Showing papers on "Phase velocity published in 1989"

Surface waves on vertically sheared flows: Approximate dispersion relations

Abstract: Assuming linear wave theory for waves riding on a weak current of 0(e) compared to the wave phase speed, an approximate dispersion relation is developed to 0(e2) for arbitrary current U(z) in water of finite depth. The 0(e2) approximation is shown to be a significant improvement over the 0(e) result, in comparison with numerical and analytic results for the full problem. Various current profiles in the full range of water depths are considered. Comments on approximate action conservation and application to depth-averaged wave models are included.

Velocity and particle-flux characteristics of turbulent particle-laden jets

Abstract: The velocity and flux of spherical glass beads with nominal diameters of 200, 80 and 40 $\mu m$ have been obtained by phase-Doppler anemometry in a round unconfined air jet over the first 28 diameters. The jet diameter was 15 mm and the exit velocity was 13 m s$^{-1}$ giving a Reynolds number of 13 000 and a timescale of 1.15 ms, which increased quadratically with axial distance: the bead inertial time constants were 298, 48 and 12 ms. The purposes of the experiments were to quantify the velocity and flux characteristics of the beads and of the gas phase in the presence of the beads as a function of bead diameter and of the mass loading in the jet nozzle. Due to the large inertia of the 200 $\mu m$ beads, the mean bead velocity downstream of the exit of the jet was constant and independent of mass loading up to 0.37 and the axial root mean square (r.m.s.) bead velocity decayed by about one-fifth: at the exit of the jet, the axial r.m.s. bead velocity was higher than that of the corresponding clean jet. The mean centreline velocity of the 80 $\mu m$ beads decayed to about one-half of the bead exit velocity by 28 diameters downstream and was independent of mass loading up to 0.86. The decay rate of the mean gas centreline velocity in the presence of the beads reduced as the loading increased because of momentum transfer from the discrete to the gaseous phase. The axial r.m.s. velocity of the beads was comparable to that of the gas phase and both decreased with increasing loading and the rate of spread of the half width of the jet increased with increasing loading. For the 40 $\mu m$ beads, the decay rate of the mean centreline velocity of the beads decreased with increasing loading and, in contrast to the 80 $\mu m$ beads, the rate of spread decreased with increasing loading up to 0.80. The axial r.m.s. velocity of the beads became largest at a position downstream of the nozzle exit, which moved downstream with increasing loading and was larger than the axial r.m.s. velocity of the clean jet, although the beads were not expected to be responsive to the frequencies of the energy-containing eddies. The bead axial r.m.s. velocity was more than twice as large as the radial r.m.s. velocity and the correlation coefficient of the cross correlation was larger than that of the clean jet. The large bead turbulence, anisotropy and strong correlation coefficient are explained by the superposition of bead trajectories from regions of different bead mean velocity and are not because of acquisition of axial turbulent motion from the gaseous phase.

Synthesis, design, and construction of ultra-wide-band nonuniform quadrature directional couplers in inhomogeneous media

Abstract: A computer-aided synthesis design procedure is given for nonuniform quadrature directional couplers in inhomogeneous media A wiggly geometry is used which effectively slows the odd-mode phase velocity to match the even-mode phase velocity The wiggly geometry results in improved isolation and increased effective dielectric constant This technique provides a shorter coupler length due to increased effective dielectric constant Cubic splines of strip width, strip spacing, and wiggle depth as functions of coupling coefficient are computed using static capacitances of uniform coupled lines These functions are then used as synthesis functions to evaluate the continuous physical parameters of nonuniform coupled lines by using the continuously varying coupling coefficient A nonuniform interdigitated coupler is introduced to realize the tight coupling values >

Surface acoustic wave device

Abstract: An IDT electrode (4) is formed on a double-layer structure comprising a diamond crystal layer (2) and a thin AlN film (3) and a third-order Rayleigh or Sezawa wave is caused to propagate along the surface of the double-layer. Alternatively a third-order Rayleigh wave is caused to propagate along the surface of a triple-layer structure comprising a diamond crystal layer (2), a thin AlN film (3) and an SiO2 film provided therebetween. With the aforementioned structure, a SAW device exhibiting a high electromechanical coupling factor and a high phase velocity is available. The SAW device for allowing a third-order Rayleigh wave to propagate along the surface thereof is fit for use as a narrow-band timing extraction filter or a band-pass filter, for use in a microwave region of several to 20 GHz whereas the SAW device for allowing the Sezawa wave to propagate therealong is fit for use as a wide-band voltage control oscillator or a wide-band-pass filter for use in wide range of frequencies covering VHF to UHF bands.

Ar II laser generated by Landau damping of whistler waves at the lower hybrid frequency.

Abstract: Lasing of the 488-nm Ar ii line has been demonstrated in the central 1.2 cm of a 4.5-cm diam rf-produced magnetoplasma at pressures of 1 Pa. The external rf antenna excites an m=1 whistler wave at the lower hybrid launch frequency which produces a highly ionized plasma. The inferred population inversion and the correspondence between measured wave phase velocity and the upper energy levels of the observed transitions suggest that Landau damping of the wave can selectively distort the electron distribution function at an energy equivalent to the phase velocity of the wave.

Observations and modeling of the backscattering of short tone bursts from a spherical shell: Lamb wave echoes, glory, and axial reverberations

Abstract: Tone bursts having durations of 3 or 4 cycles were incident on an air‐filled stainless steel shell in water. The resulting sequence of echoes included a specular reflection and echoes radiated by Lamb waves on the shell. Echo structure was studied for ka of 24 to 75, where a denotes the outer radius; b/a=0.838, where b denotes the inner radius. The amplitudes of Lamb wave echoes were modeled using an elastic generalization of the geometrical theory of diffraction (GTD) [P. L. Marston, J. Acoust. Soc. Am. 83, 25–37 (1988)]. The required Lamb wave parameters (the phase velocity cl and damping βl ) were found by the Sommerfeld–Watson method; an efficient numerical method for the computation of the required complex root νl is described. The echoes were identified by comparing arrival times with predictions; bursts reflected from a solid tungsten carbide sphere were used for a reference amplitude. Measurements with ka=24 of the largest Lamb wave echo (which was due to a flexural wave) were made at various back...

Aspect sensitivity of equatorial electrojet irregularities and theoretical implications

Abstract: We used a multi baseline 50-MHz radar interferometer at the Jicamarca Radio Observatory to study the dependence of echo strength on the aspect angle, the angle of arrival relative to normal to the geomagnetic field. We observed rms values of this angle in the range 0.1°–0.4°, which implies an aspect sensitivity somewhat greater than the nominal 10 dB/deg often quoted for auroral echoes. The technique has sufficient resolution to allow deviations from normal of less than 0.1° to be measured fairly easily, and we were able to determine variations of the aspect sensitivity with altitude, Doppler shift, and electrojet conditions. During weakly driven periods, when only type 2 echoes were observed, the width, or rms angular deviation from normal, decreased monotonically with increasing altitude, as simple linear theory would suggest, but the variation was less rapid than the variation of νe/Ωe, especially on the bottomside of the electrojet. A particularly interesting observation was that, during strongly driven “type 1” conditions, there was a pronounced variation of width with Doppler shift. The width for small phase velocities was sometimes more than twice that at the ion-acoustic velocity. We believe that this broadening is due to nonlinear three-wave mode coupling which produces a reverse cascade of energy from short wavelengths to long and an increase in the mean aspect angle. Such a cascade represents an increase in the effective diffusion coefficient for the short wavelength waves and so could provide an explanation alternative to that of the anomalous collision process of Sudan (1983) for the limitation of the type 1 phase velocity at the ion-acoustic velocity.

The acoustic scattering by a submerged, spherical shell. I: The bifurcation of the dispersion curve for the spherical antisymmetric Lamb wave

Abstract: The acoustic scattering by thin‐walled, evacuated, elastic spherical shells immersed in water is studied. The analytic structure of the scattering amplitude in the complex‐k plane is directly analyzed using Cauchy’s residue theorem, and dispersion curves are presented for the lowest elastic modes of the fluid‐loaded shell. It is found that fluid loading has a profound effect on the vacuum dynamical characteristics of the shell; the spherical equivalent of the first antisymmetric, flat‐plate Lamb wave for the fluid‐loaded shell bifurcates into two distinct modes near the frequency that the vacuum dispersion curve transitions from a subsonic to a supersonic phase velocity. By way of contrast, the spherical equivalent of the first symmetric Lamb wave is essentially unaffected. The salient features of the free‐field scattering process are also analyzed in terms of the resonance excitation of these modes.

Insights into the hydrodynamics of free falling wavy films

Abstract: On selectionne trois ondes isolees de differentes amplitudes et formes a partir de mesures sur un film liquide tombant. On calcule les champs de vitesse et de pression ainsi que la vitesse de l'onde

Phase-matched periodic electric-field-induced second-harmonic generation in optical fibers

Abstract: Phase-matched electric-field-induced second-harmonic generation is demonstrated in single-mode germania-doped silica fibers. A periodic second-order nonlinearity is induced by a simple interdigitated electrode structure, which can be rotated to permit phase matching between all propagating modes. The most efficient mode interaction between HE11ω and HE112ω is achieved at 1.064 μm by using a Q-switched Nd+3:YAG laser. In principle, phase matching at any propagating wavelength is possible. This technique could be applied to planar as well as cylindrical waveguides and can be used with many non-χ(2) materials. The asymmetry in the applied electric field enhances the optical-field overlaps between modes of dissimilar orders, and this is also demonstrated. A conversion efficiency of 4.0 × 10−4% has been obtained in unoptimized devices. Device optimization is also discussed.

Modeling of picosecond pulse propagation in microstrip interconnections of integrated circuits

Abstract: Theoretical time-domain analyses of the dispersion and loss of square-wave and exponential pulses on microstrip transmission line interconnections on silicon integrated-circuit substrates, performed using the quasi-TEM approximation, are discussed. Geometric dispersion and conductor line width, as well as losses from conductor resistance, conductor skin effect, and substrate conductance, are considered over the frequency range from 100 MHz to 100 GHz. Results show the enormous significance of the substrate losses and demonstrate the need for substrate resistivities >10 Omega -cm for high-performance circuits. The results also show the effects of geometric dispersion for frequencies above 10 GHz, the unimportance of conductor skin-effect losses for frequencies up to 100 GHz, and the transition from a high-frequency regime where losses do not affect phase velocity to a low-frequency regime where the ratio of he conductor and substrate loss coefficients determines phase velocity. >

Rayleigh Lidar Observations of Gravity Wave Activity in the Upper Stratosphere at Urbana, Illinois.

Abstract: During 13 nights of Rayleigh lidar measurements at Urbana Illinois in 1984–86, thirty-six quasi-monochromatic gravity waves were observed in the 35–50 km altitude region of the stratosphere. The characteristics of the waves are compared with other lidar and radar measurements of gravity waves and with theoretical models of wave saturation and dissipation phenomena. The measured vertical wavelengths (λ2) ranged from 2 to 11.5 km and the measured vertical phase velocities (cz) ranged from 10 to 85 cm s−1. The vertical wavelengths and vertical phase velocities were used to infer observed wave periods (Tob) which ranged from 100 to 1000 min and horizontal wavelengths (λx) which ranged firm 70 to 2000 km. There may be errors, in the inferred values of the horizontal wavelengths because they were calculated by assuming that the observed period inferred the intrinsic period. Dominant wave activity was found at vertical wavelengths between 2–4 km and 7–10 km. No significant seasonal variations were evide...

Critical size and curvature of wave formation in an excitable chemical medium

Abstract: The critical radius for the outward propagation of waves in an excitable solution of the Belousov—Zhabotinskii reaction was experimentally analyzed and found to be ≈20 μm, being in a range predicted by theory Thus, the wave initiation depends on the critical radius in an all-or-none fashion For waves having high positive curvature of wave fronts, a linear relationship between the curvature and their normal velocity was established, allowing computation of a diffusion coefficient of 19 × 10-5 cm2/s for the autocatalytic species, which agrees well with results previously obtained for negatively curved wave fronts The analysis of the dispersion of wave velocity yielded the decrease of wave velocity for small initiation periods as predicted theoretically

Direct and inverse scattering in the time domain for a dissipative wave equation. Part 4: Use of phase velocity mismatches to simplify inversions

Abstract: For pt.III see J. Math. Phys., vol.28, p.260 (1987). The one-dimensional inverse scattering problem is considered for lossy inhomogeneous media for the case in which the phase velocities at the two boundaries of the scatterer do not match that of the host medium. The model problem involves electromagnetic wave propagation in a medium of unknown thickness with spatially varying permittivity and conductivity. An inversion algorithm which is capable of simultaneously reconstructing both the permittivity and conductivity is derived and tested numerically. It is shown that the discontinuity in phase velocity simplifies the data requirements for the inverse problem in that only one scattering experiment needs to be performed, rather than two. The input data for the inversion algorithm consist of a finite time trace of the reflected field or, alternatively, portions of the reflected and transmitted fields.

Breaking of wind-generated waves: measurements and characteristics

Abstract: A method of using local wave properties to provide a detailed description of breakings in a random wave field is developed. These properties, derived through the Hilbert transform, include the angular frequency, phase velocity, and surface-velocity components. The breaking characteristics are presented, including the probability of breaking, its time- and lengthscales, its intensity, and the phase of its inception. The time- and lengthscales, of breaking events were found to be linearly proportional to the corresponding scales of underlying waves, and to indicate that the breaking region is geometrically similar. Consistent results were obtained from temporal and spatial measurements. Finally, on the basis of these results we have evaluated geometric and kinematic criteria for identifying breaking waves.

Plasma-induced efficiency enhancement in a backward wave oscillator.

Abstract: A dense background plasma is observed through computer simulation to reduce the phase velocity of the most unstable mode in a backward-wave oscillator which results in a strong efficiency enhancement. The relatively weak beam-backward plasma-wave instability introduced by the rippled waveguide wall is found to exert minimal impact on the interaction efficiency.

Critical angle measurement of elastic constants in composite material

Abstract: Application of critical angle measurement for determination of elastic constants of composite materials is described. For general orientation of the composite material relative to the plane of incidence, three critical angles exist, for quasilongitudinal and fast and slow quasitransverse waves. It is shown that, for any two‐dimensional composite material, the critical angles are directly related to the phase velocities of bulk waves in the sample plane. A simple and novel type of goniometer is developed for these measurements which utilize a cylindrical reflector for measurement of the double reflection coefficient. The values of the elastic constants are reconstructed from the measured velocity surfaces by using nonlinear least‐squares optimization fitting. Analytical relations between ultrasonic velocity and elastic constants valid for arbitrary anisotropy are implemented in the fitting optimization.

Wave Propagation in a Vertical Transversely Isotropic Medium: Field Experiment and Model Study

Abstract: Summary A down-hole experiment was carried out in the transversely isotropic Oxford Clay outcropping in the south of England. Different moveout curves for the two shear wave types and anomalous amplitude features for the SV-wave were found in the field data. Based on velocity measurements carried out formerly at the site a model study was performed to explain the results. Phase velocity and group velocity curves computed analytically with the method of characteristics, and synthetic seismograms computed with the Alekseev-Mikhailenko method, are presented. the field experiment and the model studies demonstrate that the occurrence of cuspidal triangles in the qSV-wavefront is an essential feature of wave propagation in transversely isotropic media. Even for weak transversely isotropic media there is a focusing effect into the direction of the cusp which leads to prominent shear wave amplitudes in this direction. Furthermore, we examined the effect of numerical anisotropy which can contaminate the synthetic seismograms. Velocity errors are one order of magnitude higher for shear waves than for compressional waves and increase with increasing Poisson's ratio. It was found that the error can be restricted to less than 1 percent only if using a spatial sampling of three times higher than a value that would generally be regarded as sufficient in finite difference computations.

Optically activated waveguide type phase shifter and attenuator

Abstract: A waveguide having walls defining an opening. An optically transmissive aperture in one wall allows light from an optical illumination source such as a laser diode array to illuminate the opening in which is located a semiconductor slab positioned to be illuminated. When the array illuminates the slab, the propagation characteristics (phase velocity and attenuation constant) of the waveguide changes. A continuous wave signal passing through the waveguide is thus attenuated and phase shifted. The laser array may be pulsed on and off while still maintaining the altered propagation constant.

Low-frequency electrostatic turbulence in the polar cap E region

Abstract: Electrostatic turbulent fluctuations in a broad frequency band were observed in the polar cap E region over Greenland by an instrumented rocket payload. The fluctuations were detected by potential-difference measurements on two sets of boom-mounted spherical probes. The direction and magnitude of the phase velocity of the fluctuations are determined by standard correlation techniques. The driving mechanism for the turbulence is identified as the Farley-Buneman instability. A characteristic velocity close to the sound speed is deduced while the direction of propagation deviates slightly from the E0 × B0 direction. A correlation time of 20–150 ms along the rocket trajectory is determined, indicating that the fluctuations are essentially statistically independent for altitude separations of >50 m. A conditional analysis of the signals indicates that to a good approximation they can be described by Gaussian statistics. The data exclude the possibility of wave steepening as a saturation mechanism for the linear instability. It is thus unlikely that wave energy is cascaded toward short wavelengths to be dissipated there.

The propagation of Love waves in a fluid-saturated porous anisotropic layer

Abstract: The paper concerns the propagation of Love waves in a transverse-isotropic fluid-saturated porous layer overlaying an elastic nonhomogeneous half-space. Using the Biot's theory for the porous layer and the theory of elasticity for the lower medium, the dispersion equation has been derived. This complex transcendental equation that relates frequency, phase velocity, anisotropy factor of the layer and the inhomogeneity character of the half-space has been solved with the aid of successive approximation method. The effect of anisotropy and heterogeneity has been shown graphically.

Internal gravity wave selection in the upper troposphere and lower stratosphere observed by the MU radar: Preliminary results

Abstract: Marked wavelike variations of the lower stratospheric wind observed on 7–10 May, 1985 by an MST radar in Japan (by the MU radar) are analyzed assuming that they are induced by monochromatic internal inertio-gravity waves These variations are mainly composed of two modes (periods: 22 and 24 hours), both of which have zonal phase velocities (C X ) slower than the mean westerly wind (ū) A statistical analysis of the zonal phase velocity shows that C X ≲ ū above and C X ~ ū below the tropopause jet stream, which is considered to be a vivid proof of wave selection due to the tropospheric mean flow and upward wave emission from the tropopause jet A comparison between the MU radar results and routine meteorological observations leads to the conclusion that the marked waves appear when the jet stream takes a maximum wind speed

Three-dimensional modelling of upper mantle structure under the Pacific Ocean and surrounding area

Abstract: SUMMARY Long-period (75-250 s) fundamental-mode Love and Rayleigh waves are inverted for the seismic velocity variations in the upper mantle under the Pacific Ocean and surrounding area. The data are inverted to map the regional variation of phase velocity, and then the velocity structure of the upper mantle. No a priori regionalization is used in this study, and the lateral heterogeneity is expanded horizontally into blocks (lo' X 10'). To estimate the reliability of the velocity distribution, we have calculated the resolving kernels. In the central, NW, NE and SW regions, the resolving kernels have fairly sharp peaks. In the SE region, however, resolution is not so good. The results show good correlation with surface tectonics. In the velocity map, shields and ridges are the major features in the depth interval 50-100km. Anomalies associated with the East Pacific Rise and the shields persist to 300 km. At 400 and 500 km, high-velocity anomalies appear under the eastern and southern Pacific ridges, and a low-velocity anomaly appears beneath Australia. The present study provides better resolution than previous studies because of the better path coverage. For example, a large low-velocity anomaly emerges under Hawaii down to the depth of 200 km for SH velocity. The horizontal extent of this anomaly is comparable to the sue of the Hawaiian swell. This feature supports that the Hawaii hotspot is an isolated, truly anomalous feature in the Pacific Ocean.

The linear stability of viscous compressible plane couette flow

Abstract: The structure of normal modes in viscous compressible plane Couette flow is investigated. The spectrum is found to consist of two types of modes: the viscous modes, which obtain finite phase velocities by the mechanism of mode pairing; and the sonic modes, whose phase velocity becomes distorted in the supersonic regime. This leads to mode crossings which unfold, depending on the type of crossing modes, either into purely sonic or viscous-sonic instability bands. The latter provide a new example for viscous instability. Both mode pairing of viscous modes and distortion of the phase velocity of sonic modes is caused by the shear. Critical Reynolds numbers for the instabilities are derived.

Long wavelength approximation for Lamb wave characterization of composite laminates

Abstract: A simple method for measuring Lamb wave phase velocities is used to obtain data for the lowest symmetric Lamb mode (S0) and the lowest antisymmetric Lamb mode (A0) for composite laminates. The experimental data are compared with the results from an approximate theory for the lowest Lamb modes in the low frequency, long wavelength region for a unidirectional laminate, a symmetric cross-ply laminate, a symmetric quasi-isotropic laminate and an aluminum plate. There is good correlation between the data and the results from the approximate theory, which suggests that the approximate theory works well in the low frequency, long wavelength region in these cases. Also, this experimental procedure of measuring phase velocities of the lowest symmetric and antisymmetric modes can be used to characterize laminated composite plates with and without damage since each material and stacking sequence gives distinct lowest symmetric and antisymmetric curves.

Surging of Large Amplitude and Surf-riding of Ships in Following Seas

Abstract: In the previous papers, the surf-riding of a ship in the regular following waves was examined by the self-running model tests as well as the numerical simulatione. It was clarified that the surf-riding occurs when the ship speed including the steady oscillatory component due to the surging motion, after the decay of the transitional motion, reaches the phase velocity of the wave. The numerical simulation showed that concerning the occurrence of the surf-riding there exist three ranges of the ship speed for the fixed wave condition. Under the critical speed V1Cr, the ship never makes the surf-riding but invariably makes the periodic surging motion. At the speed between V1Cr and another critical speed V1, the ship sometimes makes the periodic surging motion and sometimes makes the surf-riding motion. Which motion occurs is dependent on the initial conditions of the ship position relative to the wave trough and the surging velocity of the ship. Over the critical speed V1 the ship always drops into the surf-riding condition. It was also shown that for the low wave height, the critical speed V1Crcoincides with another critical speed V1 It was not clarified how the critical speed V1 appears.In order to make clear totally the non-linear phenomenon like the surf-riding, it is not sufficient to repeat the numerical simulations for the various initial conditions. It is necessary to use the common method of a phase plane analysis for the non-linear ordinary differential equation which expresses the surf-riding motion. In the present paper, the author examines the mechanism of the surf-riding by means of the phase plane analysis and clarifies how the speed range is separated into three parts and how the wave parameter affects the separation. The method is presented to obtain the above critical speed V1r, which may be termed as the unconditional critical speed for the occurrence of the surf-riding. It is important to know the speed at which the ship can escape from dangerous surf-riding condition. The speed is named as the pull out speed following the analogy with the pull out torque of the synchronous motor, and the chart to obtain the pull out speed is also presented. Showing the analogy with other physical phenomena such as the Josephson effect in the superconductivity, the synchronous motor and the driven damped pendulum, the surf-riding is suggested to be one of the fundamental non-linear phenomenon in the physical science.