Showing papers on "Group velocity published in 1975"
TL;DR: In this paper, the vertical propagation of near-inertial period waves has been detected in a series of recent velocity profiles by a technique of vector spectral analysis, previously applied to vector series in time, has been used to study the vertical spatial structure of velocity profiles obtained in the mid-Ocean Dynamics Experiment (MODE).
Abstract: Vertical propagation of near-inertial period waves has been detected in a series of recent velocity profiles by a technique of vector spectral analysis. This method, previously applied to vector series in time, has been used to study the vertical spatial structure of velocity profiles obtained in the Mid-Ocean Dynamics Experiment (MODE). Prior to the use of spectral analysis, however, it is necessary to minimize the influence of vertical variations of the Brunt-Vaisala frequency. The procedure was to normalize the current amplitudes and stretch the vertical coordinate according to a WKB scheme. The vector spectral analysis, applied to the normalized and stretched profiles, yielded wave polarization estimates which are related to the sign of the vertical group velocity of internal waves. The analysis of a set of velocity profiles indicates that the net energy flux of the waves near the inertial frequency is downward.
290 citations
TL;DR: The formal theory of geometric optics in a space-and time-varying plasma was developed in this paper assuming that there propagates a small amplitude wave, that there is a linear, causal, but, in general, nonlocal relation between current density and electric field, and that the background plasma does not change much in a locally defined wavelength or period.
Abstract: The formal theory of geometric optics in a space− and time−varying plasma is developed assuming that there propagates a small amplitude wave, that there is a linear, causal, but, in general, nonlocal relation between current density and electric field, and that the background plasma does not change much in a locally defined wavelength or period. The description reduces to a system of ordinary differential equations along rays everywhere tangent to the group velocity, one such system of rays for each mode. These equations are formally Hamiltonian in character. They permit the introduction of an energy density such that negative energy waves will be unstable in a lossy medium, as seen by an observer moving with the group velocity, providing that the divergence of the bundles of rays is not too great.
203 citations
TL;DR: In this paper, the contribution of tertiary resonant interactions to the total energy transfer in an inhomogeneous random field of gravity waves is calculated, and it is found to be small for open-ocean waves, but to be of some importance for shallow-water waves, where topography or mean shear currents may produce strong inhomogeneities.
Abstract: Certain tertiary resonant interactions of gravity waves which have been found previously can be obtained more easily by using a simple extension of Whitham's formalism. The contribution of these interactions to the total energy transfer in an inhomogeneous random field of gravity waves is calculated. It is found to be small for open-ocean waves, but to be of some importance for shallow-water waves, where topography or mean shear currents may produce strong inhomogeneities. The nonlinear splitting of the group velocity is found to be unimportant in wave fields with sufficiently smooth spectra.
108 citations
100 citations
TL;DR: In this paper, an array of standard long period stations is applied to measure phase velocities of seismic surface waves by way of frequency-wavenumber analysis, and the number of interfering modes is reduced by windowing the signal for successive group velocity intervals.
Abstract: An array of standard long period stations is applied to measure phase velocities of seismic surface waves by way of frequency-wavenumber analysis. The number of interfering modes is reduced by windowing the signal for successive group velocity intervals. The method is powerful, even with relatively small arrays: up to 6 higher Rayleigh modes at periods between 20 and 100 sec. have been resolved.
83 citations
TL;DR: In this article, a new technique is presented for simultaneously measuring the average, regional phase velocity of two or more surface-wave modes, even if they travel with the same group velocity.
Abstract: A new technique is presented for simultaneously measuring the average, regional phase velocity of two or more surface-wave modes, even if they travel with the same group velocity. Many observations are required over paths of varying length with earthquake sources of known focal mechanism. The phase of the signal observed at each station can be predicted if the initial phase of the source and the phase velocity and relative amplitude of each mode is known. The square of the difference between the observed phase and the predicted phase is summed over all paths for a set of trial phase velocities. The trial velocities which give the minimum sum correspond to the average phase velocity of each mode. By applying this technique to Love-wave data from the east Pacific, the dispersion of the first higher Love mode was measured for the first time in an oceanic area. The phase velocity of the fundamental mode was found to increase with increasing age of the sea floor, probably as a result of the cooling of the oceanic lithosphere. The region was found to be anisotropic for Love-wave propagation, with the fastest velocities roughly perpendicular to the ridge. The degree of anisotropy appears to increase with increasing period.
58 citations
TL;DR: Results are presented showing that the instability of flow observed in collapsible vessels can be associated with the fluid velocity approaching the phase velocity in a narrowed segment of the vessel.
Abstract: Results are presented showing that the instability of flow observed in collapsible vessels can be associated with the fluid velocity approaching the phase velocity in a narrowed segment of the vessel. Phase velocity is measured using capacitance displacement transducers, and is found to vary with frequency and with the state of collapse, reaching a minimum just prior to when opposite sides of the vessel come into contact. The mean fluid velocity is calculated from the measured area-pressure relationship for several values of flow in the range associated with instability. It is found that the mean fluid velocity and phase velocity curves intersect at the flow corresponding to instability, provided that transmural pressure is less than zero. A simple formulation is proposed to predict the critical flow at which this instability can develop.
58 citations
TL;DR: In this paper, the vertical and longitudinal component of the Lg wave can be identified with higher Rayleigh modes for crustal sources, in terms of group velocities and surface amplitude displacements.
Abstract: Summary We demonstrate in terms of group velocities and surface amplitude displacements, that the vertical and longitudinal component of the Lg wave can be identified with higher Rayleigh modes for crustal sources. Low velocity layers in the crust are not required for the existence of Lg waves. Li could be used as a sufficient but not necessary discriminant for structures containing a low velocity channel in the upper mantle. Analogous group velocity and amplitude reasoning applies to Rg waves generated by crustal shocks; such waves are associated with the fundamental mode. Also, in this case, the existence of low velocity zones in the crust is not required. Lg, Rg propagate in structures with and without a low velocity channel in the upper mantle.
51 citations
TL;DR: In this article, a simple approximation for the problem of the dispersion of marked particles in an incompressible fluid in random motion when the probability distribution of the velocity field is taken as Gaussian, homogeneous, isotropic, stationary and of zero mean was proposed.
Abstract: A simple approximation is proposed for the problem of the dispersion of marked particles in an incompressible fluid in random motion when the probability distribution of the velocity field is taken as Gaussian, homogeneous, isotropic, stationary and of zero mean. Approximations for the Lagrangian velocity correlation function and the dispersion are given and compared with exact computer calculations of Kraichnan. Agreement is found to be good except for time-independent velocity fields and singular wavenumber spectral functions.
42 citations
TL;DR: In this paper, a ray theory is applied to the problem of three-dimensional propagation of inertial-internal waves in the presence of a mean baroclinic current which does not vary in the downstream coordinate.
Abstract: A ray theory is applied to the problem of three‐dimensional propagation of inertial‐internal waves in the presence of a mean baroclinic current which does not vary in the downstream coordinate. As time increases, the Doppler‐shifted wave frequency, or intrinsic frequency, tends to a limiting value determined by the horizontal and vertical variations of the mean current and density fields. The limiting value of the intrinsic frequency determines critical surfaces where energy is transferred to the mean motion. Also, the group velocity tends to the mean current velocity, and the phase velocity tends to be oriented towards or away from the core of the mean current, depending upon whether the wave is either initially propagating with a wave number component antiparallel or parallel to the mean current.
41 citations
TL;DR: In this paper, the velocity, temperature and velocity fluctuation distributions within falling spindle oil films in an inclined rectangular channel were measured using hot-wire techniques and thin thermocouples and the results indicate that the liquid films are as a whole much more laminar-like than turbulent in a range of Reynolds numbers (4γ/μ) up to the experimental limit of 6000.
Patent•
17 Nov 1975
TL;DR: In this article, a fluid velocity measuring device for the accurate fast measurement of the velocity of a fluid whether liquid or gas using the time of passage of acoustic energy through the fluid as the frequency determining element in a continuous wave oscillator is presented.
Abstract: A fluid velocity measuring device for the accurate fast measurement of the velocity of a fluid whether liquid or gas using the time of passage of acoustic energy through the fluid as the frequency determining element in a continuous wave oscillator. The frequencies or periods of oscillations of two anti-parallel acoustic paths are used to compute fluid velocity between the electro-acoustic transducers at the ends of the acoustic paths. The device in accordance with this invention may utilize a single reversing acoustic path or two anti-parallel acoustic paths. The velocity resolution can be selected by the operator in accordance with a stated uncertainty principle limiting the ratio of frequency response to velocity resolution. Mode ambiguities due to fluid phase velocity variations are avoided by varying the path lengths. The frequency range of the oscillator is limited by a phase locked loop.
TL;DR: In this article, a model of the fluctuating velocity field in the wall region of a turbulent boundary layer has been carried out, where the Reynolds-stress distribution during bursting periods and the mean velocity profile were assumed to be known, and the linear large scale response to a random system of bursts was computed using an idealized model for the joint probability distribution in time and space of the occurrence of bursts.
Abstract: Following the ideas suggested by Landahl (1967, 1975), some model calculations of the fluctuating velocity field in the wall region of a turbulent boundary layer have been carried out. It was assumed that the turbulent stresses are generated intermittently on small scales in time and space owing to bursting-type motions. The Reynolds-stress distribution during bursting periods and the mean velocity profile were assumed to be known, and the linear large-scale response to a random system of bursts was computed using an idealized model for the joint probability distribution in time and space of the occurrence of bursts. Computed energy spectra of the streamwise velocity fluctuations display scales in the spanwise and streamwise directions and time which are in good agreement with measurements by Morrison, Bullock & Kronauer (1971). However, the wavenumber band-widths of the computed spectra are narrower than those of the measured ones. This discrepancy is probably due to the crudeness of the model employed for the Reynolds stress during bursting.
Patent•
10 Sep 1975
TL;DR: In this paper, an electronically tunable optical filter is described wherein an optical beam is diffracted by an acoustic beam the group velocity of which is noncollinear with the optical beam transmitted through the birefringent crystal medium.
Abstract: An electronically tunable optical filter is described wherein an optical beam is diffracted by an acoustic beam the group velocity of which is noncollinear with the optical beam transmitted through the birefringent crystal medium. The frequency and the direction of the phase velocity of the acoustic wave are chosen for a given incidence direction of the optical beam so that the diffraction occurs for a band of optical frequencies centered about a predetermined optical frequency and a relatively large angular distribution of incident optical beams. The noncollinear acousto-optic filter has the following advantages: (i) it allows very simple coupling of optical and acoustic beams into the interaction medium, (ii) it allows the use of multiple transducers for increasing tuning range or varying resolution, (iii) it allows a broad class of crystals to be used as filter material, (iv) it has a large degree of freedom in the filter design for optimizing efficiency or angular aperture and throughput, realizing narrow or broad optical passband and (v) it provides the spatial separation of incident and transmitted light through the filter and thus can be operated without the use of polarizers.
TL;DR: In this paper, a theory for calculating the velocity of sound in solid-gas and liquid-gas systems using mass and momentum balances was developed. But the theory can be applied only if the one phase is distributed in the other homogeneously in the form of particles, droplets or bubbles of equal size.
TL;DR: In this article, the wave fields and resonance cone of the right hand polarised (whistler mode) wave have been mapped at distances of up to 10 whistler wavelengths from a transmitting antenna.
Abstract: USING a large volume laboratory magnetoplasma the wave fields and resonance cone of the right hand polarised (whistler mode) wave have been mapped at distances of up to 10 whistler wavelengths from a transmitting antenna. The results are in good agreement with theory and suggest that energy is convected away from the antenna along the surface of the resonance cone. Considerable attention has been paid to the generation of waves by a point source in a magnetoplasma, and theoretical analyses1–5 have shown that for certain combinations of the antenna operating frequency ω, the electron gyrofrequency ωc, and the plasma frequency ωp, the fields become singular along a cone whose axis is parallel to B0, the steady magnetic field. By examining the refractive index surfaces it can be seen that the group velocity of the wave is zero when the ray vector is parallel to the resonance cone of half angle θ (when the wave normal is at an angle π/2−θ to B0). We restrict ourselves here to a discussion of the radiation pattern for frequencies ω<ωc≪ωp. Waves launched by the antenna then propagate in the right hand polarised whistler mode and the angle of the resonance cone is approximately given by θ=sin−1 (ω/ωc).
TL;DR: In this paper, the fundamental equations of the electrodynamics of moving media are presented, and the treatment is carried out by the Mandel'shtam-Tamm method, which permits introduction of potentials and of the Hertz tensor for the description of the electromagnetic field in a moving medium.
Abstract: Recently there has been an increase of interest in the electrodynamics of moving media. This is primarily due to the emergence of new experimental possibilities. High-current accelerators give dense beams of relativistic electrons or of plasma cluster. In addition, moderating structures exist in which the velocity of propagation of electromagnetic waves is much less than the velocity of light in a vacuum, and this facilitates observation of relativistic effects. These successes have rendered realistic the consideration of a whole number of applications. These include the amplification of electromagnetic waves and the augmentation of frequency by reflection from interfaces with moving media, and also the diagnostics of material flows. Various astrophysical and ionosphere applications are of interest. In this review, the fundamental equations of the electrodynamics of moving media are presented. The treatment is carried out by the Mandel'shtam- Tamm method, which permits introduction of potentials and of the Hertz tensor for the description of the electromagnetic field in a moving medium. The laws of propagation of free electromagnetic waves are considered. A derivation is given of Green's function in the electrodynamics of moving media. This makes possible a unified determination of the fields in the presence of sources. Consideration is given to peculiar effects that occur at faster-than-light velocity of motion of the medium (when the velocity of motion of the medium exceeds the phase velocity of light in the rest system of the medium). In the appendix, expressions are found for the fields of a stationary point charge and magnetic dipole, and the Lienard?Wiechert potentials in a moving medium are also obtained.
TL;DR: In this paper, the formation heights of lines that do not exhibit Zeeman splitting are calculated using an LTE, partial non-LTE, and full non-lTE approach.
Abstract: Heights of formation of lines that do not exhibit Zeeman splitting are calculated using an LTE, partial non-LTE, and full non-LTE approach. Non-magnetic (g=0) lines are valuable for velocity investigations in quiet-Sun magnetic field regions, and a knowledge of their formation heights is useful for obtaining three dimensional velocity profiles in these regions.
TL;DR: In this paper, an experimental and theoretical investigation of laminar boundary layer response to harmonic oscillations in velocity associated with a travelling wave imposed on an otherwise constant freestream velocity and convected in the free-stream direction is described.
Abstract: This paper describes an experimental and theoretical investigation of laminar boundary layer response to harmonic oscillations in velocity associated with a travelling wave imposed on an otherwise constant freestream velocity and convected in the freestream direction. An oscillatory flow wind tunnel and recording system were set up to produce and measure laminar boundary layer velocity profiles over frequencies of 2–10 H z for freestream amplitudes of up to 14 % of the mean velocity. An analysis on the lines of Lighthill’s theory but applying for any travelling wave convection velocity has been developed for both the low and high frequency cases. The experiments show that for a wide range of amplitude and frequency of oscillation the mean flow characteristics are the same as those of steady flow. This supports a major assumption of the theory which is linear in terms of the oscillating perturbations. Comparisons between theory and experiment show satisfactory agreement although the experimental results are largely for frequencies between the extreme ranges of the theories and they display features which are special to that intermediate frequency range. It is found that the boundary layer response is predominantly affected by the travelling wave convection velocity and frequency. In the experiments the freestream oscillation amplitudes increased with downstream distance but the effects of this increase are shown to be negligible.
TL;DR: It is proposed that genes responsible for a specific morphological character produce oscillators characterized by the same period, and control the phase difference between neighbouring oscillators so that waves invariant in period are produced.
TL;DR: In this article, the instability of the upper branch (ω ≳ ωce; ω ∼ kzV) is shown to be either convective or absolute depending on the specific beam and plasma parameters.
Abstract: The linear theory of a mono−energetic electron beam interacting with a cylindrical, homogeneous, Maxwellian magnetoplasma is investigated numerically. Using standard criteria the instability of the upper branch (ω ≳ ωce; ω ∼ kzV) is shown to be either convective or absolute depending on the specific beam and plasma parameters. In the weak beam limit, nb ≪ np, a cubic dispersion equation is derived to describe the same system. The cubic equation is analyzed to show that the instability is convective when the group velocity of the plasma wave is positive. The instability is absolute when the group velocity of the plasma wave is negative and when the beam density exceeds a threshold density.
TL;DR: In this article, the scattering attenuation and velocity of elastic waves propagating in two-phase microstructures are computed by an extension of multiple scattering analysis, and the measured values agree qualitatively with the predicted ones, and physical reasons are proposed to account for the agreement.
Abstract: The scattering attenuation and velocity of elastic waves propagating in two‐phase microstructures are computed by an extension of multiple scattering analysis. The computation is based on a model of an array of isotropic spherical scatterers embedded in an isotropic matrix. Attenuation α is predicted to increase with volume fraction and number density of scatterers and to approach a plateau with frequency. Group velocity vg is predicted to decrease with volume fraction and frequency. Ultrasonic measurements of α and vg are made on model microstructures consisting of Cu spheres embedded in a polymethylmethacrylate matrix. The measured values agree qualitatively with the predicted ones, and physical reasons are proposed to account for the agreement. The inability of the theory to provide accurate quantitative predictions of these quantities is discussed.Subject Classification: 35.26; 20.30, 20.35.
01 Jan 1975
TL;DR: In this article, the stability of the electron cyclotron frequency in an electron plasma consisting of a cold component and a hot component with a weak "loss-cone" perpendicular velocity distribution is investigated.
Abstract: The stability of electrostatic waves above the electron cyclotron frequency in an electron plasma consisting of a cold component and a hot component with a weak “loss-cone” perpendicular velocity distribution is investigated. A simple marginal stability algorithm permits a rapid estimate of the unstable frequency band as a function of two ratios, the hot to cold density, and the cold upper hybrid to electron cyclotron frequency. The growth rate peaks near but below the cold upper hybrid frequency. However, the group velocity parallel to the magnetic field can have zeroes near the odd half-harmonics of the cyclotron frequency, suggesting that the instability is non convective under certain conditions, possibly accounting for observations of narrow band emissions near 3/2, and sometimes near 5/2 of the electron cyclotron frequency in the magnetosphere.
TL;DR: In this paper, the authors measured group velocities for Rayleigh waves and Love waves to periods of almost 200s for nine paths across Australia, using a new process of summing cross-correlograms of a large number of earthquakes with moderate magnitudes.
Abstract: Summary Group velocities and phase velocities for Rayleigh waves and Love waves have been measured to periods of almost 200s for nine paths across Australia. This extended range of dispersion data was obtained by the new process of summing cross-correlograms of a large number of seismograms of earthquakes with moderate magnitudes (average mb was 5.8) prior to the non-linear computation of phase. This is an unbiased averaging process that enhances the signal at longer periods. Westerncentral Australia has the same dispersion as shield areas of other parts of the world; eastern Australia may be catalogued tectonic or ‘ aseismic platform’. Group velocity for eastern Australian paths has a pronounced minimum value, possibly less than 3.4 km s-’, between 100and 200-s period. Smoothed Rayleigh wave phase velocities were obtained by integration of regionally averaged group velocity curves. A usable estimate of fundamental mode Love wave phase velocities was obtained by Fourier analysis of sums of cross-correlograms, but Love wave group velocities could not be resolved by frequency-time analysis.
TL;DR: In this paper, the authors measured the time delay of a P (20) short pulse propagating through a high-pressure CO2 amplifier under small-signal-gain conditions, which is proportional to the small signal gain divided by the linewidth.
Abstract: We have measured the time delay of a P (20) short pulse propagating through a high−pressure CO2 amplifier under small−signal−gain conditions. The reduced velocity agrees with the group velocity, which is about 0.92c. The effect is proportional to the small signal gain divided by the linewidth.
TL;DR: In this paper, it was shown that radiation forces are proportional to wave vectors for charged particles as well as for optical pulses in an inhomogeneous anisotropic medium and that the trajectories in space and time-dependent potential coincide when the dispersion surfaces are the same.
Abstract: The motion of a charged particle in a space- and time-dependent potential and the motion of an optical pulse in an inhomogeneous anisotropic medium coincide when the dispersion surfaces are the same. For the trajectories in space to coincide, it is sufficient that the wave vectors be proportional. It follows from the general expression of the average stress-energy density (∂L¯/∂K→)K→ where L¯ denotes the average lagrangian density and K→ denotes the 4 wave vector, that radiation forces are proportional to wave vectors for charged particles as well as for optical pulses. Because of these relations, many results in mechanics are applicable to optics. In particular, the constancy of the horizontal component of the velocity of a bullet on earth has, as a counterpart in optics, the constancy of the axial component of the group velocity of optical pulses propagating in thick tapered dielectric slabs. It follows from this observation that thick tapered dielectric slabs are not suited for long-distance communication, because of the large pulse spreading that they introduce. Slabs with moderate thickness, however, may exhibit low pulse spreading.
TL;DR: In this article, an externally excited ion wave in an ion beam-plasma system was found to grow spatially in the case where the ion beam velocity was nearly equal to an ion acoustic velocity.
Abstract: An externally excited ion wave in an ion beam‐plasma system was found to grow spatially in the case where the ion beam velocity is nearly equal to an ion acoustic velocity. The phase velocity and growth rate are in good agreement with the results based on the kinetic dispersion equation.
TL;DR: In this paper, a rather weak electron beam is injected into the magnetic field and the wave is amplified due to convective instability, whose wave vector k is determined as follows: the wave number component k ∥ paralell to the field satisfies the Cherenkov excitation condition (k ∥ υ b ≈ω), and then, the component k ⊥ perpendicular to field is determined by the dispersion relation K (ω, k ∈, k ∆, k ⌉ )=0.
Abstract: The Bernstein wave propagating obliquely to the magnetic field is excited by the coaxial probe and is heavily damped by the Landau and/or cyclotron damping with respect to the direction along the field, whose propagation direction may be coincident with that of the maximum value of group velocity (∂ω/∂ k ). When a rather weak electron beam is injected, the wave is amplified due to the convective instability, whose wave vector k is determined as follows: the wave number component k ∥ paralell to the field satisfies the Cherenkov excitation condition ( k ∥ υ b ≈ω), and then, the component k ⊥ perpendicular to the field is determined by the dispersion relation K (ω, k ∥ , k ⊥ )=0. Increasing the intensity of the electron beam above the threshold value, the spontaneous excitation of the wave is observed, which can be explained consistently as the result of the convective instability of thermal noise in plasma.
TL;DR: In this article, a luminescence method which uses a pulse light was investigated to visualize and measure quantitatively flow velocity distributions, a method by which flow velocity can be measured regardless of the widths of excitation time and photograph exposure time was developed.
Abstract: To visualize and measure quantitatively flow velocity distributions, a luminescence method which uses a pulse light was investigated. A method by which flow velocity can be measured regardless of the widths of excitation time and photograph exposure time was developed. Some optical and fluid characteristics of glycerin aqueous solutions in which luminescence particles are well dispersed are reported. The spatial resolving power of this method was found to be 100-300 mu m. The apparatus which has mechanical shutters with rotating discs was used to measure the velocity distribution of two-dimensional flows.