Showing papers on "Group velocity published in 1985"

Noise-sustained structure, intermittency, and the Ginzburg-Landau equation

Abstract: The time-dependent generalized Ginzburg-Landau equation is an equation that is related to many physical systems. Solutions of this equation in the presence of low-level external noise are studied. Numerical solutions of this equation in thestationary frame of reference and with anonzero group velocity that is greater than a critical velocity exhibit a selective spatial amplification of noise resulting in spatially growing waves. These waves in turn result in the formation of a dynamic structure. It is found that themicroscopic noise plays an important role in themacroscopic dynamics of the system. For certain parameter values the system exhibits intermittent turbulent behavior in which the random nature of the external noise plays a crucial role. A mechanism which may be responsible for the intermittent turbulence occurring in some fluid systems is suggested.

Magnetic resonance imaging the velocity vector components of fluid flow.

Abstract: Encoding the Precession phase angle of proton nuclei for Fourier analysis has produced accurate measurement of fluid velocity vector components by MRI. A Pair of identical gradient pulses separated in time by exactly ½ TE, are used to linearly encode the phase of flow velocity vector components without changing the phase of stationary nuclei, Two-dimensional Fourier transformation of signals gave velocity density images of laminar flow in angled tubes which were in agreement with the laws of vector addition. These Velocity profile images provide a quantitative method for the investigation of fluid dynamics and hemodynamics.© 1985 Academic Press,Inc.

Evolution of the velocity distribution in galactic disks

Abstract: This paper presents a numerical investigation of the evolution of the three-dimensional velocity distribution and of the vertical density distribution in galactic disks. The physical mechanism is the scattering of stars off giant molecular clouds (GMCs) which heat up the stellar populations. A population of GMCs is embedded in the fixed potential of a constant scale height exponential disk and a nearly isothermal halo. The stars orbit in the fixed axisymmetric potential and are scattered by the GMCs which are modeled as soft particles. The equations of motion are integrated directly. Initially, the three velocity dispersions each grow as sigma(t)proportional(1+(t/tau))/sup 0.38/. Asymptotically the velocity dispersions in the plane grow as the quarter power of time while the vertical dispersion grows as sigma/sub z/(t)proportionalt/sup 0.31/. The velocity ellipsoid grows slowly rounder with time. Typically it has an axial ratio of about 0.6. The functional form and growth rate for the velocity dispersions are in fairly good agreement with published theoretical predictions based on the Fokker-Planck equation. The numerical growth rates are sufficient to explain the velocity dispersions of young stellar populations in the solar neighborhood. It is, however, necessary to postulate higher masses or larger numbers of GMCs at earlier timesmore » in order to explain the velocity dispersion of the hottest disk populations. The velocity distribution is vertically isothermal and Gaussian. The vertical density distribution is also Gaussian.« less

The stability of confined radio jets - The role of reflection modes

Abstract: The linear stability of a confined radio jet is reinvestigated. The roles of both absolute (temporal) and convected (spatial) instability are considered, and it is demonstrated that the two are related through the group velocity. The dispersion relation is analyzed asymptotically for the fundamental and reflection modes. Numerical results are presented for pinching modes. A geometrical interpretation of the modes is presented in terms of the propagation angle and is visualized by contour plots of the pressure perturbation. A confined jet theta M = arc sine (1 + sq rt eta)/M, where eta is the ratio of the internal to the external gas density and M is the Mach number of the jet. The connection between these linear modes and the cross-shaped shock patterns which are seen in laboratory jets, and the implications of these calculations for the development of large-scale features in extragalactic radio jets, are discussed.

Stationary External Rossby Waves in Vertical Shear

Abstract: The structure of stationary Rossby waves in the presence of a mean westerly zonal flow with vertical shear is examined. There is typically only one stationary vertical mode, the external mode, trapped within the troposphere. For more than one tropospheric mode to exist, we find that vertical shears must be smaller than those usually observed in extratropical latitudes. The vertical structure, horizontal wavenumber and group velocity of the external mode, and the projection onto this mode of topographic and thermal forcing are studied with continuous models (a linear shear profile as well as more realistic basic states), and a finite-differenced model with resolution and upper boundary condition similar to that used in GCMs. We point out that the rigid-lid upper boundary condition need not create artificial stationary resonances, as the artificial stationary vertical modes that are created are often horizontally evanescent. The results are presented in a form which allows one to design the equival...

Trapping‐desorption scattering of argon from Pt(111)

Abstract: Measurements of the velocity and angular distributions for trapping‐desorption scattering of argon from a clean, well characterized Pt(111) single crystal are reported. For certain experimental conditions, both the characteristic velocity and angular distributions deviate markedly from that predicted using equipartition arguments (i.e., a Maxwellian flux distribution in velocity and a cosine distribution in angle). The average kinetic energy for the flux exiting normal to the surface at 100 K is only 80% of that expected for a Maxwellian at TS. This kinetic energy deficit decreases and approaches zero as the detector is rotated away from the surface normal. The angular flux distribution is found to be broader than cosine. These results are discussed in terms of microscopic reversibility which permits estimates of the velocity dependent condensation coefficient to be obtained.

The angular velocity associated with the optical flowfield arising from motion through a rigid environment

Abstract: The instantaneous optical flowfield due to a camera moving through a rigid environment may be compatible with up to three distinct values for the angular velocity, but three is the maximum number that can occur. Each angular velocity is associated with a particular set of relative depths of points in the environment. A method of constructing all flowfields compatible with more than one value of the angular velocity is given.

The Backus—Gilbert approach to the three-dimensional structure in the upper mantle — I. Lateral variation of surface wave phase velocity with its error and resolution

Abstract: Summary. The Backus–Gilbert method is applied to obtain the phase velocity variations on a sphere from the measured phase velocity. Narrow peak kernels, with radii of about 2000 km, are obtained for almost everywhere on the sphere. The phase velocity results are thus interpreted as an average within such regions. The most trouble comes from the antipodal peak in the resolution kernel. This is evaluated as contamination and is incorporated in the error estimation. The total error, which is a root mean square of contamination from the antipodal peak and statistical error estimated from the data covariance matrix, is about 1 per cent of the phase velocity in the average earth model, which is the Preliminary Reference Earth Model (PREM). However, there is about a factor of 2 variation of errors on the sphere. Maximum variations of phase velocity are about 3–4 per cent of the phase velocity in the average earth model, and thus there still remain anomalies which exceed estimated errors. The estimated errors correspond to one standard deviation under the assumptions of uncorrelated Gaussian distribution. For high confidence interval, they show that statistically significant anomalies are scarce for the current data set. Generally, Love-wave phase velocity maps show more resolved features than Rayleigh-wave maps and we can see, in high confidence maps, fast velocities in old oceans and old continents and slow velocities in tectonically active regions like the East Pacific Rise and various back-arc regions.

Effect of rotation and relaxation times on plane waves in generalised thermo-elasticity

Abstract: The propagation of harmonically time-dependent thermo-elastic plane waves of assigned frequency in infinite rotating media is studied using the theory of thermo-elasticity recently proposed by Green and Lindsay. A more general dispersion equation is deduced to determine the effect of rotation and relaxation times on the phase velocity of the coupled waves. The solutions for the phase velocity and the attenuation coefficient are obtained for small thermo-elastic coupling by a perturbation technique. Cases of low and high frequencies are also studied to determine the effect of rotation, the relaxation parameters and thermo-elastic coupling on the phase velocity and the attenuation coefficient of the waves.

Calculation of dispersion curves and amplitude‐depth distributions of love channel waves in horizontally‐layered media*

Abstract: We present dispersion curves, and amplitude-depth distributions of the fundamental and first higher mode of Love seam waves for two characteristic seam models. The first model consists of four layers, representing a coal seam underlain by a root clay of variable thickness. The second model consists of five layers, representing coal seams containing a dirt band with variable position and thickness. The simple three-layer model is used for reference. It is shown that at higher frequencies, depending on the thickness of the root clay and the dirt band, the coal layers alone act as a wave guide, whereas at low frequencies all layers act together as a channel. Depending on the thickness, and position of the dirt band and the root clay, in the dispersion curves of the group velocity, secondary minima grow in addition to the absolute minima. Furthermore, the dispersion curves of the group velocity of the two modes can overlap. In all these cases, wave groups in addition to the Airy phase of the fundamental mode (propagating with minimum group velocity) occur on the seismograms recorded in in-seam seismic surveys, thus impeding their interpretation. Hence, we suggest the estimation of the dispersion characteristics of Love seam waves in coal seams under investigation preceding actual field surveys. All numerical calculations were performed using a fast and stable phase recursion algorithm.

Synthesis of realistic oceanic Pn wave trains

Abstract: The synthesis of realistic oceanic Pn phases was accomplished using wave number integration. Wave trains with durations of the order of 100 s following the initial compressional wave arrival were generated for a laterally homogeneous, vertically inhomogeneous oceanic lithosphere model. The excitation of these long wave trains is primarily a result of near-receiver water and sediment reverberations and does not involve scattering. A late arriving wave train with a group velocity of 1.6 km/s having an emergent onset and substantial duration, characteristic of oceanic abyssal T phases, was also generated even with phase velocities restricted to be greater than 5.5 km/s. The synthetic Pn wave train was compared to data collected in the southwest Pacific during the Ngendei Seismic Experiment. Many of the spectral characteristics associated with sediment and water reverberation observed in the synthetics were also observed in the data. First, it was found that the amplitude falloff rate of the Pn wave train is a strongly increasing function of frequency, in direct contrast to results predicted for forward scattered coda. This leads to a predominance of low frequencies late in the wave train which is easily interpreted in terms of the constructive interference of different modes of reverberation. Second, the presence of spectral peaks at frequencies associated with both sediment and water reverberations was observed. The predicted frequencies were computed using values of the water depth, sediment thickness, and sediment velocity obtained in an independent study. Strong alignment of the spectral peaks with the predicted frequencies illustrates the reverberating nature of the Pn wave train. The presence of substantial power in excess of 15 Hz can be attributed to the confinement of Pn to the oceanic lithosphere. The oceanic Pn phase is thus characterized as a refraction from the lower lithosphere with multiple reverberations in the oceanic water column and sediment layer comprising the subsequent coda. Complicated oceanic lithosphere models are not needed to explain the gross characteristics of Pn propagation.

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.

Fall Velocity of Particles in Oscillating Flow

Abstract: The paper presents results of harmonic analysis in studying particle motion in oscillating flows. An approximate equation is derived to solve the zeroth harmonic equation, which governs the effective fall velocity ν¯s, of particles in oscillating flows. The equation reveals that the drag force on the particles is significantly modified by the instantaneous relative velocity between particles and fluids. Three major factors that govern the variation of ν¯s (as compared to the terminal velocity in still water are the terminal velocity Reynolds number, the phase lag, and the velocity amplitudes of the flow and particle oscillations. The dimensionless equation is given. Applying to the sediment suspension under wave action, the analysis suggests that an enhancement of suspension should occur.

Rossby waves in opposing currents

Abstract: A barotropic Rossby wave incident to a region of increasing mean flow velocity opposing the wave group velocity undergoes a reversal of direction at a stopping point where the mean flow velocity and local wave group velocities are equal and opposite. Incident wave amplitude increases approaching this stopping point, which may be referred to as a group velocity critical layer, but eventually suffers a decrease along its trajectory so that the reflected wave amplitude and energy tend to zero on approach to a phase velocity critical layer located where the opposing flow vanishes. Some applications of this process to observations of synoptic scale Rossby waves are suggested and an example of the interaction of an incident wave with a barotropic model of the Hadley circulation is presented to illustrate these ideas.

The whistler mode in a Vlasov plasma

Abstract: In this study, properties of small-amplitude parallel and oblique whistler-mode waves are investigated for a wide range of plasma parameters by numerically solving the full electromagnetic Vlasov-dispersion equation To investigate the cold-plasma and electrostatic approximations for the whistler mode, the results are compared with results obtained using these descriptions For large wavelengths, the cold-plasma description is often accurate, while for short wavelengths and sufficiently oblique propagation, the electrostatic description is often accurate The study demonstrates that in a Vlasov plasma the whistler mode near resonance has a group velocity more nearly parallel to the magnetic field than that predicted by cold-plasma theory

Upper crustal shear velocity models from higher mode Rayleigh wave dispersion in Scotland

Abstract: Summary. Group velocities for first and second higher mode Rayleigh waves, in the frequency range 0.8-4.8 fk, generated from a local earthquake of magnitude 3.7 ML in western Scotland, are measured at stations along the 1974 LISPB line. These provide detailed information about the crustal structure west of the line. The data divide the region into seven apparently homogeneous provinces. Averaged higher mode velocity dispersion curves for each province are analysed simultaneously using a linearized inversion technique, yielding regionalized shear velocity profiles down to a depth of 17 km into the upper crust. Shear wave velocity is between 3.0 and 3.4 km s-' in the upper 3, km, with a slow increase to around 3.8 km s-'. P-wave models computed using these results agree with profiles from the LISPB and LUST refraction experiments.

Altitude dependence of vertical velocity spectra observed by VHF radar

Abstract: Vertical velocity data observed by SOUSY VHF radar from May 29 to June 2, 1978, are systematically analyzed. The altitude dependences of frequency spectra and wave number spectra are presented, and their physical implications are given on the basis of existing theoretical models.

Surface acoustic waves velocity perturbation in LiNbO3 by proton exchange

Abstract: It is shown that the exchange of Li+ ions in LiNbO3 by protons leads to a large decrease of the (group) velocity of surface acoustic waves propagating in the x-direction on Y- and Z-cut samples. Changes up to about 20% were measured at a frequency of 180 MHz. This effect can be used to construct strip waveguides for surface acoustic waves.

The group velocity of some numerical schemes

Abstract: The performances of various numerical schemes used to model hyperbolic/parabolic equations have been studied by the calculation of their numerical group velocities. Numerical experiments conducted with one dimensional linear and quadratic Lagrangian finite elements with a Crank-Nicolson finite differencing in time confirm the results of the analysis. The group velocity analysis supplements the well-known amplitude and phase portraits introduced by Leendertse1 and helps explain the occurrence and behaviour of numerical oscillations in both finite difference and finite element schemes.

Anisotropic propagation of P- and S-waves in the western Pacific lithosphere

Abstract: Summary Apparent velocities for oceanic P and S phases from NW circum-Pacific earthquakes recorded on an ocean bottom hydrophone array near Wake Island vary with azimuth of approach. The apparent velocity data from events in the Mariana Islands are fast, whereas velocities of events between the Izu-Bonin Islands and the Kurils are slower. For data showing slow apparent velocities, the path average group velocity exceeds the local apparent velocity. The azimuthal variation of oceanic P and S apparent velocity is consistent with azimuthal anisotropy, and the slow direction of propagation is nearly parallel to the strike of local magnetic lineations. Propagation paths that parallel the local magnetic lineations near the OBH array are more perpendicular to lineations in the region of the NW Pacific basin where the paths originate. The observation of path group velocity faster than local apparent velocity for oceanic P and S is qualitatively consistent with a re-orientation of anisotropy as manifested in the magnetic lineations along the propagation path between source and receiver. Results suggest that the western Pacific lithosphere is azimuthally anisotropic for P- and S-wave propagation.

On the velocity relaxation of a Rayleigh gas: III. The relaxation of the heavy-particle velocity averages☆

Abstract: The relaxation of the most important velocity averages of the heavy component of a Rayleigh gas is considered. The relaxation process is studied first exactly in the Maxwell model, and, subsequently, by using the approximate equations following from the usual kinetic equation, in the Rayleigh limit. In some cases non-negligible discrepancies appear between the exact and the approximate results found for a Rayleigh gas in which a heavy-particle-light-particle Maxwellian interaction takes place. In particular it is shown that in certain situations the heavy-particle mean-square velocity components relax, in the approximate theory, in an unphysical way, unless an appropriate limitation on the initial heavy-particle mean velocity is imposed.

Sound propagation in the rest atmosphere with linear sound velocity profile

Abstract: Sound propagation is considered in the rest atmosphere where the sound velocity varies linearly with height. With the results of the ray theory of refraction being introduced to the asymptotic solution of spherical wave propagating over a locally reacting ground surface, the approximated solution of the sound field is obtained. The results of calculation by this theory explains the measurements satisfactorily, as a result quantitative prediction of excess attenuation is available.