Showing papers on "Phase velocity published in 1976"

Stability of slowly diverging jet flow

Abstract: Coherent axisymmetric structures in a turbulent jet are modelled as linear instability modes of the mean velocity profile, regarded as the profile of a, fictitious laminar inviscid flow. The usual multiple-scales expansion method is used in conjunction with a family of profiles consistent with similarity laws for the initial mixing region and approximating the profiles measured by Crow & Champagne (1971), Moore (1977) and other investigators, to deal with the effects of flow divergence. The downstream growth and approach to peak amplitude of axisymmetric wave modes with prescribed real frequency is calculated numerically, and comparisons are made with various sets of experimental data. Excellent agreement is found with the wavelength measurements of Crow & Champagne. Quantities such as the amplitude gain which depend on cumulative effects are less well predicted, though the agreement is still quite tolerable in view of the facts that this simple linear model of slowly diverging flow is being applied far outside its range of strict validity and that many of the published measurements are significantly contaminated by nonlinear effects. The predictions show that substantial variations are to be expected in such quantities as the phase speed and growth rate, according to the flow signal (velocity, pressure, etc.) measured, and that these variations depend not only on the axial measurement location but also on the cross-stream position. Trends of this kind help to explain differences in, for example, the preferred Strouhal number found by investigators using hot wires or pressure probes on the centre-line, in the mixing layer or in the near field.

On the existence of surface‐wave solutions for anisotropic elastic half‐spaces with free surface

Abstract: A proof is developed that for a given direction of propagation on the free surface of a half‐infinite anisotropic crystal, a surface‐wave solution with a certain phase velocity vR

A numerical model of the air flow above water waves

Abstract: A numerical model is proposed for the flow in a deep turbulent boundary layer over water waves. The momentum equations are closed by the use of an isotropic eddy viscosity and the turbulent energy equation. For small amplitudes the results are similar to those of Townsend's (1972) linear model, but nonlinear effects become important as the ratio of wave height to wavelength increases. With uniform surface roughness zo, the predicted fractional rate of energy input per radian advance in phase, ζ, decreases slightly with increasing amplitude and is of the same order of magnitude as in Miles’ (1957, 1959) and Townsend's linear theories. If zo is allowed to vary with position along the wave, however, the fractional rate of energy input can be significantly increased for small amplitude waves. If the variation in zo is half the mean value and the maximum wave slope zak is 0.01, we find ζ ≈ 60 (ρair/ρwater) (uo/c)2, where uo is the friction velocity and c the wave phase speed. Comparison is also made with recent laboratory and field data.

Whistler wave propagation in a large magnetoplasma

Abstract: A large collisionless quiescent plasma source is developed for investigating the phase and amplitude distribution of antenna-launched whistler waves in a specified parameter regime relating wave frequency to electron cyclotron frequency. Wave dispersion is studied both by interferometer techniques with monochromatic waves and by propagation of short phase-coherent wave bursts. The wave damping mechanism is examined by propagating perfectly ducted whistler waves. The dispersion of single frequency waves and wave packets is demonstrated. Trough ducting for wave frequency to electron cyclotron frequency ratio greater than 1/2 is verified, and new eigenmodes in nonuniform plasmas at ratio values less than 1/2 are observed. It is shown that geometric effects due to ray divergence and wave refraction dominate over collisional damping.

Theory of the ubiquitous mode

Abstract: Standing modes along the magnetic field lines and with frequencies between the mean ion transit and electron bounce frequencies are driven unstable by a combination of effects including inverse Landau damping, collisional de-trapping of electrons and magnetic curvature drifts in a magnetically confined plasma. The mode phase velocity, depending on the plasma parameters and on the mode perpendicular wavelength, is either in the direction of the electron diamagnetic velocity (electron drift mode) or in the direction of the ion diamagnetic velocity (ubiquitous mode). An intermediate region exists where the mode becomes fluid-like and is driven by the magnetic curvature drift. This fluid-like instability is shown to appear for wavelengths longer than the ion gyroradius and is expected to affect significantly the rate of particle and thermal energy transport in high-temperature toroidal-confinement devices.

Array analysis of seismic surface waves: Limits and possibilities

Abstract: The dispersion of higher modes of surface waves over a region covered by an array of stations can be measured by applying a frequency-wavenumber transform to segments of the signals in these stations, centered at a number of group-velocities. Thus, at a fixed period, modes appear as separate maxima in a display of the power spectrum on a phase-velocity vs. group velocity plane.

Evaluation of Polymer Flooding in a Layered Reservoir With Crossflow, Retention, and Degradation

Abstract: Oil recovery by polymer flooding is influenced by reservoir heterogeneity not only through its effects on crossflow, but also through the dependence of polymer retention, inaccessible pore volume and polymer shear degradation on permeability A simulator is described that accounts for all of these factors, and experimental data, obtained using field and Berea cores, are included that demonstrate the permeability dependence of these factors Use is made of a standard 2-dimensional reservoir simulator with the added feature of point-tracking capability For each of the different layers, one chain of points is identified with the front of the polymer bank and another chain with the rear Retention and inaccessible pore volume can be accounted for through a factor which is the ratio of the velocity of the moving points to the wetting phase velocity (15 refs)

Interplanetary magnetic field power spectra - Mean field radial or perpendicular to radial

Abstract: A detailed frequency analysis of Pioneer-6 interplanetary magnetic field data is carried out for 5 to 15 hour periods during which the mean interplanetary field is approximately radial or perpendicular to radial. The reason why these data sets were chosen is that by making the usual assumption that the phase speed of any wave present is much less than the mean solar wind speed, the measured frequency spectra can be interpreted in terms of the wave number parallel or perpendicular to the mean field, without such additional assumptions as isotropy or the dominance of a particular mode and without measurements of velocity and density. The details of the calculation of the magnetic field power spectra, coherencies, and correlation functions are discussed, along with results obtained directly from the data (such as spectra, slopes, anisotropies, and coherencies). The results are interpreted in terms of MHD theory, and are related to work in other areas.

Solar magneto-atmospheric waves. I. An exact solution for a horizontal magnetic field

Abstract: The linearized theory of magneto-atmospheric waves (involving the combined restoring forces due to buoyancy, compressibility, and magnetic field) is developed for the case of a horizontal magnetic field. A general propagation equation is derived for adiabatic perturbations with arbitrary vertical distributions of the sound speed c, Alfven velocity v/subA/, and local density scale height H. An exact analytical solution to the propagation equation is obtained for the case of an isothermal atmosphere permeated by a uniform horizontal magnetic field, without making the usual short-wavelength assumption. This solution is applied to an idealized model of the low-corona--chromosphere transition region for comparison with observations of flare-induced coronal waves. The results show that disturbances may propagate horizontally in the low corona in a wave guide formed by the sudden density increase into the chromosphere below and by the rapidly increasing Alfven velocity with height in the corona. The group velocity of the guided wave modes is nearly independent of wavelength, so that a disturbance propagates as a compact wave packet. (AIP)

Single‐mode saturation of the bump‐on‐tail instability: Immobile ions

Abstract: A one‐dimensional collisionless electron plasma is considered with a velocity distribution of the ’’bump‐on‐tail’’ type. The ions are immobile and the eigenmodes are separated by finite periodic boundary conditions. The electron number density is increased above the neutral‐stable value by a small fractional amount Δ. A single mode moves on to the positive slope region and grows until saturated at small amplitude by nonlinear effects. The saturated amplitude, frequency shift, and modified electron distribution function are determined in terms of Δ. The solution is shown to be stable and conserves energy and momentum. All singular functions appearing in higher harmonics are identified as generalized functions, and a correction to the class 1c mode adjoint is obtained. The solution of the ’’inflection‐on‐tail’’ problem is also given.

Seasonal variation of planetary waves in the stratosphere observed by the Nimbus 5 SCR

Abstract: The structure and behaviour of planetary-scale temperature waves in the stratosphere are described by the use of observations from the Selective Chopper Radiometer on the Nimbus 5 satellite during the two years from January 1973 to December 1974. From a latitude-height diagram of monthly root-mean-square wave amplitudes, it is found that the planetary wave of wavenumber one is predominant in the upper stratosphere at middle and high latitudes throughout the year for both hemispheres. Waves of higher wavenumbers are rather weak in the summer hemisphere. Power spectral analysis of monthly r.m.s. wave amplitude for 24 months shows that the 12-month period oscillation is prominent in middle and higher latitudes, while a 6-month periodicity is observed in tropical latitudes for wavenumber one. The phase of maximum of the 6-month cycle is about one month after the equinoxes, suggesting that planetary wave activity in lower latitudes is closely related to the semiannual oscillation of the equatorial zonal current in the upper stratosphere. Further analyses are made of seasonal characteristics of ‘transient’ waves to find the relationship between the wave motion and the mean zonal wind velocity. The predominant period (or phase velocity) is determined by a power spectral analysis using the Doppler effect due to the east-west motion of waves. With wavenumber one in the upper stratosphere, a 15- to 20-day period standing oscillation is observed in wintertime, while a 10-day period westward moving wave is found in the summer hemisphere. During the spring and autumn, a standing oscillation with a period of about 3 weeks can be seen together with an 8- to 10-day period westward motion. Higher wavenumbers show eastward motion in winter and no significant periodicity is found in other seasons as the wave activity is weak. These characteristic features of transient waves are explained by the theory of critical line absorption for vertical wave propagation through the mean zonal wind.

Multi-layered substrate for a surface-acoustic-wave device

Abstract: This invention provides a multi-layered substrate for a surface-acoustic-wave device which substrate comprises a piezoelectric layer on a base, the temperature coefficient of a phase velocity of the surface-acoustic-wave in the piezoelectric layer being different from that of the base, the piezoelectric layer having a thickness less than a wavelength of the SAW. This multi-layered substrate can have a large electromechanical coupling and controlled temperature coefficient of the phase velocity.

Stability of oblique modulation on an ion‐acoustic wave

Abstract: Modulation instability is shown to be a general property of a wave in a nonlinear and dispersive medium when the modulation is allowed in the direction oblique to that of the wave phase velocity. As an example a modulation on an ion‐acoustic wave is shown to be unstable even if this wave is modulationally stable in the case of parallel or perpendicular modulation.

Radar measurements of neutral winds and temperatures in the equatorial E region

Abstract: The phase velocity of type 1 irregularities in the equatorial electrojet, which can be easily measured by radar, depends upon both the ion acoustic velocity (and hence the temperature) in the medium and the neutral wind velocity. By measuring the phase velocity at several zenith angles both of these quantities in principle can be determined. This note describes the technique and its limitations and presents a few preliminary results obtained at 50 MHz at the Jicamarca Radar Observatory in Peru. These results show E region east-west wind velocities as large as 100 m/s, temperature variations of greater than 100°K, and substantial longitudinal variations, at times, in both wind velocity and temperature.

Relativistic Electron-Beam-Generated Coherent Submillimeter Wavelength Cerenkov Radiation

Abstract: A cylindrical wave guide lined with thin dielectric layer can be used as a slow wave structure. As the dielectric filling factor becomes arbitrarily small and as the dielectric constant of the load material approaches unity the wavelength at which the phase velocity of the guide modes become less than the speed of light becomes arbitrarily short. The azimuthally symmetric TM modes of this structure will couple to an axially propagating electron stream and the resulting linearized dispersion relation has roots which correspond to exponentially growing waves. Relativistic electron beams will permit operation at millimeter wavelengths without resorting to high loss dielectric loads. The intensity of the available beams is such that high power operation can be expected. Intense relativistic electron beams propagating in structures of the type described above have already been used to make coherent sources at wavelengths in the 5mm range [1,2].

The velocity field associated with the birth of sunspots

Abstract: A velocity field is found to occur prior to the birth of sunspots or during the rapidly developing phase of new spots. Fraunhofer lines are always shifted redwards in the observed active regions which are situated at various distances from the disk center. The velocity amplitude derived from Na i D1-line, λ 5895.940, amounts to, at maximum, 1.5 km s−1 which is always a little larger than that derived from the weaker line, NI i λ 5892.883. The velocity field disappears when the spot ceases to grow. The lifetime of the velocity is, at least, 1 hr. The velocity field is interpreted in terms of the continuous downward flow in the process of formation of sunspots. Bray and Loughhead (1964) regard the disturbance in the granulation pattern accompanying the birth and growth of sunspot pores as an evidence of the existence of rising loops of magnetic flux. In view of the similarity of the phase of development of active regions and the lifetime in the observations by Bray and Loughhead and by us, we suggest that the velocity field may be a spectroscopic feature accompanying the rising magnetic loops in the photosphere and the chromosphere. We briefly discuss the observed mode of penetration of the magnetic flux to the solar surface before and after the appearance of AFS's.

Mechanisms for Coherent Scattering of Electromagnetic Waves from Relativistic Electron Beams

Abstract: In 1968, Pantell et al. [1] proposed that strong submillimeter radiation could be produced by coherent scattering of a microwave signal from a counterstreaming relativistic electron beam. The merit of this proposal is clear since it involves the conversion of incident photons at a low frequency, ω o , into an output of scattered photons at a high frequency, ω s , via the Doppler effect. Thus, according to the Manley-Rowe relationship, the ratio of output wave energy to incident wave energy can be as large as W s /W o - ω s /ω o and good device efficiency is possible. This may be contrasted to the case of optically pumped submillimeter lasers which convert high frequency photons into lower frequency photons and thus produce an output wave that is much weaker than the pump wave so that efficiency is inherently low.

Phase velocity determination of fundamental Love and Rayleigh waves

Abstract: A detailed description is given of a data analysis procedure for phase velocity determination from long period seismograms.

Two‐point turbulence measurements downstream of a heated grid

Abstract: Two‐point turbulence data from hot and cold wire anemometry are presented which describe the temperature and velocity fields downstream of a heated grid in a low speed wind tunnel. The velocity and temperature statistics are found to differ in that (a) the velocity energy spectrum has no inertial subrange while the temperature spectrum displays a significant region of −5/3 slope and (b) for lateral probe displacements the temperature coherence is larger than that of velocity. This result is surprising since both fields were generated by the same grid, and since the temperature field appears to have been passive. Phase measurements indicate that at least the lower turbulence wavenumbers move with equal convection velocities, thereby supporting Taylor’s hypothesis of quasi‐frozen pattern, but this convection velocity appears to be slightly greater than the mean fluid velocity. Cross correlations from the signals of two spatially separated probes are presented for both the velocity and temperature fields. In general, they agree with expectations derived from the theory of isotropic turbulence.

The dispersion relation for a nonlinear random gravity wave field

Abstract: The dispersion relation for a random gravity wave field is derived using the complete system of nonlinear equations. It is found that the generally accepted dispersion relation is only a first-order approximation to the mean value. The correction to this approximation is expressed in terms of the energy spectral function of the wave field. The non-zero mean deviation is proportional to the ratio of the mean Eulerian velocity at the surface and the local phase velocity. In addition to the mean deviation, there is a random scatter. The root-mean-square value of this scatter is proportional to the ratio of the root-mean-square surface velocity and the local phase velocity. As for the phase velocity, the nonzero mean deviation is equal to the mean Eulerian velocity while the root-mean-square scatter is equal to the root-mean-square surface velocity. Special cases are considered and a comparison with experimental data is also discussed.

Propagation of a coherent acoustic wave through a turbulent shear flow

Abstract: A collimated ’’monochromatic’’ acoustic wave (sinusoidal wave of 3–90 kHz) was directed across a two‐dimensional turbulent jet perpendicular to its plane of symmetry. Extensive study of the statistical properties both of the turbulent medium and of the received signal (random amplitude and phase modulation) offers physical insight into the general phenomenon of a periodic wave (pressure) scattered by random inhomogeneities (solenoidal velocity field).Subject Classification: [43]28.60.

A Cyclesonde View of Coastal Upwelling

Abstract: In August 1973, 320 vertical profiles of temperature and horizontal velocity were recorded during a 64 h period by an array of three Cyclesondes in the coastal upwelling region off Oregon. The mean interior along-shore velocity was geostrophic and a linear function of density, with a near-surface, equatorward jet at mid-shelf, and a poleward undercurrent at the shelf break. The mean cross-shelf flow was relatively weak and substantially ageostrophic; it was suggestive of a two-cell (co-rotating) circulation within the mid-shelf frontal zone and a two-cell (counter-rotating) circulation near the shelf break. The direction of the mean, near-bottom, cross-shelf flow was consistent with a bottom Ekman layer driven by the mean near-bottom alongshore flow. At mid-shelf, near-inertial motions with a vertical wavelength of 50 m, upward phase velocity, and downward group velocity persisted throughout the record. The hourly vector shears indicated a layer of persistent shear instability at the base of the ...

The Wind Drift and Wave Breaking

Abstract: When the wind blows across the water, a highly sheared current develops which extends a few millimeters into the water and amounts, at the surface, to 3–4% of the wind speed. Banner and Phillips (1974) have pointed out that the wind drift, as this thin surface current layer is called, may he sufficiently augmented by interaction with the orbital velocity field of the wave that the maximum particle speed may exceed the phase speed and the wave breaks. If a longer gravity wave is also present, the wind drift may be further augmented and the short gravity wave may break prematurely. We have examined both the basic breaking condition and the diminution (straining) of the short gravity waves by longer waves experimentally in wave tanks. We find that actual wave breaking occurs at substantially higher winds than predicted and that the diminution is substantially less at the higher winds. The observed wind speed dependence of this diminution appears to be contrary to prediction and points to direct coup...

Measurements of ion cyclotron instability characteristics in a mirror‐confined plasma

Abstract: Frequency spectrum, wavelength, and phase velocity measurements of ion cyclotron oscillations in a mirror‐confined plasma are described. The measured potential amplitudes reach, but do not exceed, the electron temperature. Other experiments in this device, not discussed here, reveal a wide range of plasma conditions where these oscillations are not detected.

Extension of the Thomson—Haskell method to non-homogeneous spherical layers

Abstract: Summary. Amplitude spectra of Rayleigh and Love waves in a layered nongravitating spherical earth have been obtained using as a source, displacement and stress discontinuities. In each layer elastic parameters and density follow specified functions of radial distance and the solutions of the equations of motion are obtained in terms of exponential functions. The Thomson-Haskell method is extended to this case. The problem reduces to simple calculations as in a plane-layered medium. Numerical results of phase and group velocities up to periods of 300 s in various earth models when compared with earlier results (obtained by numerical integration) show that the present method can be used with sufficient accuracy. The differences in phase velocity, group velocity and amplitude (also surface ellipticity in the case of Rayleigh waves) between spherical- and flat-earth models have been investigated in the range 20-300-s period and expressed in polynomials in the period.