velocity of the radiation beat (ponderomotive) wave to equal to the speed of light. This removes one of the limiting factors, phase detuning between the accelerated electrons and the beat wave, in determining the maximum energy gain in the plasma beat wave accelerator.

Wave structures in jets of arbitrary shape. III. Triangular jets

Abstract: The generalized shooting method, previously developed for the analysis of spatial instability modes of arbitrary shape jets, is applied to incompressible jets with triangular core regions of constant flow. The instability modes of these jets are classified, and calculations are carried out for spatial growth rates, phase velocities, and velocity fluctuation eigenfunctions of three fundamental and two overtone modes. All of the calculated eigenfunctions show negligible velocity fluctuations at the triangle vertices, in good correlation with experimental findings.

An unambiguous determination of the propagation of a compressional Pc 5 wave

Abstract: A compressional Pc5 event observed by the ISEE-1 magnetometer and Medium Energetic Particle Experiment instrument on August 21 and 22, 1978, is examined. The propagation properties of the compressional waves were determined using a technique which utilizes the finite Larmor radius effects in the signature of the multichannel energetic ion detector. It is shown that this technique determines unambiguously the propagation characteristics of the wave in both the azimuthal and the radial directions in the plane perpendicular to the background magnetic field; the results remained valid even though heavy energetic ions with Larmor radii larger than proton Larmor radii were present in the plasma.

Limiting forms for capillary-gravity waves

Abstract: The form of steep capillary waves is of interest as a possible initial condition for the formation of air bubbles at a free surface. In this paper the limiting forms of pure capillary waves and of quasi-capillary waves are studied analytically. Crapper's finite-amplitude solution is expressed in a simple form, and is shown to be one of several exact elementary solutions to the pure-capillary free-surface condition. Among others are the solution z = w+sinh w, where w is the velocity potential, and also z = w3. The latter solution, though it represents a self-intersecting flow, can be used as the first in a sequence of approximations to the form of the steepest wave. Hence it is shown that the influence of gravity on the shape of the limiting ‘bubble’ is very small. The result is confirmed by an examination of Hogan's numerical calculations of limiting capillary-gravity waves.In the crest of a limiting wave the particle velocity is almost constant and equal to the phase speed. This property makes it possible to apply a quasi-static approximation so as to determine the form of the crest, and hence to find an expression for the complete profile of a capillary-gravity wave of limiting steepness. It appears that there exists a solitary wave of capillary-gravity type on deep water.

Wave propagation in a fluid‐filled fracture — An experimental study

Abstract: A laboratory experimental study has been carried out to investigate the mode trapping characteristics of a fluid-filled fracture between two elastic solids. Using a small circular cylindrical receiver of 2.7 mm diameter, we were able to measure the wave motion directly inside a 2.8 mm thick fracture and to obtain array data for the propagating waves. The data was processed using Prony's method to give velocity of the wave modes as a function of frequency. The experimental results agree with the theoretical predictions quite well. Specifically, in a “hard” (aluminum) fracture where the shear velocity of the solid is greater than the fluid velocity, four normal modes were detected in the frequency range up to 2.4 MHz. Whereas in a “soft” (lucite) fracture where the shear velocity is smaller than the fluid velocity, four leaky-P modes were detected in the same frequency range. In both cases, a fundamental mode analogous to Stoneley waves in a borehole was detected. In particular, the velocity of this mode approaches zero in the low frequency limit, as indicated by the theory and confirmed by the experiment in a low frequency range down to 25 kHz.

Interpretation of the structure of mesospheric turbulence layers in terms of inertia gravity waves

Abstract: MU radar observations with good time-height resolution have found that inertia gravity waves play an important role in producing turbulence layers in the mesosphere. When the Richardson number modified by the inertia gravity wave was larger than 1, the inertia gravity wave confined the altitude region with relatively small Richardson number, where smaller scale perturbations superposed on the wave seemed to make the Richardson number smaller than the critical values for instabilities, and produce turbulence. Scattering layers showed a descending motion at a vertical phase velocity of a monochromatic inertia gravity wave, and appeared at the altitude of the minimum Richardson number modified by the wave. A mixture of several layers with different descending motions was observed when wind fields consist of several gravity waves with different vertical wavelengths and phase velocities. On the other hand, when the Richardson number modified by the inertia gravity wave became as small as 0, the wave itself seemed to be dissipated through instabilities, and produce thicker turbulence layer than that in other cases. The radial wind velocities showed large fluctuations with a period of 9 min, which showed a phase reversal near the altitude of minimum Richardson number. The fluctuation seemed to be attributed to the shear instability induced by the saturated inertia gravity wave.

Beat wave current drive with intense pulsed free-electron lasers

Abstract: High power free-electron lasers make possible new methods for driving current in toroidal devices with electromagnetic waves. Earlier considerations of beat wave current drive are applied to a hot magnetized plasma and an arbitrary beat wave. Here the beating of two electromagnetic waves resonantly excites a low frequency beat wave that accelerates and heats electrons and leads to a current. The absolute current drive efficiency depends nonlinearly on the two pump wave intensities and is constrained by the Manley-Rowe relations. Accessibility at high plasma densities is not a difficulty, but a degree of frequency tunability of the wave sources is required. Particle simulations indicate that there is good coupling to an electron velocity tail for a Langmuir beat wave with a phase velocity 1.5 to 3 times (Te/me)½, so that all of the high frequency wave source is absorbed and the beat wave damps completely on the electrons. A novel diagnostic, based on an analytical solution for the linearized Fokker-Planck equation describing electron scattering and slowing down, is added to the particle code. This permits the computation of the current drive efficiency, including both the non-linear beat wave coupling and the collisional relaxation of the electron distribution. A realistic scenario for a beat wave current drive experiment in the Livermore Microwave Tokamak Experiment is calculated using the TORAY toroidal ray tracing code, and the scaling to an engineering test reactor plasma is described.