Showing papers on "Group velocity published in 1978"

The fine-scale structure of the turbulent velocity field

Abstract: The existence of universal similarity of the fine-scale structure of turbulent velocity fields and the validity of the original Kolmogorov local similarity theory and the later reformulations were investigated. Recent studies of the fine-scale velocity field for many different flows, e.g. grid flows, wakes, jets and the atmospheric boundary layer, are shown to provide considerable evidence for the existence of Kolmogorov normalized spectral shapes which are universal in the sense that they describe the high wave-number spectral behaviour of all turbulent flow fields with a similar value of the turbulence Reynolds number Rλ. The normalized spectral shapes vary with Rλ in a manner consistent with the later reformulations. The Reynolds number dependence of the normalized spectra is demonstrated for the Rλ range from about 40 to 13 000. Expressions for the Kolmogorov normalized spectral functions are presented for three values of Rλ. Also revealed in this study is the importance of considering effects on spectra caused by deviations from Taylor's approximation in high intensity turbulent flows. Lumley's (1965) model is used to correct the high frequency portion of the measured one-dimensional spectra for these effects. An analytical solution to Lumley's expression is presented and applied to the data.

The Measurement of Optical Radiation Pressure in Dispersive Media

Abstract: The paper describes the details of a repetition of the Jones-Richards experiment (1954) to compare the recoil of a mirror due to the radiation pressure of light striking it in an optically dense medium with the recoil of the same mirror from the same light in air. A more than tenfold improvement in precision has been possible through the development of the laser and of multilayer reflectors of high reflectivity and low absorption. The new experiment confirms, to a precision of about 0.05%, that the momentum associated with electromagnetic radiation increases directly with the refractive index of the medium into which it passes, discriminating substantially in favour of the phase velocity ratio and against the group velocity ratio. The experiment also shows that the magnitude of recoil of a mirror in oblique incidence does not vary, within the foregoing precision, when the plane of polarization is changed from perpendicular to parallel to the plane of incidence.

A new model for nonlinear wind waves. Part 1. Physical model and experimental evidence

Abstract: A new interpretation of a nonlinear wind-wave system is proposed. It is proposed that, for steady wind blowing in one direction, a nonlinear wind-wave system can be completely characterized, to a good first approximation, by a single nonlinear wave train having a carrier frequency equal to that of the dominant frequency in the wind-wave spectrum. In this model, the spectral components of the wind-wave system are not considered a random collection of free waves, each obeying the usual dispersion relation, but are effectively non-dispersive bound-wave components of a single dominant wave, travelling at the speed of the dominant wave. To first order, the nonlinear wind-wave system is considered to be a coherent bound-wave system which propagates energy only at the group velocity of the dominant wave and is governed by nonlinear self-interactions of the type found in amplitude-modulated wave trains. The role of short free waves in the system is discussed. Results of laboratory experiments performed by the authors and by Ramamonjiarisoa & Coantic (1976) are found to provide evidence supporting the applicability of such a model to wind waves under virtually all laboratory conditions. Preliminary consideration is given to possible application of the model to oceanic wind waves and conditions are identified for which the model would be most likely to apply.

Near-bottom velocities in waves with a current

Abstract: Bakker (1974) developed a mathematical model concerning the sand concentration and velocity distribution in an oscillatory turbulent flow, with or without resultant current. The flow is assumed to be uniform in horizontal direction. The present paper reports on an experimental verification of this theory. Furthermore, the numerical accuracy of the model has been investigated and diagrams are presented which enable the computation by hand of global velocity profiles.

Solar wind velocity estimation from multi-station IPS

Abstract: Three-station and four-station observations at 74 MHz are used to study the spatial structure and temporal rearrangement of the intensity pattern of interplanetary scintillations (IPS) in weak scattering. Velocity estimators from three models, two of which include rearrangement, are applied to the data and evaluated. It is shown that for certain radio sources the spatial anisotropy of the pattern is determined by elongated source structure. An upper bound on the average pattern axial ratio for an isotropic ecliptic source is 1.3 for data of mid-1972. An upper bound on the average random velocity for the same period is 40% of the bulk velocity. We discuss a simple velocity estimator that is independent of the spatial anisotropy and has a low sensitivity to the random velocity.

Seismic surface waves and crustal and upper mantle structure

Abstract: Seismic surface wave data have been used to infer details of earth structure over various propagation paths. Experimental methods for measuring surface wave dispersion include the Fourier phase method, the time correlation method, the band-pass filtering method, the group delay time method, and various digital ‘moving window’ techniques. Surface wave data exhibit distinctive observational characteristics for different tectonic provinces such as shields, aseismic continental platforms, rifts, oceans, and mountains. Inversion procedures used to determine velocity models from dispersion measurements utilize trial and error procedures or application of partial derivatives of phase and group velocity with respect to model parameters combined with linear inverse theory. The observed surface wave data emphasize that there are pronounced lateral variations in crustal and upper mantle structure and the continents and oceans are themselves inhomogeneous. Shield areas possess the highest values of shear wave velocities with depth and a relatively weak mantle low-velocity zone. On the other hand, rift areas have much lower shear velocities and a very pronounced low-velocity zone. Under the oceans the lid overlying the low-velocity zone is variable in thickness and thickens with the increasing age of the ocean floor. The average velocity above 170–200 km is less under oceans than under continents. Surface waves propagating over oceanic paths are attenuated more than continental paths, but detailed regional studies are lacking.

Crustal structures inferred from Rayleigh-wave signatures of NTS explosions

Abstract: An improved method for determining plane-layered earth models that accurately represent the important features controlling the amplitude and wave form of surface waves is presented. The method includes a formal inversion of phase and group velocity data determined from observed seismograms and is applied to the Rayleigh waves from Nevada Test Site (NTS) explosions recorded at Albuquerque, New Mexico and Tucson, Arizona. For both paths the observed dispersion agrees with that from the models with a maximum residual of only 0.01 km/sec. Further, the models are consistent with other available information about these paths (e.g., from refraction surveys). To properly account for local differences in the material at the source, an approximate theory is constructed in which the amplitude excitation is computed in a source structure and the dispersion in a separate path structure. Using this theory and the crustal models from the inversion, synthetic seismograms are computed that match the observed seismograms remarkably well.

The Magneto-Optical Filter. II. Velocity Field Measurements

Abstract: In this paper we describe a filter which utilizes magneto-optical effects for velocity fields measurements. The working principle of the instrument is described and its transmission profiles are given. Velocitygrams are shown of the five minutes oscillations (FMO) and the results compared with the expected (theoretical) signal from the instrument. We found a Vrms of 400 m s−1 for the FMO.

Geological control on the three-component spectra of Rayleigh-wave microseisms

Abstract: Microseisms in the band 1 to 15 Hz propagate principally as multi-mode Rayleigh waves. Comparison of some previously published spectra from sites over unconsolidated sediments, with theoretical Rayleigh-wave dispersion curves shows a high correlation between observed broad spectral maxima and theoretical group-velocity minima. This gives practical support to a recent prediction of this relationship. Comparison of three-component spectra with theoretical Rayleigh-wave dispersion curves and particle motion figures shows that fine structure in the observed spectra can be correlated with changes in the particle motion figures for different Rayleigh modes. Thus both broad and fine spectral features are affected by local geology and can give useful control when inverting microseism data to obtain a seismic model. The Rayleigh wave nature of microseisms implies that direct interpretation of spectra in terms of body-wave seismic resonances of the earth is incorrect. However, since an approximate correspondence exists between theoretical group velocity minima and body-wave resonant frequencies, some spectral maxima do occur near such frequencies.

Relaxation process of the electron velocity distribution in neon

Abstract: The relaxation process from an initial velocity distribution to the equilibrium distribution for electrons in neon is calculated by a finite difference method for the ratios of electric field to gas number density E/N between 56.6 and 566 Td (E/p0=20 and 200 V cm-1 Torr-1 at 0 degrees C) without using the usual two-term spherical harmonics expansion of the velocity distribution. The pulsed Townsend condition, in which the evolution of all the electrons involved in an avalanche is observed as a function of time only, is assumed. The results suggest that the electron velocity distribution reaches through randomisation the equilibrium distribution which has a structure with a minimum near the origin in the velocity space.

Simultaneous inversion of surface wave phase velocity and attenuation: Love waves in western North America

Abstract: A formalism is developed for simultaneous inversion of surface wave phase velocity and attenuation to determine shear wave velocity and Q−1 in the earth. A simultaneous inversion takes full account of the dependence of surface wave velocity and attenuation on both the elastic and the dissipative part of an earth structure and permits inclusion of the physical relationship between anelasticity and intrinsic dispersion that arises from linearity. The procedure is mathematically more complete than the approach of correcting phase velocity data for the intrinsic dispersion due to anelasticity and inverting the corrected velocity data alone, and it gives different results. The proposed formalism, including resolution analysis, weighted least squares inversion, and extremal inversion, is applied to Love waves in western North America. Various intrinsic dispersion-attenuation relations are tested, including Q independent of frequency, Q varying as a power of frequency, and Q specified by a sum of relaxation mechanisms. The results of the inversions confirm the coincidence of the low-velocity and low Q zones beneath western North America for frequencies in the surface wave band. Compared with previous inversion of Q−1 data alone, the simultaneous inversion results in improved depth resolution of Qs−1 and the elimination of an apparent incompatibility of low-attenuation data at 20- to 25-s periods. The Love wave data do not discriminate among the various dispersion-attenuation relations, though a constant Q leads to the removal of the requirement for a low-velocity zone at frequencies above 1 Hz. The predicted intrinsic dispersion within the low-velocity zone varies from 1% to 10% between 0.01 and 1 Hz for the various models; broadband measurements of body wave dispersion offer the greatest promise for choosing among the models.

Velocity of a Perturbation in Infinite Lattice Systems

Abstract: The problem of defining and estimating the velocity of disturbances in a crystal is investigated. Some results are given for plane rotors and anharmonic systems.

On Alfvén's critical velocity for the interaction of a neutral gas with a moving magnetized plasma

Abstract: A theory for the interaction of a neutral gas with a moving magnetized plasma is given. The Alfven expression for the critical velocity is identified with that for the terminal velocity while another expression for the threshold velocity for interaction is given. The implications of these results to the Alfven-Arrhenius model for the solar system are discussed.

The four-dimensional group velocity

Abstract: The advantages of using the 4-dimensional group velocity are demonstrated. After first giving its purely kinematic definition for an arbitrary wave field, the discussion turns to packets of electromagnetic waves in electrically and magnetically anisotropic media which possess space-time dispersion and are smoothly nonuniform in space and slowly varying in time. In particular, a simple expression is obtained for the energy-momentum 4-tensor in terms of the group-velocity 4-vector. Finally, it is shown how the 4-dimensional notation simplifies the derivation of the conditions of orthogonality and conservation of the adiabatic invariant. A note by M. L. Levin which follows this paper contains a brief account of the basis results of W. R. Hamilton's investigations relating to the velocity of wave motion.

Group velocity of whistlers in a two‐ion plasma

Abstract: Computations of the group velocity of whistlers in a two-ion plasma show that a quasi-longitudinal (QL) right-handed polarized wave (electron wave) has a minimum group velocity at the so-called crossover frequency; a QL left-handed polarized wave has a maximum group velocity at the same frequency. A quasi-transverse (QT) electron wave has a minimum group velocity at the ion hybrid frequency. In an oxygen/hydrogen plasma this minimum occurs only for almost perpendicular waves, whereas in a helium/hydrogen plasma it occurs also for waves propagating off perpendicular to the magnetic field. We also find that a small concentration of helium in a hydrogen plasma introduces a ‘stop band’ for quasi-transverse waves with frequencies just above the helium gyrofrequency. The theoretical results are used to interpret satellite observations of quasi-transverse low-frequency whistlers.

Negative group velocities of Lamb waves

Abstract: Negative group velocities, which mean that the direction of propagation of wave energy and that of wave phase are opposite, were found experimentally in S2 mode of Lamb waves excited on an A 1 plate of 1 mm thick at frequencies near 3 MHz. A stroboscopic schlieren technique was used to observe an ultrasonic pulse reradiated in water from the Lamb mode, together with specular‐reflected and transmitted pulses. The phase velocity of the Lamb mode was derived from the angle of incidence, and the direction of group velocity was determined from the displacement of reradiated pulse relative to the specular reflection. Phase velocities observed at various frequencies were in good agreement with theoretical predictions, which also described negative group velocities appearing at phase velocities above 10 km/s. Such a high phase velocity is negligibly affected by water loading. Existence of negative group velocity seems inherent in S2 mode and independent of plate materials. Also in S4 mode, negative group velocities are predicted in a very narrow frequency range.

Three‐field electroacoustic parametric interactions in piezoelectric crystals

Abstract: We derive the coupled mode equations governing the Thompson–Quate experiment, that is, the parametric interaction of two counterpropagating bulk acoustic waves and a spatially uniform electric field oscillating at the second harmonic of the acoustic frequency. The derivation applies to propagation of any acoustic mode type in any direction in any piezoelectric or pyroelectric crystal. A new result of the derivation is a general but explicit expression for the material interaction coefficient that governs the strength of the process. We also find that the equations differ from the generic equations assumed by Thompson and Quate by the replacement of a phase velocity with the component of the group velocity normal to the crystal surface. As an aid to this derivation we also derive the coupled mode equations governing the parametric interaction of three acoustic waves. This derivation applies to the propagation of any mode types in any directions (consistent with being close to or at phase matching) in any d...

Induced velocities of grains embedded in a turbulent gas

Abstract: A theory is presented for the dynamics of dust particles in an incompressible turbulent fluid. Grain-gas coupling occurs through friction forces that are proportional to the mean grain velocity relative to the gas. This test particle theory is applied to the case of a Kolmogoroff spectrum in a protostellar cloud. The mean turbulence induced grain velocity and the mean turbulent relative velocity of two grains are calculated. Whereas the former should determine the dust scale height, grain-grain collisions are influenced by the latter. For a resonable strength of the turbulence, the mean induced relative velocity of two particles turns out to be at least as large as the corresponding terminal velocity difference during gravitational settling.

Application-Oriented Ray Theory

Abstract: This is a tutorial presentation of the subject of ray theory as provided for third-year students of electrical engineering. The concepts of the eikonal and dispersion equation, group velocity, wave...

Measurements of velocity distributions in the laminar wake of a flat plate

Abstract: The two-dimensional wake of a thin flat plate parallel to the stream was maintained laminar and steady at Reynolds numbers up to 3000 in a low-turbulence wind tunnel. Velocity distributions in the wake were measured in detail for Reynolds numbers from 20 to 3000. One of the interesting results is the appearance of a velocity overshoot, namely that the velocity in the outer part of the shear layer exceeds that of the uniform flow in the vicinity of the trailing edge. Comparisons between the experimental results and Goldstein's theoretical predictions show good agreement in the far wake irrespective of the Reynolds number, but not in the near wake even at higher Reynolds numbers, in particular immediately behind the trailing edge.

Motion of an electron wave packet in a uniform electric field

Abstract: Energy eigenstates are superimposed in order to form the wave packet for an electron propagating in one dimension under the influence of a uniform, time‐independent electric field. Flux velocity, phase velocity, and envelope velocity are considered. Asymptotic expressions are derived which describe the motion when the electric field is small and/or the wave packet is far away from the classical turning point. A graphical method is presented by which one can obtain both the position and shape of the envelope at a time t if the position and shape are known at some initial time.