Showing papers on "Group velocity published in 1973"

Spectral transfer of scalar and velocity fields in heated-grid turbulence

Abstract: For locally isotropic, homogeneous fluid turbulence, a digital Fourier analysis method of measuring directly the net scalar and velocity spectral transfer Tn(k) of scalar and kinetic energy to a pa;rticular wavenumber from all other wave-numbers is described and applied to heated-grid turbulence. The technique uses the imaginary part of a particular cross-spectrum to obtain the one-dimensional net spectral transfer function Ln(k1) of velocity and scalar turbulence, and is a refinement of that used previously by Van Atta & Chen for measuring the velocity kinetic energy transfer.The detailed spectral transfer Tn(k, k′) from one wavenumber to any other is related to the imaginary part of a particular three-dimensional bispectrum. Tn(k, k′) can be, in principle, computed from a particular two-dimensional triple correlation. Unlike Tn(k), which can be obtained from Ln(k1), Tn(k, k′) cannot be determined from the measurable one-dimensional bippectrum B1, n, n (k1, k1′) nor the one-dimensional transfer spectrum Ln(k1, k1′).The measured net transfer spectra Tn(k) have been used to determine the extent of validity for heated-grid turbulence of the dynamical equations for the three-dimensional power spectra of temperature and velocity in locally isotropic turbulence. The measured temperature transfer spectrum is also compared with those obtained from the power spectra of velocity and temperature by using various simple hypotheses.

Group velocity and nonlinear dispersive wave propagation

Abstract: By the use of a Hamiltonian formulation, a basic group velocity is defined as the derivative of frequency with respect to wavenumber keeping action density constant, and is shown to represent an incremental action velocity in the general nonlinear case. The stability treatment of Whitham and Lighthill is extended to several dimensions. The water-wave analysis of Whitham (1967) is extended to two space dimensions, and is shown to predict oblique-mode instabilities for kh smaller than 1.36. A treatment of Lighthill's (1965) solution in the one-dimensional elliptic case resolves the problem of the energy distribution in the solution past the critical time.

Solid earth tide and observed change in the in situ seismic velocity

Abstract: Means for the continuous monitoring of seismic phase velocity to precision finer than one part in 104 have been used to detect in situ periodic velocity variations apparently related to solid earth tides. The magnitude of the velocity change implies that the elastic moduli of crustal rock are much more stress sensitive in situ at shallow depths than in laboratory tests on small rock samples.

Topographic Rossby waves in a rough-bottomed ocean

Abstract: The object is to predict the nature of small-amplitude long-period oscillations of a homogeneous rotating fluid over a ‘sea bed’ that is nowhere level Analytically, we are limited to special choices of bottom topography, such as sinusoidal corrugations or an undulating continental slope, so long as the topographic restoring effect equals or exceeds that due to planetary curvature (the beta-effect) (Very slight topographic features, on the other hand, provide weak, resonant interactions between Rossby waves)Integral properties of the equations, and computer experiments reported elsewhere, verify the following results found in the analytical models: typical frequencies of oscillation are [lsim ]fδ, where f is the Coriolis frequency and δ measures the fractional height of the bottom bumps; an initially imposed flow pattern of large scale will rapidly shrink in scale over severe roughness (even the simplest analytical model shows this rapid change in spatial structure with time); and energy propagation can be severely reduced by roughness of the medium, the energy velocity being of order fδa, where a is the horizontal topographic scale (although in an exceptional case, the sinusoidal bottom, the group velocity remains finite for vanishingly small values of a)

On the Structure of the Low Velocity Zone

Abstract: Summary Body wave observations from large nuclear explosions at the Nevada Test Site have been used to model the P-velocity and Q structure along the top of the mantle. The amplitudes of short period waves in the range 1–4 degrees and 12–35 degrees indicate substantial absorption in the low velocity zone with Qα. of the order of 50. With the source treated as a known quantity we used the amplitude ratio of short to long period motion as a criterion in modelling structure. The Cagniard-de Hoop technique is used to compute synthetic seismograms for proposed models. The model obtained has a high velocity lid above a thin pronounced low velocity layer with a small positive gradient existing to depths of 220 km. The shadow zone boundary occurs near 12 degrees.

On the Nonlinear Schrodinger Equation for Langmuir Waves

Abstract: A direct derivation of the nonlinear schrodinger equation for Langmuir waves is presented, based upon the nonlinear wave packet ansatz of Karpman and Krushkal. Both fluid and Vlasov equation formulations are used. The results obtained are essentially equivalent to those found earlier by Taniuti, et al. using reductive perturbation theory, including the importance of wave particle resonances at the group velocity for the long time behavior of the amplitude of modulated waves. Separating the wave packet considerations from the calculation of the nonlinear frequency shift makes it possible to attack the latter with whatever method facilitates the analysis of that part of the problem. In addition, certain ambiguities concerning singularities in velocity integrations are resolved, and the connection with a well-posed initial value problem is made somewhat clearer. This method can be used equally well for other waves, and may be of help particularly in situations where it is not clear, a priori, what scaling to...

Dispersion Curves for the Generalized Bernstein Modes

Abstract: Dispersion curves are plotted for the extraordinary branch of the electron- and ion-cyclotron harmonic waves propagating perpendicularly to the static magnetic field in a non-relativistic, hot Maxwellian plasma, without invoking the electrostatic approximation. It is found that, except in the vicinity of the cyclotron harmonics and the hybrid resonances, either the cold-plasma or the electrostatic approximation are accurate representations of the exact solution. The hybrid resonances of the cold-plasma model become monotonically shrinking regions of low group velocity as the temperature is increased, till all discernible evidence of these resonances disappears as the parameters corresponding to the thermonuclear plasmas are approached.

Mean motions and impulse of a guided internal gravity wave packet

Abstract: Second-order mean fields of motion and density are calculated for the two-dimensional problem of an internal gravity wave packet (the waves are predominantly of a single frequency o and wavenumber k ) propagating as a wave-guide mode in an inviscid, diffusionless Boussinesq fluid of constant buoyancy frequency N , confined between horizontal boundaries. (The same mathematical analysis applies to the formally identical problem for inertia waves in a homogeneous rotating fluid.) To leading order the mean motions turn out to be zero outside the wave packet, which consequently possesses a well-defined fluid impulse [Iscr ]. This is directed horizontally, and is given in magnitude and sense by \[ {\cal I} = \alpha{\cal M};\quad\alpha = \frac{2c_{\rm g}(c-c_{\rm g})(c+2c_{\rm g})}{c^3-4c^3_{\rm g}}. \] Here [Mscr ] is the so-called ‘wave momentum’, defined as wave energy divided by horizontal phase velocity c ≡ ω/ k , and c g = c ( N 2 –ω 2 )/ N 2 , the group velocity. If the wave packet is supposed generated by a horizontally towed obstacle, [Mscr ] appears as the total fluid impulse, but of this a portion [Mscr ]-[Iscr ] in general propagates independently away from the wave packet in the form of long waves. When the wave packet itself is totally reflected by a vertical barrier immersed in the fluid, the time-integrated horizontal force on the barrier equals 2 [Iscr ] (and not 2 [Mscr ] as might have been expected from a naive analogy with the radiation pressure of electromagnetic waves.)

Ion streaming instabilities with application to collisionless shock wave structure

Abstract: The electromagnetic dispersion relation for two counterstreaming ion beams of arbitrary relative strength flowing parallel to a dc magnetic field is derived. The beams flow through a stationary electron background and the dispersion relation in the fluid approximation is unaffected by the electron thermal pressure. The dispersion relation is solved with a zero net current condition applied and the regions of instability in the k-U space (U is the relative velocity between the two ion beams) are presented. The parameters are then chosen to be applicable for parallel shocks. It was found that unstable waves with zero group velocity in the shock frame can exist near the leading edge of the shock for upstream Alfven Mach numbers greater than 5.5. It is suggested that this mechanism could generate sufficient turbulence within the shock layer to scatter the incoming ions and create the required dissipation for intermediate strength shocks.

Graded-index planar dielectric waveguides

Abstract: Properties of planar dielectric waveguides having a diffusion-induced index of refraction distribution are investigated. It is found that the spatial distribution of modes, group velocity, and mode spectrum of these guides differed qualitatively from the corresponding properties found in a slab waveguide. These results were experimentally verified by measuring the mode spectrum of a dielectric waveguide having an assumed complimentary error-function distribution of refractive index.

Propagation of sound waves in a rock undergoing phase transformations

Abstract: The velocity of compressional waves in a limestone is determined up to 25 kb. Two phase transitions occur in this range of pressure. The first (at about 15 kb) is associated with a pronounced and continuous decrease in velocity and a marked increase in attenuation; the second (at 23 kb) is associated with a discontinuous jump in velocity and no appreciable change in attenuation. The velocity of shear waves is determined up to 15 kb; a decrease in velocity similar to that in the P velocity appears at about this pressure. Poisson's ratio computed from the velocity data drops from 0.29 at 13 kb to 0.19 at 15 kb. A detailed study of strain up to 21.5 kb reveals no discontinuous change in volume and suggests that on a macroscopic scale the first transition is a high-order phase transition. Using data from the velocity measurement and the strain measurement, we estimated the characteristic time for the first transition to be about 0.05 μsec. Not enough data are available to estimate the characteristic time for the second transition, but it must be very much longer. Inside the earth a phase transition with a characteristic time of about or less than 0.1–1 sec may affect the propagation of seismic waves in much the same way as the first calcite transition affects the propagation of the ultrasonic waves and thus result in a pronounced decrease in velocity and a marked increase in attenuation. The decrease in Poisson's ratio may serve as a criterion for differentiating phase transitions from other possible causes for low-velocity layers.

An Evaluation of the Heat Pulse Anemometer for Velocity Measurement in Inhomogeneous Turbulent Flow

Abstract: A velocity measuring probe that creates a train of heat pulses at one point in the flow and detects their arrival at a sensing wire a short distance downstream has been developed for the measurement of turbulent flows of unknown composition. In such a turbulent flow the detected pulses are highly disturbed, but reconstruction of a mean pulse, by digital computer, from several hundred pulses enables calculation of a mean velocity and a velocity fluctuation level. To illustrate the application of this technique, velocity profiles were measured in inhomogeneous turbulent jets over a wide range of jet ambient density ratios.

Ultrasonic Measurement of Phase and Group Velocity Using Continuous Wave Transmission Techniques

Abstract: : AMMRCCTR-73-2(*composite materials, nondestructive testing), (*halocarbon plastics, ultrasonic radiation), test methods, test equipment, propagation, velocity, attenuationphase, velocity, group velocity, tetrafluoroethylene resins, *ultrasonic testsPhase and group velocities V and U, respectively, were measured in the 100:1 frequency range 50 kHz to 5 MHz using longitudinal and shear ultra-sonic continuous waves in teflon and in a dispersive three-dimensional reinforced composite. A new transmission approach was developed which utilized broadband transducers and a pair of wedges to obtain V BY A DIFFERENTIAL PATH, FIXED FREQUENCY TECHNIQUE, AND TO OBTAIN U by fixed-path, differential frequency technique. The path or frequency was incremented to fit additional whole wavelengths in the path, as indicated by 2 pi phase shifts in a Lissajous pattern. Cross-checks between U AND V confirmed the validity of the approach at least for the two materials investigated. (Author-PL)

Effect of collisions on the random electron density fluctuations in a plasma

Abstract: The random fluctuation spectrum of the electron density is calculated by orbital statistics for arbitrary electron velocity distributions, and for a velocity dependent collision frequency nu . It is shown that collisions produce two effects: spectral broadening due to phase interruption, and spectral narrowing due to a reduction of the forward velocity by dynamical friction. For a Maxwellian velocity distribution all results are expressed in terms of the error function of complex argument and, for constant nu , they are practically equivalent to results obtained earlier from the autocorrelation function of a Brownian particle.

Dispersion and attenuation of superthermal "monochromatic" phonons in He II

Abstract: The propagation of phonons in He II at 0.1 K, in the frequency range (2 to 9)×10 10 Hz, has been studied using superconducting Al-film generators. Such superthermal waves (hω>>kT) are shown to be long-lived propagating excitations in the liquid and to have negligible dispersion (group velocity varies by less than 0.5%). These measurements reveal that the current theories of phonon lifetimes in He II are inadequate.

High frequency edge waves on an exponential shelf

Abstract: The theory is presented for high frequency edge waves on a convex exponential profile, having zero depth at the coastline. Dispersion relations are found in terms of the longshore wave number. Certain bounds are determined for the frequency of the waves, in particular, the high frequency waves have a lower frequency bound which is expressed in terms of the order of the wave. The group velocity of the high frequency waves attains a maximum value but tends to zero at very high and very low longshore wave numbers. The group velocity is shown to be less than half the phase velocity and to always be less than a critical velocity which is a function of the shelf parameters. This critical velocity is about 26 m/s for the shelf off Sydney.

Lower-Hybrid-Resonance Heating of a Plasma in a Parallel-Plate Waveguide

Abstract: Wave propagation in a parallel-plate metallic waveguide partially filled with an inhomogeneous, anisotropic plasma column is studied as an eigenvalue problem using the complete cold-plasma dielectric tensor. Although the accessibility condition may not be met, the collisional energy absorption at the lower-hybrid resonance greatly exceeds the resistive loss at the waveguide walls resulting in a very high plasma heating efficiency. The heating continues to be effective even for very low collision frequencies encountered in thermonuclear plasmas. Detailed numerical results for the heating efficiency, energy flux into the plasma, energy density and dissipation density in the plasma column as well as group velocity are presented. Also the effects of density profile, collision frequency, and waveguide eigenmodes are discussed.

Eddy power flow of electromagnetic waves

Abstract: The energy transport velocity of electromagnetic waves is reformulated to interpret the energy transport of non-piano waves by extending the classical concept of the stored energy flow of plane waves. The dyadic phase velocity, dyadic energy velocity, and stored energy vector are proposed. A new concept of eddy power flow is given, with which a well-known contradiction of energy transport velocity in waveguides can be solved.

Effect of the Energy Transfer from Electrons upon the Sound Wave Velocity in Weakly Ionized Plasma

Abstract: The phase velocity of sound wave is measured as a function of electron density in a weakly ionized plasma. The large increase of sound velocity density increased is observed, which cannot be explained by considering only the effect that electrons and ions are perturbed by the sound wave, which in turn modifies the sound wave. The increase of sound velocity can be explained consistently, if the increase of equilibrium temperature of neutrals due to the energy transfer from electrons by elastic collisions is taken into account and stationary temperature distribution in space is assumed to be attained in finite system. The temperature of neutrals, which has not been measured, can be estimated by the experimental conditions with the aid of the heat conduction theory.

Microwave oven having controlled wave propagating means

Abstract: A high frequency microwave energy propagation and restricting device uses a structural arrangement which propagates applied electromagnetic energy with counter-directional phase and group velocity, and the phase velocity is made to be lower or higher than the phase velocity which the electromagnetic energy is propagated. The directionalizing and restriction of the input electromagnetic energy into the device is controlled by means of an arrangement using a high-pass filter wherein the phase velocity and the group velocity of the electromagnetic waves are opposed to each other; alternatively, the device uses a low-pass filter wherein the group velocity and phase velocity of the electromagnetic waves have the same direction. The high-frequency energy propagation and restricting devices as of the present invention may be advantageously utilized and applied in microwave energy ovens or furnaces which may be of the static or the conveyor type. The device of the invention makes it possible to prevent and/or monitor loss of microwave energy from the zone in which energy is intended to be utilized to treat a workpiece or a product.