Showing papers on "Group velocity published in 1972"

Wave mechanics of breakdown

Abstract: Kinematic wave theory is used to determine under what conditions breakdown of a steady or unsteady laminar flow into high frequency oscillations should occur. The analysis of a small-scale secondary wave riding on a large-scale inhomogeneity, such as that produced by a finite amplitude primary instability wave, reveals that the breakdown mechanism has three basic ingredients: (i) a self-excited secondary wave with a group velocity near the propagation velocity (phase velocity) of the primary wave, (ii) space-time focusing of the secondary wave train on the primary wave crest and (iii) a nonlinear filtering mechanism leading to rectification of the secondary wave.The theory is applied to a laminar shear flow. Good quantitative agreement with the experiments on boundary-layer transition by Klebanoff, Tidstrom & Sargent (1962) is found for the critical condition leading to breakdown. Also, the theory is able to explain all the main qualitative breakdown features observed by Klebanoff et al. and others, such as the rapid localized onset, and the formation of a hairpin vortex lifting up from the surface downstream of the primary wave crest.

Measurement of the Velocity Field in a Simulated Tornado-Like Vortex Using a Three-Dimensional Velocity Probe

Abstract: A three-dimensional velocity probe, incorporating hot-film anemometry, is developed to study the mean flow field of a simulated turbulent tornado-like vortex interacting with a smooth, flat boundary. The flow characteristics are essentially controlled by a dimensionless parameter ϵc and a Reynolds number Ret. The parameter is the ratio of sink strength to the product of the free-stream circulation and the vortex core radius. Flow fields for two different ϵc (0.022 and 0.51) are studied, with Ret>105 in both cases. It is found that. 1) the tangential velocity profiles at more than three core radii from the axis are similar to those of a turbulent flow over a flat plate; 2) the radial velocity close to the boundary is directed inward due to a positive radial pressure gradient, while it changes direction and approaches a constant at a height of two core radii from the boundary; 3) the vertical velocity depends strongly on ϵc, and is directed downward near the vortex axis in case 1 and upward in case...

The Vavilov-Cerenkov Effect and the Doppler Effect in the Motion of Sources with Superluminal Velocity in Vacuum

Abstract: It is customary to consider only "subluminal" light sources, or sources moving with a velocity v lower than the velocity of light in vacuum (c). It is assumed in this connection that the Vavilov-Cerenkov effect and the anomalous Doppler effect are possible only in media and waves for which the refractive index n(ω) > 1. For this reason, the phase velocity of the waves is cph = [c/n(ω)] cph. Yet, as is well known, there exist also "superluminal" sources, with velocity v > c. Examples are light spots produced on a remote screen by a rotating source of light or particles. The spot velocity is v = ΩR, where Ω is the angular velocity of source rotation and R is the distance to the screen. The condition v > c can be realized on the Earth, and is practically always realized under astronomical conditions for pulsar radiation. It is emphasized in the article that superluminal sources are equivalent in a wide range to subluminal ones, and, concretely, can generate Cerenkov radiation in vacuum and in a medium with n(ω) < 1. The article considers several corresponding possibilities. From this point of view of radiation theory, a major difference between the superluminal and subluminal sources is that the former can not be individual particles (electrons, protons, etc.), since their velocity is always smaller than c. Superluminal sources, which must thus consist of aggregates of particles, must thus have nonzero dimensions, and this leads to a corresponding formation of a spectrum of the radiated frequencies on the short-wave side. Regardless of whether superluminal sources will find interesting applications in physics and astronomy, a study of the radiation of superluminal sources of electromagnetic and gravitational waves (and possibly also neutrinos) is in the authors' opinion of undisputed physical interest.

Finite-Amplitude Baroclinic Wave Packets

Abstract: A theory is presented for the propagation of wave packets in a slightly unstable baroclinic shear flow in a quasi-geostrophic two-layer model on the beta plane. The theory for inviscid motions is considered and packet solutions resembling solitary waves are found. It is shown that the propagation speed of the packet, which is a function of its amplitude, exceeds the most naturally defined group velocity. A physical explanation is presented and it is suggested that the enhancement of the signal velocity above the group velocity is a general property of systems possessing linear instability and nonlinear stability.

Hydrodynamic Theory of the Angular Velocity Autocorrelation Function

Abstract: The angular velocity correlation function is computed using a frequency dependent version of Stokes' Law. The drag torque on a sphere rotating nonuniformly about one of its diagonals is used to compute the relaxation of the angular velocity. It is shown that the asymptotic time dependence of this function goes as t−5/2. Consequences of this persistence in the orientational relaxation of molecules is discussed.

The velocity of a wave packet in an anisotropic absorbing medium

Abstract: The field of a pulsed beam (a ‘wave packet’), travelling through a medium with moderate absorption, is calculated by the saddle-point method. The packet velocity (i.e. the velocity of the spatial amplitude maximum) has the same direction as the velocity Re (∂ ω /∂ k ), a generalization of the group velocity ∂ ω /∂ k in non-absorbing media. It differs from the absolute value of this velocity by a correction factor depending on the absorption, beam width and pulse duration. This factor is unity for vanishing absorption and infinite beam width. The velocity Im (∂ ω /∂ k ) has no apparent physical meaning.

Electrostatic resonances associated with the maximum frequencies of cyclotron-harmonic waves

Abstract: Resonances associated with the maximum frequencies of cyclotron-harmonic waves (Bernstein modes) are observed on Alouette and Isis ionograms at both high and low latitudes; these are called the fQn resonances. Dispersion equations for oblique propagation in a hot magnetoplasma have been used to do ray tracing at frequencies near fQ2. The waves responsible for the observed resonance effects have group velocities that are very nearly equal to the the satellite velocity for the duration of the observed resonance; in contrast, other workers using ray tracing have found that the group velocity for the plasma-frequency and upper hybrid-frequency resonances changed considerably in a time equal to the observed resonance duration. The decay of the observed resonance with time is not due to Landau or collisional damping and hence may be due to spatial spreading. At low latitudes, the fQn resonances usually float, that is, the signals are weak immediately after the transmitter pulse. The resonance signals also often exhibit an interference pattern.

On Wave Propagation In Inhomogeneous Media

Abstract: Familiar relations between phase and group velocity for wave propagation in homogeneous media are generalized to the inhomogeneous case. The constant velocity ``c'' is merely replaced by an appropriate weighted average. The key tool lies in the stationary property of the frequency as a functional of the wavefunction.

Direct measurement of the (baseband) frequency response of multimode fibers.

Abstract: Incoherent light, transmitted via multimode fibers, represents a potential carrier for information that is directly modulated on the light envelope. The amplitude and phase characteristics of the envelope (baseband) signal are affected by the fiber waveguide because of group delay differences among the modes. We report on a technique that determines the baseband frequency response of the fiber system by comparing the beat spectra of light from a free-running laser before and after transmission through the fiber. As an example, we describe the measurement of 30 m of cladded multimode fiber. The 3-dB bandwidth was 700 MHz, somewhat larger than predicted on the basis of the computed group velocity differences.

A coupled-mode analysis of mode locking in homogeneously broadened lasers

Abstract: The coupled-mode equations are solved for homogeneously broadened lasers modulated near the axial mode separation frequency. The character of the oscillations changes rapidly when the modulation period is tuned through the round-trip delay at the group velocity. Specifically, this is the region in which phase modulation leads to pulsing and loss modulation leads to pulsing at normal power. The present method agrees with the results of Kuizenga and Siegman for this region, but gives a countable set of supermodes in addition. There is some reason to believe that these other modes have already been observed. When the group velocity condition is not satisfied, a more complete description is given than has been previously reported. Most importantly, the dependence of laser power on modulator drive and frequency can be predicted.

Investigation of the surface acoustic wave properties of heteroepitaxial ZnO layers on Al2O3

Abstract: Experimental data are given showing the relationship of phase velocity, group velocity, and electromechanical coupling coefficient as a function of the normalized thickness h/λ for epitaxial (1120) ZnO on (0112) Al2O3. Delay time vs frequency for dispersive delay lines fabricated from epitaxial ZnO on Al2O3 is also given. Using these data, design criteria and assessments are made for the use of this composite material in fabrication of a dispersive delay‐line device.

Vector velocity system

Abstract: Apparatus and method for measuring the angular velocity of an object in a single illumination utilizing a coherent system such as is utilized in a conventional doppler radar for radial velocity measurements. Apparatus and method for selecting specific frequency and bandwidth signals in the echo from the object illuminated by the coherent system, with the selected signal providing the data for subsequent computation to produce an output corresponding to the angular velocity of the object.

Excitation and propagation of an upstreaming electromagnetic wave in the solar wind

Abstract: Two types of circularly polarized hydromagnetic waves that can propagate upstream in the solar wind exist. One type is right-hand polarized with respect to the ambient magnetic field and has both its phase and group velocities directed upstream. It is a Doppler-shifted whistler mode that in a stationary frame has a much larger phase velocity than the solar-wind velocity. The other is left-hand polarized with respect to the ambient field and has its phase velocity directed downstream, but its group velocity is directed upstream. It is shown that the latter mode, which is also a Doppler-shifted whistler mode but which propagates backward in the moving frame, can be excited at the bow shock through a two-stream type instability between the solar wind and the magnetosheath plasma. The instability occurs around the local proton cyclotron frequency, and the generated wave can be convected upstream by this mode with a group velocity approximately equal to the solar-wind velocity. This instability, because of its scale size, is shown also to be a possible candidate for the shock formation.

Cavity Phase Dependent Frequency Shifts in Cesium Beam Frequency Standards

Abstract: The influence of the atomic velocity distribution in cesium beam atomic frequency standards on the frequency shift due to Ramsey cavity phase difference is discussed. The atomic resonance is shifted and its shape distorted to a degree dependent not only on the exciting power level and cavity phase difference, but also on the actual velocity distribution which exists in the standard. Calculations carried out for the NRC 2.1 metre primary standard show that, for the velocity distribution which probably exists in this standard, the resonance distortion gives rise to a power dependence of the frequency shift of about an order of magnitude less than that expected for a Maxwellian velocity distribution in the beam. Experimental measurements tend to support this result.

Theory of discrete wave packets in the solar wind

Abstract: Discrete wave packets were observed by Ogo 5 and earlier satellites. These waves were believed to be in the whistler mode. Since their group velocities were found to be smaller than the solar-wind speed, these waves could not have been generated in the bow shock and could not have propagated upstream later. The present theory discusses a mechanism similar to that of the echo phenomenon in plasma physics discovered in recent years. The present theory enables us to explain (a) why the wave packets were associated with the bow shock, (b) why the wave packets were characterized by coherent oscillations, and (c) why the wave packets had group velocities smaller than the solar wind and yet could still occur in the solar wind. In short, our theory is able to interpret all the essential features deduced from the observational data.

High-Resolution Precision Digital Tachometer

Abstract: A new approach to the digital measurement of angular velocity is presented. This new instrument performs the division by time that has been carefully avoided in the existing instruments. The accuracy and resolution of the transducer does not depend upon the number of quantizations/revolution. The measurements can be made in a very short time, leading to up to 14700 samples per second. An important feature of this instrument is that even at speeds close to zero (or at zero), the error is less than 0.02 percent and 1600 samples of the angular velocity can be obtained/second. This makes the instrument particularly suitable for the study and control of the transient behavior of motors and other rotating devices.

Apparatus for measuring the angular displacement and the angular velocity of a rotation member

Abstract: Apparatus for measuring the angular displacement and the angular velocity of a rotating member. Mechanical energy causing angular motion of the rotating member is transformed into electrical energy in the form of a plurality of electrical pulses which are counted during a preselected time interval. Variations in the magnitude of the cycle do not alter the accuracy of the apparatus. Thus, the angular displacement and the angular velocity of the rotating member can be economically measured with greater accuracy than has previously been possible with voltage dependent apparatus.

Vavilov--cherenkov effect and anomalous doppler effect in a medium in which the wave phase velocity exceeds the velocity of light in a vacuum.

Abstract: where Cph = c/n is the phase velocity of the generated waves, n(w) is the refractive index corresponding to these waves, and c is the speed of light in vacuum. In the anomalous Doppler effect, the angle (} between k and v satisfies the condition(}< 80• Thus, the V-C effect and the anomalous Doppler effect are possible only if\"the source velocity v ~ Cph· It is usually assumed that the source velocity v < c, and consequently theV-C effect and the anomalous Doppler effect are possible only in a medium with n > 1, i.e., at Cph = c/n cat R > 3 x 104 em.

Method for Calculating Surface Rayleigh Waves in a Vertically Inhomogeneous Half-Space

Abstract: As is well-known [1], displacements in Rayleigh waves are expressed in terms of the eigenvalues and eigenfunctions of the following boundary value problem.

Velocity of the solar wind as determined from interplanetary scintillations.

Abstract: The method of smooth perturbations is used to derive the equations for interplanetary scintillation in a (statistically) spherically symmetric solar wind with constant wind velocity. The expressions, valid in the limit of small scintillation index, are used to discuss the relation between the radial wind velocity and the observed projected velocity of the scintillation pattern. It is found that the pattern velocity is systematically less than the wind velocity by a substantial fraction, depending on the radial variation of the density fluctuations. If the fluctuations fall off as 1/r-squared the correction is 18 percent, whereas if the fluctuations are proportional to 1/r the correction is 57 percent. The effects may be even more severe if the solar wind is not spherically symmetric.

Torsional wave under initial stress

Abstract: In this paper, the frequency equation for phase velocity of torsional wave in a rod of circular cross section under initial tension has been obtained. The graphs are plotted to compare the velocity with that in the absence of initial tension. Some analytical informations have been obtained for instability of the body under initial compression.

Propagation of Electromagnetic Waves in Media Which Vary Slowly with Position and Time

Abstract: Using WKB methods we have considered the propagation of electromagnetic waves in isotropic lossless media which vary slowly with both position and time. It is found that in such media the meaning of various quantities, such as the group velocity, must be reinterpreted. The theory is applied to study propagation in space-time, varying dielectrics, and plasmas.