Showing papers on "Group velocity published in 1982"

Linear Pulse Propagation in an Absorbing Medium

Abstract: The pulse velocity in the linear regime in samples of GaP: N with a laser tuned to the bound $A$-exciton line is measured with use of a picosecond time-of-flight technique. The pulse is seen to propagate through the material with little pulse-shape distortion, and with an envelope velocity given by the group velocity even when the group velocity exceeds 3\ifmmode\times\else\texttimes\fi{}${10}^{10}$ cm/sec, $\mathrm{equals}\ifmmode\pm\else\textpm\fi{}\ensuremath{\infty}$, or becomes negative. The results verify the predictions of Garrett and McCumber.

Influence of the velocity ratio on the spatial instability of mixing layers

Abstract: The linear spatial instability of the tanh and Blasius mixing layers is studied for different values of the ratio between the difference and the sum of the velocities of the two co‐flowing streams. The growth rate, phase velocity, and perturbation velocity distributions are determined numerically and the results are compared with expansions for small shear or low frequency. It is found that the maximum growth rate is approximately proportional to the velocity ratio. This is shown to be consistent with the observed variation of shear layer spreading rate with velocity ratio and with a recent model of flight effects on jet mixing noise.

Worldwide distribution of group velocity of mantle Rayleigh waves as determined by spherical harmonic inversion

Abstract: We have determined the worldwide distribution of group velocity of mantle Rayleigh waves for periods between 100 and 300 sec without assuming any regionalization. Group slowness 1/u(θ, φ) is expressed by spherical harmonics, and the coefficients, up to angular order 7, have been determined from travel times of Rayleigh waves by a least-squares method. From these, u(θ, φ) has been synthesized. Since we cannot obtain information about the odd terms of the expansion from one circuit measurements around the world, we have used group velocities of mainly R_2 and R_3. The overall pattern of u(θ, φ) for periods between 100 and 200 sec is consistent with results of previous pure-path and regional studies. Group velocities for tectonically active regions are low, and those of the shields and the northwestern Pacific are high.

Properties of the Eliassen-Palm Flux for Planetary Scale Motions.

Abstract: In an investigation of the properties of the quasi-geostrophic Eliassen-Palm (EP) flux for planetary-scale motions, particular attention is given to the relation between the EP flux divergence and the meridional flux of eddy potential vorticity, and the relations between the EP flux, group velocity, and the zonal mean refractive index in the Wentzel-Kramers-Brillouin-Jeffreys limit This latter diagnostic has appeared in a number of different forms as that quantity whose gradient determines the refraction of group velocity paths or EP flux trajectories The question is considered which, if any, of these forms holds for planetary scale motions In this investigation, a planetary-scale motion is formally defined to be one for which Burger's (1958) quasigeostrophic theory is appropriate

General concepts on the generation of auroral kilometric radiation

Abstract: Auroral kilometric radiation (AKR) has a peak intensity at 250 kHz and is associated with discrete aurora in regions where ωp/ωc 0 because of the magnetic mirroring force, and diffusion of trapped electrons in the upgoing loss cone with R-X waves are toward decreasing energies, so that wave growth is possible. To determine which frequency and wave vector (k, θ) is associated with each resonant contour, we solve the cold plasma dispersion relation for ωR, k, and θ, where ωR > ωx, the right-hand cutoff frequency. Growing waves will be associated with those contours that pass through regions of velocity space where ∂f/∂υ⊥ > 0 is large. A simple criterion is given to show which R-X waves will have large positive growth rates. Finally, we calculate the group velocity of R-X waves and show that R-X waves with large, positive growth rates also have small group velocities (Vg/c ≪ 1), implying a very small convective growth length ∼10 m. The intense wave generation should occur at wave frequencies just above the right-hand cutoff frequency and have wave normal angles 75° 0 is large) associated with either the upgoing loss cone or the downgoing precipitating electrons that are undergoing mirroring.

Short wavelength electrostatic waves in the Earth's magnetosheath

Abstract: Recent observations with the ISEE-1 spacecraft have found electric field emissions in the dayside magnetosheath whose frequency spectrum is modulated at twice the spacecraft spin period. The upper frequency cut-off in the frequency-time spectrum of the emissions has a characteristic parabola shape or festoon shape. The low frequency cutoff ranges from 100 Hz to 400 Hz, while the high frequency limit ranges from about 1 kHz to 4 kHz. The bandwidth is found to minimize for antenna orientations parallel to the wave vectors. The wave vector does not appear to be related to either the local magnetic field direction of the plasma flow velocity. The spacecraft observed frequency spectrum results from the spacecraft antenna response to the Doppler shifted wave vector spectrum which exists in the plasma. Imposed constraints on the plasma restframe wave vectors and frequencies indicate that the emissions occur within the frequency range from about 150 Hz to 1 kHz, with wavelengths between about 30 meters and 600 meters. These constraints strongly suggest that the festoon-shaped emissions are ion-acoustic waves. The small group velocity and k direction of the ion-acoustic mode are consistent with wave generation upstream at the bow shock and convection downstream to locations within the outer dayside magnetosheath.

Up-conversion of subpicosecond light pulses

Abstract: Harmonic generation and frequency mixing in nonlinear media pumped by subpicosecond pulses are studied. The propagation and interaction of subpicosecond pulses in a dispersive medium is influenced by group velocity "walk through" and spreading of the light pulses. The amplitude and spectrum of the N th harmonic are calculated taking into account both the group velocity and group velocity dispersion. Conditions for group velocity matching in crystals and mixtures of metal vapors and gases are considered, together with their relation to the phase velocity matching. An example of using four-wave mixing to generate ultrashort pulses with tunable duration over a wide range by proper group velocity matching is discussed.

Free-surface flow past oscillating singularities at resonant frequency

Abstract: This paper analyses the problem of a flow past an oscillating body moving with constant velocity, below and parallel to a free surface. Special attention is given to frequencies of oscillation in the neighbourhood of the critical frequency ωc= 0.25 g/U, where the classical linearized solution yields infinitely large wave amplitude. As a result both the lift and drag forces acting on the oscillating body at the resonant frequency are singular. It is demonstrated in the paper how this resonance is elimi- nated by considering higher-order free-surface effects, in particular the interaction between the first- and third-order terms. The resulting generalized solution yields finite wave amplitudes at the resonant frequency which are O(e½) and O(eloge) for 2 and 3 dimensions respectively. Here 6 is a measure of the singularity strength. It is also shown that inclusion of third-order terms causes a shift in the wavenumber and group velocity which eliminates the singularity in the lift and drag expressions at the resonant frequency. These results are illustrated by computing the lift and drag experienced by a submerged oscillating horizontal doublet in a uniform flow.

Precision Measurement of Rayleigh Wave Velocity Perturbation

Abstract: We have developed a technique for imaging variation in the surface characteristics of a sample by measuring the local perturbation of the Rayleigh wave velocity. A 50 MHz acoustic microscope operated out-of-focus is excited with a very short tone burst so that the on-axis longitudinal and off-axis Rayleigh reflection pulses are temporally separated. The relative phase between these two signals is measured using a synchronous detection scheme. This technique has a potential sensitivity of 10 ppm. We have demonstrated experimentally that we can detect a 240 A thick film of indium deposited on glass which corresponds to a velocity perturbation of 0.18%.

Measurement of velocity mismatch in traveling-wave electrooptic modulators

Abstract: For traveling-wave electrooptic modulators, we describe an experimental method to determine the sign and magnitude of velocity mismatch between electrical and optical wave. To this end the waves are counterpropagated and frequencies yielding modulation nulls are determined. Such a measurement does also reveal dispersion of the modulator structure.

Measurement of interstation phase and group velocities and Q using Wiener filtering

Abstract: A method for calculating interstation phase and group velocities and attenuation coefficients using a Wiener (least-squares) filtering technique is presented. The interstation Green9s (or transfer) function is estimated from surface wave data from two stations laying along the same great circle path. The estimate is obtained from a Wiener filter which is constructed to estimate the signal recorded at the station further from the source from the signal recorded at the nearer station. The interstation group velocity is obtained by applying the multiple-filtering technique to the Green9s function, and the interstation phase velocity from the phase spectrum of the Green9s function. The amplitude spectrum of the Green9s function is used to calculate average attenuation between the two stations. Using synthetic seismograms contaminated by noise, it is shown that the Q values calculated from the Green9s function are significantly more stable and accurate than those obtained by taking spectral ratios. The method is particularly useful for paths involving short station separations and is applied to a surface wave path crossing the Iranian Plateau.

Brillouin revisited: Signal velocity definition for puise propagation in a medium with resonant anomalous dispersion

Abstract: The theoretical problem of wave propagation and the definition of the signal velocity in a medium exhibiting resonant, absorptive, anomalous dispersion is investigated. The special case of a dilute medium is considered, such as the upper atmosphere with dispersion due to resonant line structure (e.g., the water vapor or oxygen lines in the microwave region), as opposed to plasma dispersion, which is not resonant. Signal velocity definitions analogous to those first made by Brillouin were derived in another work and are called to question as a result of an exact solution of the problem derived here, using a Bessel function series, which allows exact wave forms to be calculated and displayed. When one represents the signal development by using the simulations, it is found that one cannot realistically separate signal from precursor. The pulse envelopes do have some interesting ringing characteristics which are shown to depend upon the density of absorbers and the resonance linewidth. Qualitative experimental results are presented that verify the simulations. The measurement of this ringing appears to be a more sensitive technique than does differential absorption for determining constituent number densities.

Existence and properties of flow structure waves in two-phase bubbly flows

Abstract: Structure waves occur in two-phase flows because one phase drifts with respect to the other, the drift flux being primarily a function of the flow structure. The wave properties provide information on the closure laws required in engineering models. Experiments made with an air-water bubbly mixture flowing in a vertical annular test section are reported. Void fluctuations involving structure disturbances were detected by capacitance measurements, the effect of individual bubbles being always negligible. Only low frequency disturbances were present, high frequency disturbances being strongly damped. Within the low frequency range, the wave velocity is independent of the frequency, and the damping is small. The wave velocity is always comprised between the average liquid velocity and the average gas velocity.

Wave propagation and stability for finite difference schemes

Abstract: : This dissertation investigates the behavior of finite difference models of linear hyperbolic partial differential equations. Whereas a hyperbolic equation is nondispersive and nondissipative, difference models are invariably dispersive, and often dissipative too. We set about analyzing them by means of existing techniques from the theory of dispersive wave propagation, making extensive use in particular of the concept of group velocity, the velocity at which energy propagates. The first three chapters present a general analysis of wave propagation in difference models. We describe systematically the effects of dispersion on numerical errors, for both smooth and parasitic waves. The reflection and transmission of waves at boundaries and interfaces are then studied at length. The key point for this is a distinction introduced here between leftgoing and rightgoing signals, which is based not on the characteristics of the original equation, but on the group velocities of the numerical model. The last three chapters examine stability for finite difference models of initial boundary value problems.

Continental shelf waves off the Fukushima coast

Abstract: Past observations and theories have indicated the importance of the constitution of the lowest-mode of shelf waves to the velocity field. However, significant contributions of the higher mode waves to current velocity fluctuations in the vicinity of the coast are suggested in observational results obtained along the Fukushima coast in Pt. I of this study (Kubotaet al., 1981). To understand the importance of the higher modes, the generation of shelf waves is investigated theoretically by two methods. First, the generation of long shelf waves by monochromatic forcing is examined, and it is concluded that near the coast the second mode's contribution to the longshore velocity is the largest for the Fukushima coast. Second, the response of shelf waves to broad-band forcing is investigated by taking the dispersive characteristics of shelf waves into consideration. It is concluded that shelf waves with zero group velocity are selectively excited if the forcing has a broad-band spectrum. According to observational results obtained along the Fukushima coast, the wind spectrum has a broad peak at about 100 hours (Kubotaet al., 1981). Since the third mode of shelf waves has zero group velocity around the period of 100 hours, the third mode can be selectively generated off the Fukushima coast. From this it is suggested that the Fukushima coast is in the forced region and that observed current fluctuations are motions associated with the second- and third-mode shelf waves.

The application of kinematic wave theory to wave trains and packets with small dissipation

Abstract: The validity of kinematic wave theory for linear waves with small dissipation propagating through a homogeneous medium is examined with the aid of the higher‐order theory of Chin. It is shown that both for nondissipative and weakly‐dissipative waves the kinematic theory holds with errors of order e2 for times of order e−1 times the wave period, where e is a measure of the nonuniformity of the wave train. For longer times, of order e−2 times the period, secular terms arise, which makes the theory invalid when wave dispersion becomes vanishingly small. By selecting a complex wavenumber chosen such as to make the group velocity real, it is possible to remove the first‐order secular terms and thus produce a modified theory uniformly valid within the longer time period. This modification is also applied to wave trains propagating in a nonhomogeneous medium. General solutions are presented for wave trains or packets of arbitrary initial conditions.

Can one measure the one‐way velocity of light?

Abstract: As Fung and Hsieh maintain, one can readily measure the speed of light in one direction if it is different from c/(1−α cos ϑ) 0?α?1. On the other hand, if the velocity of light is c/(1−α cos ϑ), the properties observed upon reflection from a plane mirror do not allow one to conclude α = 0 (as they claim) but rather that α cannot be close to unity. Finally, it is shown that if the one‐way velocity is c/(1−α cos ϑ), a wide variety of experiments fail to yield a value for α.

Dislocations in diffraction patterns: continuous waves and pulses

Abstract: When a monochromatic wave is scattered by fixed objects it produces a stationary three-dimensional diffraction pattern, but if the driving oscillation is a quasimonochromatic pulse the diffraction pattern naturally changes with time. Both the fixed and the moving patterns may be usefully characterized by their dislocation lines, where the amplitude is zero and the phase is indeterminate. The paper studies the relation between the fixed dislocation lines (continuous wave (c.w.) null lines, interference fringes) of the monochromatic pattern and the moving lines of the pulse pattern. The latter sweep out surfaces, called the dislocation trajectories. A simple model system with two interfering beams illustrates how dislocation lines can appear and disappear from the head or tail of the pulse and how pairs of dislocations can be created in two different ways. It also shows how the shape and bandwidth of the pulse affect not so much the positions of the trajectories, but their lengths and the way they are traversed in time by the dislocations. In a general theory the pulse is regarded as a slightly perturbed continuous wave and its behaviour is deduced from the continuous wave response of the (linear) system within the bandwidth of the pulse. The method is based on obtaining the fastest initial convergence of a functional series. For very small bandwidth it leads to a generalization of the concept of group velocity. In this case dislocations by interference appear only very close to c.w. nulls. For larger, but still small, bandwidth, moving dislocations appear whose trajectories are approximately parts of frequency minimum surfaces , that is, surfaces in the continuous-wave diffraction pattern where the amplitude is a minimum with respect to changes in frequency. These surfaces contain the c.w. null lines. In the next approximation it is found that the trajectory surfaces nearly, but not quite, contain these lines. In certain two-dimensional cases the trajectories follow valleys in the landscape defined by the continuous-wave amplitude pattern. The prediction of the arrival times of the dislocations is delicate. General formulae, suitable for numerical computation, are given in terms of frequency derivatives of the continuous-wave diffraction pattern. They give successful results in three applications to pulsed wave fields: the diffraction pattern near a cusped caustic, the two-beam model, and a piston radiator.

Global Q estimates from antipodal Rayleigh waves

Abstract: Global average estimates of the group velocity and attenuation of long-period (120–300 s) Rayleigh waves were made using seismograms from the epicenter's antipode (Δ≃180°). Focusing at the antipode produced amplified arrivals with favorable signal-to-noise ratios. The high-quality data yielded very stable attenuation values, with excellent agreement between the results from successive Rayleigh arrivals for a single event and between the results for two different events. Lateral heterogeneities in earth structure can cause systematic biasing of attenuation measurements based on antipodal records. The initial, uncorrected results therefore provide a lower bound estimate of global Q. An ellipsoidal perturbation in shape was used to simulate the effects of lateral velocity heterogeneities on Rayleigh wave propagation. Using the agreement of repeated attenuation measurements as a constraint, we estimated both the bias in those measurements and the splitting widths of the Rayleigh modes. At a period of 200 s, the estimated splitting width is 0.30% this agrees closely with calculations by Luh (1974) for an earth model with different continental and oceanic velocity profiles. The estimated bias varied from 30% to zero over the 120- to 260-s band. After correcting for bias, the antipodal Q values range from 108 at 120 s to 188 at 260 s. These Q are within the range of previous measurements but are lower than the mean values from typical great circle studies, implying that the globally averaged upper mantle is slightly more attenuative than has been generally recognized.

The drift velocity of a hard-sphere Lorentz gas

Abstract: Studies the Boltzmann equation for a Lorentz gas with scattering on stationary hard spheres in the presence of a constant field E. The exact initial and asymptotic time evolutions are given and compared with numerical calculations. Starting with an initial equilibrium velocity distribution the authors study the influence of the initial temperature T on the drift velocity of the Lorentz gas. The drift velocity quickly reaches a maximum and then decreases slowly towards zero. In particular an upper bound, close to 0.8 E1/2 lambda 1/2, exists for the drift velocity. Here lambda =( pi a2n)-1 is the mean free path, related to the density n and radius a of the scatterers. In an initially cool gas the drift velocity slows down as t-1/2 soon after the maximum is passed. In an initially hot gas, however, there are two asymptotic regimes. After a time of order lambda 1/2E-1/2 the drift velocity stays constant for a time interval whose length is proportional to T3/2, and eventually decays as t-1/2.

An Exact Analysis of Propagation Modes Group Velocity for in Optical Fibers

Abstract: A method for calculating exactly the group velocity of propagation modes in optical fibers is proposed. In this analysis, optical fibers can contain uniaxial and dispersive media. The group velocity obtained by using the scalar approximate analysis is compared numerically with the rigorous group velocity computed by this method for square-law index optical fibers.

Wave-equation migration in the presence of lateral velocity variations

Abstract: An algorithm for three‐dimensional wave equation migration in the presence of lateral velocity gradients is developed. The algorithm is based geophysically on the exploding reflector model and mathematically on integral solutions to the scalar wave equation. In addition, the velocity is assumed to vary slowly over a seismic wavelength. The primary application of the algorithm is to stacked sections. However, if the velocity is a function of depth only, the algorithm may be used to migrate and/or image common‐depth‐point gathers.