Showing papers on "Group velocity published in 1979"

On the Euler-Lagrange transformation and the stokes' drift in the presence of oscillatory and residual currents

Abstract: It is shown that in an Eulerian velocity field consisting of a spatially varying component on which a uniform oscillatory component is superimposed, the residual mass transport velocity at a certain place is in general different from the residual Lagrangian velocity of a parcel labeled at that place. The approximation of the rigorous Euler-Lagrange transformation leading to the familiar derivation of the Stokes' drift is examined. The latter is a two-fold truncation of expansions of the former in a series of equations and a Taylor series of derivatives. The truncation of the latter series breaks down in cases of considerable spatial variability of the current velocity field, whereas the truncation of the former series may still be used if the uniform current velocity component energetically dominates the spatially varying component. It is then shown that the error introduced by substituting the local mass transport velocity for the residual Lagrangean velocity depends on the ratio of the amplitude of horizontal displacement, due to the uniform oscillatory component, to the integral length scale of the spatially varying component of the velocity field. Errors are largest if this ratio is of order 1. Such a situation may occur particularly in shallow tidal areas of complicated geometry.

Nonlinear wave packets in the Kelvin-Helmholtz instability

Abstract: The instability of two layers of immiscible inviscid and incompressible fluids in relative motion is studied with allowance for small, but finite, disturbances and for spatial as well as temporal development. By using the method of multiple scaling, a generalized formulation of the amplitude equation is obtained, applicable to both stable and marginally unstable regions of parameter space. Of principal concern is the neighbourhood of the critical point for instability, where weakly nonlinear solutions can be found for arbitrary initial conditions. Among the analytical results, it is shown that (1) the nonlinear effects can be stabilizing or destabilizing depending on the density ratio, (2) the existence of purely spatial instability depends upon the frame of reference, the density ratio, and whether the nonlinear effects are stabilizing, (3) exact nonlinear solutions of the amplitude equation exist representing modulations of permanent form travelling faster than the signal velocity of the linear equation (in particular, a solution is found that represents a solitary wave packet), and (4) the linear solution to the impulsive initial value problem has 9fronts’ which travel with the two (multiple) values of the group velocity (the packet as a whole moves with the mean of the two values). Numerical solutions of the amplitude equation (a nonlinear, unstable Klein-Gordon equation) are also presented for the case of nonlinear stabilization. These show that the development of a localized disturbance, in one or two dimensions, is highly dependent on the precise form of the initial conditions, even when the initial amplitude is very small. The exact solutions mentioned above play an important role in this development. The numerical experiments also show that the familiar uniform solution, an oscillatory function of time only, is unstable to spatial modulation if the amplitude of oscillation is large enough.

Angular velocity gradients in the solar convection zone

Abstract: We test the hypothesis that the weak influence of rotation upon solar supergranulation, resulting in fluid particles conserving their angular momentum while moving radially, is responsible for the outward decrease in angular velocity inferred from the difference between photospheric plasma and sunspot rotation rates. This test is performed using numerical integrations of a Boussinesq spherical convection model for a thin shell at small Taylor number (implying weak influence of rotation). We find that the convection does maintain an outward decrease in angular velocity, which approaches the limit implied by angular momentum conservation as the Rayleigh number or driving for convection is increased.By examining the energetics of the motion, we verify that the dominant process maintaining the calculated angular velocity profile against viscous diffusion is the inward transport of angular momentum by the convection. Axisymmetric meridional circulation plays virtually no role in this process. We further find there is no tendency for convection weakly influenced by rotation to form an equatorial acceleration. We argue from these and earlier calculations that the origin of the Sun's latitudinal gradient of angular velocity is deep in the convection zone. At these depths there may be a strong tendency for angular velocity to be constantmore » on cylinders, implying a positive radial gradient of angular velocity. The latitude gradient is transmitted to the photosphere by supergranulation which locally produces the negative radial gradient in the top layers. We suggest from the rotation of various magnetic features that the transition from negative to positive radial angular velocity gradient occurs near the bottom of the supergranule layer. We argue that angular momentum conservation in radially moving fluid particles should produce a similar angular velocity profile in compressible convecting fluid layers.« less

Picosecond Time of Flight Measurements of Excitonic Polariton in CuCl

Abstract: The group velocity of excitonic polariton in CuCl has been measured at 4.2 K using picosecond light pulses. It is derived by measuring both the time delay of light pulses and the thickness of samples. Experimental results are well explained by the dispersion relation of excitonic polariton including spatial dispersion. In addition, the translational effective mass of exciton in CuCl is directly derived, i.e. M =(2.0 ±0.1) m 0 .

A normal mode theory of acoustic Doppler effects in the oceanic waveguide

Abstract: This paper considers the problem of computing the acoustic field generated by a moving point source. In particular, the acoustic field is obtained in terms of the normal modes of a horizontally stratified ocean. The source motion is assumed to be uniform (unaccelerated), but is not restricted to a path radial to the receiver. The structure of the Fourier inversion integral is carefully analyzed and an evaluation is carried out by the method of stationary phase. The stationary phase point is explicitly computed as an expansion in powers of the ratio of the source speed to the mode group velocity. The resulting expression for the velocity potential is examined for Doppler effects for both instantaneous (modal) Doppler as well as Doppler determined by a finite bandwidth Fourier transform.

A parametric study of electron multiharmonic instabilities in the magnetosphere

Abstract: This paper presents numerical calculations of spatial growth rates of multiharmonic electron-cyclotron instabilities driven by a loss-cone energetic distribution, in the presence of colder electrons. When the cold electron density is comparable to the hot, nonconvective instability is possible in harmonic bands below or including the cold upper-hybrid frequency. When the cold electron density is larger than the hot, nonconvective instability is possible only in that band containing the cold upper-hybrid frequency. Increasing the cold electron temperature in relation to the hot eventually removes all nonconvective behavior. Convective instability is still possible above the cold upper-hybrid frequency.

Phase velocity and Q of mantle Rayleigh waves

Abstract: Summary We analysed the long-period Rayleigh waves that were generated by the Kurile Islands earthquake (1963), its largest aftershock, the Alaskan (1964) and the Tokachi-oki (1968) earthquakes. A deconvolution technique has been successfully applied to calculate the phase velocity and Q. We found significant regional differences in Rayleigh wave Qs which are closely correlated with regional variations in phase velocity and obtained pure-path phase velocities and Q for five tectonic provinces. The Rayleigh waves suffer small attenuation along the shield region where the phase velocity is high and large attenuation over the tectonically active regions where the phase velocity is low. Applying the Q-correction to the pure-path phase velocities the regional differences in phase velocity are considerably reduced. Studies of the frequency dependence of Q by the broad-band measurements of body waves are required in order to interpret correctly surface wave dispersion and free oscillation periods. Although the Q of the model MM8 (Anderson, Ben-Menahem & Archambeau) is appropriate as an average representation of the observed Q in the period range from 200 to 300s, the differences for different great-circle paths are very large and the average Q values at periods below 200 s are lower than those of MM8.

A velocity interferometer technique to determine shear‐wave particle velocity in shock‐loaded solids

Abstract: An optical technique is described which uses velocity interferometers to determine the large particle velocity changes associated with plane shear‐wave propagation. In this technique two velocity interferometers are used to monitor different diffracted laser beams from a surface which undergoes both longitudinal and shear motion. Fringes produced in the interferometer are proportional to a linear combination of both the longitudinal and shear components of the free‐surface velocity. The technique has been used successfully to monitor the free‐surface velocity of a Y‐cut quartz specimen impacted by an X‐cut quartz plate. Although the present shear‐wave velocity profiles are limited to an accuracy of ±10%, the accuracy can be easily increased by an order of magnitude by using longer delay legs and larger diffraction angles.

Velocity distributions in the flow of solid particles in an inclined open channel

Abstract: The velocity of solid particles flowing in an inclined open channel of which the bottom plate was covered with very rough sandpaper was measured for three kinds of particle. Except for the region near the bottom plate, the velocity distribution normal to the bottom plate appeared to be linear. The velocity gradient in that region was almost independent of the thickness of the particle layer and increased as the slope of the channel became steep. These observed velocity distributions were analyzed based on the variational principle, by which the velocity distribution could be obtained as the solution which minimized a certain integral consisting of several energy terms. It was found that such analysis could explain the main feature of the particle flow in an inclined channel, and the following relation between stress and rate of deformation was obtained. τyz=kτy-kμy(dvz/dy) It was also found that the critical inclination angle of the channel, which was anticipated by the analysis, corresponded to the angle of repose.

Oceanic upper crustal structure from variable angle seismic reflection – refraction profiles

Abstract: Summary. The travel times of reflected and refracted arrivals observed on variable angle seismic profiles can be inverted to produce a first approximation to the variation of seismic velocity with depth. A method is discussed for deducing the interval velocity above a reflector by finding the best match between the observed variable angle reflection travel times and those derived by ray tracing through a series of trial models. Further constraints can be placed on the rate of change of velocity with depth by consideration of the amplitudes of both reflections and refractions. Synthetic seismograms calculated by the reflectivity method demonstrate that different kinds of velocity structure in the oceanic volcanic basement layer produce characteristically different variations of amplitude with range. In particular, the exact nature of the shear wave velocity transition at the top of the basement has a marked effect on the compressional wave reflection amplitudes. Pre-critical reflection amplitudes are seen to be generally more sensitive to the velocity structure at the sediment-basement interface than are post-critical reflections, whilst head wave amplitudes are strongly dependent on the velocity gradient in the upper part of the basement. The second part of the paper presents an analysis of variable angle seismic profiles obtained over the Madeira abyssal plain in the North Atlantic, using the travel time and amplitude interpretation techniques discussed earlier. It is concluded that the velocity structure of this area of typical oceanic crust comprises a stack of distinct layers within each of which the velocity increases smoothly with depth. An upper basement layer 600 to 700 m thick is a remnant of an originally lower velocity seismic layer 2A which is found on younger crust. Beneath this upper layer the compressional wave velocity increases with a gradient of less than 0.7/s to the base of seismic layer 2. The velocity gradient within the underlying seismic layer 3 is constrained by refraction amplitudes as less than 0.1/s.

Lithospheric structure of the Walvis Ridge from Rayleigh wave dispersion

Abstract: Rayleigh wave group velocity dispersion has been used to study the lithospheric structure along the Walvis Ridge and for a nearby South Atlantic path. Group velocity is anomalously low in the period range of 15--50 s for both surface wave paths. Results of a formal inversion for the ridge suggest crustal thickening to 12.5 km and anomalously low mantle shear velocity of 4.25--4.35 km/s to depths of 45 km. Lowering the density in this region during inversion does not raise the shear velocity to the oceanic norm. A nearby off-ridge path that covers the Cape Basin and part of the western Walvis Ridge shows no sign of thickened crust. No significant differences from normal oceanic lithosphere exist below 50 km, and no signs of thinning of the lithosphere under the Walvis Ridge are apparent. Other geophysical data rule out a thermal cause for the low mantle shear velocity, and it is likely that unusual mantle composition is responsible.

Shear velocity structure in the Eastern United States from the inversion of surface-wave group and phase velocities

Abstract: : Single-station group velocities at periods between 4 and 70 seconds and single-station phase velocities at periods between 10 and 50 seconds are obtained for a broad region of the eastern United States for both Rayleigh and Love waves. These data were obtained by the single-station method using earthquakes with known fault-plane solutions in the central United States. The group velocity data are combined with earlier acquired attenuation data to yield Q values for Rayleigh and Love waves in the eastern United States. Inversions of the dispersion curves for shear-velocity models of the crust and upper mantle indicate that all of the data can be explained satisfactorily by a single model which is isotropic in its elastic properties. This model includes a surface layer of low-velocity sediments, and is characterized by upper crustal shear- wave velocities which increase from 3.4 to 3.7 km/sec with increasing depth, by lower crustal shear-wave velocities between 4.0 and 3.8 km/sec, and by an upper- most mantle shear-wave velocity of about 4.8 km/sec. The fundamental-mode data of this study do not require a low-velocity zone in either the crust or upper mantle. Higher-mode velocities and wave forms, although having potentially greater resolving power than the fundamental-mode data, were too inconsistent to contribute to the elucidation of detailed features of the crust-upper mantle model.

Computer Calculations of Traveling-Wave Periodic Structure Properties

Abstract: The versatility and accuracy of programs such as LALA and specially SUPERFISH to calculate the rf properties of standing-wave cavities for linacs and storage rings is by now well established. Such rf properties include the resonant frequency, the phase shift per periodic length, the E- and H-field configurations, the shunt impedance per unit length and Q. While other programs such as TWAP have existed for some time for traveling-wave structures, the wide availability of SUPERFISH makes it desirable to extend the use of this program to traveling-wave structures as well. That is the purpose of this paper. In the process of showing how the conversion from standing waves to traveling waves can be accomplished and how the group velocity can be calculated, the paper also attempts to clear up some of the common ambiguities between the properties of these two types of waves. Good agreement is found between calculated results and experimental values obtained earlier.

Light Scattering and Pair-Correlation Functions in Fluids with Nonuniform Velocity Fields

Abstract: We study fluctuations in a fluid with a stationary, linear shear. We find that the pair-correlation function gains a long-ranged part. The Brillouin components of scattered light are enhanced or reduced compared to equilibrium depending on the scattering angle. The Landau-Placzek ratio no longer holds and the total scattering intensity is $k$ dependent. We suggest a simple light-scattering experiment to test our predictions. The new features are explained by the differential attenuation of sound modes.

Particle velocity distribution measurement by holography.

Abstract: A number of particle fields having a 1-D velocity distribution are recorded holographically by double exposure. The reconstructed fringe patterns in the Fraunhofer plane are sampled on-line using a linear photodiode array, and the computed velocity distributions are compared with the input functions. For wider distributions a velocity-shifting technique using a translating photographic plate has been applied to two liquid spray systems.

Multiradar Tracking System Using Radial Velocity Measurements

Abstract: Multiradar tracking using both position and radial velocity measurements is discussed. The measurement of two or more different radial velocity components allows the calculation of rectangular velocity components. The measurement noise of the velocity components is filtered using a Kalman filter in the same way as the Cartesian position components. Before the conversion of velocity components from radial to Cartesian coordinates, the radial velocities are aligned on a time scale to account for the time shift of the radar measurements. In order to compare multiradar tracking system performance with and without radial velocity, some simulation tests have been performed for typical paths. The simulation results show a significant improvement when radial velocity is used for tracking.

Power flow and energy distribution of magnetostatic bulk waves—In dielectric‐layered structure

Abstract: This paper presents a theoretical investigation of guided propagation of the magnetostatic bulk waves in a normally magnetized ferrite film separated from a perfect conductor by a dielectric layer. Starting from the generalized Poynting theorem for dispersive media, the expressions for time‐averaged power flow and energy density have been obtained in the magnetostatic approximation. The velocity of time‐averaged energy flow has been shown to be equal to the group velocity, which establishes the consistency of magnetostatic approximation from the energy point of view.

Waves in parallel or swirling stratified shear flows

Abstract: The dispersion relations for infinitesimal internal gravity waves (A) and axisymmetric waves in swirling streams (B) are considered. In both cases the mainstream may be sheared and density stratified in the transverse (vertical in case A, radial in case B) direction. The following results are proved for either case: If the maximum speed W max (or minimum speed W min) (in a meridian plane in case B) of the mainstream occurs at an interior point in the fluid, then the phase speed of any mode takes all values from the W max (or W min) to +∞ ( —∞) as the overall Richardson number λ2 varies from 0 to ∞. If W max(W min) is attained at a boundary point with finite rate of strain, there is a positive non-zero critical Richardson number below which one or both branches of the dispersion relation terminate. These results employ variational methods and correct erroneous results concerning problem B stated in Chandrasekhar's treatise on hydrodynamic stability. Furthermore, bounds are given on the group velocity for both branches of the dispersion relation. From these bounds it is shown that in the absence of reversals of the mainstream (W min > 0) upstream propagation of wave energy is impossible whenever upstream propagation of constant phase surfaces is impossible.

Propagation Path Effects for Rayleigh and Love Waves (Surface Wave Studies of the Bering Sea and Alaska Area)

Abstract: : The area of the Bering Sea and Alaska was studied in terms of shear- velocity, density and compressional-velocity structure by applying a generalized linear inversion method to fundamental-mode Rayleigh-wave group-velocity dispersion relationships in the period range from 10 to 100 sec. Group velocity dispersion relationships in the area were obtained by applying the phase-matched filtering technique to digitally recorded surface-wave data. A new exact analytical method for the computation of Rayleigh-wave phase-velocity partial derivatives with respect to Earth parameters was formulated. With the phase- velocity partial derivatives determined, the group velocity partial derivatives were computed by use of the fast and accurate method of Rodi, and were successfully incorporated into a generalized linear inversion method. In continental Alaska, the crustal thickness is 43 +or- km, and a low velocity zone extendes from a depth of about 113 km to about 213 km. In the Bering Shelf region, the depth to the Mohorovicic discountinuity is 28 +or- 4 km, and a low velocity zone ranges in depth from about 108 km to about 213 km. In the Aleutian Basin, the thickness of the crust is 18 +or- 4 km, and a low velocity zone extends from a depth of about 60 km to about 220 km.

The influence of upper mantle discontinuities on the toroidal free oscillations of the Earth

Abstract: In the simplest approximation the high-frequency toroidal mode dispersion is simply related to the intercept time ~ p ( p ) as a function of slowness p derived from SH-wave travel times. Velocity and density gradients in the Earth introduce perturbations to this simple relation. More pronounced effects arise when the mantle contains discontinuities in elastic properties and these disrupt the regular spacing of eigenfrequencies with radial order at fixed slowness p , a ‘solotone’ effect. A simple iterative approach is introduced which enables the solotone effect to be calculated for an earth model with multiple discontinuities. At futed frequency the discontinuities give rise to a distinctive pattern with varying slowness, particularly in the group velocity behaviour. The perturbations due to the discontinuities depend on the reflection coefficients at these interfaces and so are large for modes with slownesses corresponding to turning points near the discontinuities. For mode phase velocities greater than 9 km/s the details of the solotone perturbation are dominated by beating between the effects of different discontinuities. The theoretical results are illustrated by computations for model 1066B, both directly and using the asymptotic approach. This allows an assessment of the influence of velocity gradients and upper mantle discontinuities on the dispersion. Also the sources of systematic error in Brune’s approach to determining toroidal mode dispersion are discussed and bounds on the errors estimated from the calculations.

Holographic particle velocity measurement in the Fraunhofer plane.

Abstract: Double exposure holograms of a moving particle field having a 1-D velocity distribution are produced. The Fraunhofer plane is observed on reconstruction, and it is shown that for a Gaussian velocity distribution, the fringes which modulate the diffraction pattern have spacings characteristic of the peak velocity. Known and measured peak velocities are compared, and the effect of the velocity distribution width on the fringe contrast is demonstrated.

Effect on the anatomical structure of the arterial tree on the measurement of pulse wave velocity in man

Abstract: The introduction of an individual anatomical parameter R, taking into account the different lengths of the aorta and of the iliaca-femoralis-tibialis, reduces the individual variability in the measurement of the pulse wave velocity. The dependence of pulse wave velocity on age and pressure is discussed in terms of results obtained by a multivariate analysis of experimental data.