Showing papers on "Group velocity published in 1980"

Sound velocity of supercooled water down to -33 °C using acoustic levitation

Abstract: The sound velocity in supercooled water has been measured at 54 kHz down to −33 °C by means of an acoustic levitation method. The accuracy of the results is estimated to be within ±1.3%. Comparison with published data obtained at 5 GHz and 925 MHz indicates an anomalous sound velocity dispersion.

Nonlinear Electron Waves in Strongly Magnetized Plasmas

Abstract: Weakly nonlinear dispersive electron waves in strongly magnetized plasma are considered A modified nonlinear Schrodinger equation is derived taking into account the effect of particles resonating with the group velocity of the waves (nonlinear Landau damping) The possibility of including the ion dynamics in the analysis is also demonstrated As a particular case the authors investigate nonlinear waves in a strongly magnetized plasma filled wave-guide, where the effects of finite geometry are important The relevance of this problem to laboratory experiments is discussed

Velocity analysis in transversely isotropic media

Abstract: In transversely isotropic media, the moveout velocity obtained from common‐depth‐point (CDP) analysis may be significantly different from the horizontal velocity of the pseudo‐P wave. In Levin’s (1978) paper, he discusses, among other things, the problem of velocity determination in a medium in which the pseudo‐P wave surface produced by a point source is an ellipsoid of revolution. He points out that one would expect many sedimentary rocks to be transversely isotropic with a vertical axis of symmetry. In his Appendix he proves that an ellipse (using two dimensions for convenience) is one possible shape for the wave surface in such a medium. He also shows, as have others, that in this case CDP velocity analysis measures the velocity of horizontal propagation.

Higher‐mode surface waves and structure of the Great Basin of Nevada and western Utah

Abstract: Observed seismograms and dispersion data for crust and mantle higher mode surface waves in the Great Basin are compared with theoretical seismograms and dispersion curves computed for the Great Basin model of Priestley and Brune [1978]. This structure was originally derived from fundamental mode surface wave and refraction data. Phases identified as Sa [T∼13 s] are observed to have a phase velocity of 4.50±0.03 km s−1. Crustal second Rayleigh mode (first shear mode) waves have predominant periods varying from about 5 s on some paths to about 8 s on others. The observed excitation and phase velocity of the Sa phase are in agreement with theoretical seismograms and computed phase velocities for a modified Great Basin model. The agreement provides added support, in an unexpected way, for the existence of a mantle lid of velocity about 4.5 km s−1 in the Great Basin. The crustal higher mode group velocity observations, i.e., the predominant periods of the second Rayleigh mode along various paths, reflect variations in crustal thickness within the Great Basin. Crustal thicknesses of approximately 25 km are indicated for some paths in northwestern Nevada and southeastern Oregon, whereas crustal thicknesses of greater than 35 km are indicated for east central Nevada. The crustal thickness of 35 km in the Great Basin model is probably most appropriate for the central part of the Great Basin.

Ultrasonic attenuation and velocity in AS/3501-6 graphite fiber composite

Abstract: The ultrasonic group velocity and attenuation were measured as a function of frequency for longitudinal and shear waves in the epoxy matrix (3501-6) and in the principal directions of the unidirectional graphite/epoxy composite (AS/3501-6). Tests were conducted in the frequency ranges 0.25 Mz to 14 MHz and 0.5 Mz to 3 MHz for longitudinal and shear wave modes, respectively. The attenuation increased with frequency for all wave modes, but the group velocity was independent of frequency for all wave modes. The effects of pressure and couplant at the transducer-specimen interface were studied and it was found that for each transducer type there exists a frequency dependent 'saturation pressure' corresponding to the maximum output signal amplitude.

Optical determination of the phase velocity of short gravity waves

Abstract: Images of short wind-driven gravity waves were taken from an offshore platform, using a charge coupled device television camera recording diffuse sky radiance reflected from the ocean surface. A two-dimensional power spectrum was calculated from nine statistically independent images. The resultant ensemble-averaged spectrum exhibited good statistical stability and provided information on the angular spread and direction of the wave components present. One-dimensional sampling of each image in a sequence allowed a space-time image to be constructed which clearly shows the effects of wave dispersion as well as the modulation of the phase velocities of the short wavelength waves by the long wavelength components. An ensemble-averaged space-time spectrum, when combined with the directional parameters, is compared with the predictions of linear gravity wave dispersion theory. Two distinct wave systems were present: the local wind driven system showed a space-time spectrum in agreement with linear theory out to ∼1 cyc/m, but with excess phase velocity at higher spatial frequencies. The second wave system, which was presumably generated by a distant wind field, showed a deficiency in phase velocity when compared to linear theory.

Wave modulation in a nonlinear dispersive medium

Abstract: A model describing the simultaneous amplitude and phase modulation of a carrier wave propagating in a nonlinear dispersive medium is developed in terms of nonlinear wave‐wave interactions between the sidebands and a low frequency wave. It is also shown that the asymmetric distribution of sidebands is determined by the wavenumber dependence of the coupling coefficient. Digital complex demodulation techniques are used to study modulated waves in a weakly ionized plasma and the experimental results support the analytical model.

The microinstabilities of a high-β plasma flow with a non-uniform velocity profile

Abstract: The microinstabilities of a high-pressure plasma moving along a magnetic field with a non-uniform velocity profile are investigated. A similar problem was studied earlier by Dobrowolny on the basis of hydromagnetic equations with an oblique viscosity tensor. The present paper, unlike Dobrowolny's work, gives a kinetic analysis. Perturbations with transverse wavelength both larger and smaller than the ion Larmor radius are considered. The analysis indicates that there is a large family of microinstabilities of the ‘drift’ type whose mechanism differs from the classical Kelvin–Helmholtz instability.

A first-order scattering solution for modelling elastic wave codas — I. The acoustic case

Abstract: Summary A corrected, first-order solution for modelling acoustic wave scattering in layered halfspaces containing random inhomogeneities is derived. Energy lost to higher order scattering and intrinsic attenuation is included in the correction, which is constructed so that energy is conserved to first order. The complex propagation effects of the layering are overcome by representing the motion as a sum of normal modes. This approach renders the kinematic description of the scattering two dimensional, with the wave vectors of incident and scattered modes lying parallel to the layering. At each level in the halfspace, the inhomogeneities are resolved into two-dimensional Fourier spectra also parallel to the layering. The root mean square (rms) motion of a scattered mode depends on the correlation between spectra at different levels and the group velocity of the mode. To simplify the solution, it is assumed that the inhomogeneity spectra are piecewise constant and that the energy of a normal model propagates only at its group velocity. The final step of the theory establishes a criterion for the source—receiver separations over which the results are accurate. Numerical calculations have been carried out for a single layer of inhomogeneities over a halfspace. The spectra of the inhomogeneities were assumed band limited, and several different spectra were examined. The results suggest the existence of a diagonal selection rule whereby a wavelet of mode order n scatters mostly to wavelets of the same order. Moreover, a resonant frequency of scattering occurs, causing the rms signal to appear monochromatic. The frequency of the resonance is controlled by the inhomogeneity spectra band limits. With the aid of the diagonal selection rule, the simplified solution allows for both rapid computation of synthetic signals and inversion of data for scattering cross-section. Existing data suggest the theory may be applied to obtain approximate models of local earthquake codas. The synthetic signals of the single layer cases, for example, have codas similar to published observations. To illustrate the inversion of data with the theory, a preliminary scattering cross-section for the lunar crust is presented.

Theory of nonlinear pulse propagation in optical waveguides

Abstract: We present an approximate theory of nonlinear pulse propagation in homogeneous and inhomogeneous waveguides. Our analysis takes account of physical effects arising from transverse confinement, dispersion, and nonlinearity. We find that both bright and dark solitons may be supported by typical waveguides under a variety of conditions. Moreover, it is possible to achieve a condition of “zero dispersion,” in which a soliton of arbitrarily small amplitude may be propagated, independent of pulsewidth. In the presence of weak longitudinal inhomogeneity, we find that solitions continue to propagate without a change of shape, but that their group velocity becomes time dependent.

Propagation of Barotropic Continental Shelf Waves over Irregular Bottom Topography

Abstract: Using a geometry which roughly approximates that of a typical continental shelf and slope, the effects of a random bottom topography on free barotropic shelf waves are found. The bathymetric irregularity induces damping of the coherent wave due to scattering, as well as Phase velocity Changes. For a representative realization of the bottom topography, the damping of low-mode long waves due to scattering is apparently comparable to that due to turbulent bottom friction. Damping peaks occur at frequencies where the coherent wave scatters into modes having a zero group velocity. Generally, the breadth of the peaks is a maximum when the alongshore topographic scale and the zero group velocity wavelength are comparable. Strong scattering to high modes, which have low phase velocities, may be prevented by the presence of a mean alongshore flow.

Surface wave studies of the Bering Sea and Alaska area

Abstract: The area of the Bering Sea and Alaska was studied in terms of shear velocity, density, and compressional velocity structure by applying a generalized inversion method to surface wave dispersion relationships in the period range from 10 to 100 sec. Group velocity dispersion relationships in the area were obtained by applying the phase-matched filtering technique (Herrin and Goforth, 1977) to digitally recorded surface wave data. Corrections for instrument response and the sphericity of the Earth were applied to the dispersion observations. A new exact analytical method for the computation of Rayleigh wave phase velocity partial derivatives with respect to Earth parameters was formulated. With the phase velocity partial derivatives determined, the group velocity partial derivatives were computed by use of the fast and accurate method of Rodi et al. (1975), and were successfully incorporated into a generalized inversion method. The study area was found to consist of three physiographic provinces, and the structure of the three regions was estimated as follows: in continental Alaska, the crustal thickness is about 43 km, and a low velocity zone extends from a depth of about 113 km to about 213 km. In the Bering Shelf region, the depth to the Mohorovicic discontinuity is about 28 km, and a low velocity zone ranges in depth from about 108 km to about 213 km. In the Aleutian Basin, the thickness of the crust is about 18 km, and a low velocity zone extends from a depth of about 60 km to about 220 km.

Sound propagation in parallel sheared flows in ducts: the mode estimation problem

Abstract: We consider the inviscid, linear propagation of discrete frequency sound in an infinitely long, two-dimensional duct, possibly with soft walls, carrying a steady parallel sheared flow. Completely explicit expressions are obtained for the amplitudes of the sound modes associated with the discrete wavenumber spectrum generated upstream and downstream of a specified source distribution. By comparison with a less explicit solution for this problem given by Swinbanks (I975) we obtain an explicit expression for the group velocity of a mode in the case of rigid duct walls. Explicit expressions for the mode amplitudes can also be obtained in the case that the pressure, axial pressure gradient and transverse velocity are specified at one axial station. In the case of the problem of expanding a pressure profile in terms of modes entirely of the downstream or upstream family it is shown that in general this results in the need to solve an infinite set of linear simultaneous equations. Two such sets can be developed, suggesting that in fact non-trivial constraints exist on the kinds of initial pressure profiles that are ami-enable to expansion in such a partial set of eigenfunctions. A necessary condition for the 'optimum impedance' problem is also derived. The entire analysis is based on a new approach to non-classical eigenvalue problems that combines the elements of residue theory and Sturm-Liouville theory and that is first illustrated by consideration of a non-classical vibrating string problem.

Spatial Stability of Concentric Annular Flow

Abstract: Spatial stability of fully-developed axial flow in a concentric annulus to infinitesimal, axisymmetric as well as non-axisymmetric disturbances is investigated. The solution employs a selective application of the Gram-Schmidt orthonormalization procedure in order to control the parasitic error during numerical integration. Results presented in the form of neutral stability curves for several values of the diameter ratio and angular wavenunaber show that the flow is, more unstable to non-axisymmetric disturbances than to the axisymmetric ones. The sequence for the values of angular wavenumber in order of increasing critical Reynolds number depends on the diameter ratio of the annulus. As the angular wavenumber increases, the phase velocity of the neutral disturbances approaches a constant, about 1/4th of the maximum velocity of axial flow through the annulus. The results match, in the limit, with those for the plane-Poiseuille flow.

Three-dimensional stability of growing boundary layers

Abstract: A theory is developed for the linear stability of three-dimensional growing boundary layers. The method of multiple scales is used to derive partial-differential equations describing the temporal and spatial evolution of the complex amplitudes and wavenumbers of the disturbances. In general, these equations are elliptic unless certain conditions are satisfied. For a monochromatic disturbance, these conditions demand that the ratio of the components of the complex group velocity be real and thereby relate the direction of growth of the disturbance to the disturbance wave angle. For a nongrowing boundary layer, this condition reduces to d-alpha/d-beta being real, in agreement with the result obtained by using the saddle-point method. For a wavepacket, these conditions demand that the components of the group velocity be real.

Mode analysis of graded-index optical fibers using a scalar wave equation including gradient-index terms and direct numerical integration

Abstract: A new mode analysis is proposed for optical fibers with arbitrary refractive-index profile. Scalar wave equations including gradient-index terms and characteristic equations including an abrupt change of the refractive index at the core-cladding boundary are derived for HE, EH, TE, and TM modes. The propagation constant, cutoff frequency, group velocity, and field distribution of each mode are calculated with high accuracy by direct numerical integration of a differential equation and the numerical solution of a transcendental equation.

Orbital velocities in irregular waves

Abstract: Experimental and theoretical study to determine the applicability of linear wave theory for the description of the velocity field in irregular waves. A comparison between theory and measurement was executed both in frequency and in time domain. In frequency domain by means of the experimentally and theoretically determined frequency response functions of wave motion to orbital velocity, and in time domain by means of the measured and computed time records of the velocities. The time records for the velocities were computed from the measured waterlevel fluctuations by using the impulse response function method. The orbital velocities were measured contactless with laser-doppler equipment.

Polarization transmission characteristics of optical fibers with elliptical cross section

Abstract: In the transmission via optical fibers connected to laser diodes, optical switches, optical filters, etc., or in high-sensitivity high-selectivity optical heterodyne detection system, polarization characteristics become important in addition to transmission loss and dispersion. The polarization transmission characteristics of optical fibers with elliptic cross-section are calculated by characteristic matrix method for large values of ellipticity. For two orthogonal polarization modes (oHE11 and eHE11 modes) the transmission velocity, group velocity and their difference (elliptic double refraction) are obtained. The group delay difference among modes is very small but elliptic double refraction greatly affects the polarization characteristics.

Coupled cavity traveling wave tube with velocity tapering

Abstract: A coupled cavity traveling wave tube (10, 10') is provided having a velocity taper, i.e., gradual velocity reduction, which affords beam-wave resynchronization and thereby enhances efficiency. The required wave velocity reduction is achieved by reducing the resonant frequencies of the individual resonant cavities as a function of the distance from the electron gun (16, 16'), through changes in internal cavity dimensions. The required changes in cavity dimensions can be accomplished for example, by gradually increasing the cavity radius (R 2 , R 3 , R 4 ) or decreasing the gap length (l 1 , l 2 ), from cavity to cavity. With this approach the velocity reduction is carried out without an increase in circuit resistive losses and the upper and lower cut off frequencies are reduced in approximately the same manner.

Measurement of ultrasonic wave velocity in steel for various structures and degrees of cold-working

Abstract: A pulse-echo technique based on the averaging of a large number of measurements (up to 10 7 is described for the accurate estimation of longitudinal and transverse wave propagation velocity at megahertz frequencies This technique was used for the investigation of slight velocity changes associated with different low-alloy steel microstructures derived by graded tempering of martensite Further measurements show the marked influence of the rolling process on ultrasonic transverse wave velocity in austenitic 304L and 316L steels