Showing papers on "Group velocity published in 1981"
TL;DR: In this paper, the displacement height of rough-wall boundary layers is defined as the level at which the mean drag on the surface appears to act, which coincides with the average displacement thickness for the shear stress.
Abstract: The displacement height appears in the logarithmic velocity profile for rough-wall boundary layers as a reference height for the vertical co-ordinate. It is shown that this height should be regarded as the level at which the mean drag on the surface appears to act. The equations of motion then show that this also coincides with the average displacement thickness for the shear stress.A simple analytical model, experimental results and dimensional analysis are all used to indicate how the displacement height depends upon the detailed geometry of the roughness elements.
530 citations
TL;DR: In this paper, the relevance of group velocity to the behavior of finite difference models of time-dependent partial differential equations is surveyed and illustrated, and applications involve the propagation of wave packets in one and two dimensions, numerical dispersion, the behaviour of parasitic waves, and the stability analysis of initial boundary value problems.
Abstract: The relevance of group velocity to the behavior of finite difference models of time-dependent partial differential equations is surveyed and illustrated. Applications involve the propagation of wave packets in one and two dimensions, numerical dispersion, the behavior of parasitic waves, and the stability analysis of initial boundary-value problems.
477 citations
TL;DR: In this paper, the predictions of the nonlinear Schrodinger equation have been tested by passing 5.5psec optical pulses through a 70m single-mode optical fiber, and dramatic reshaping of the input pulses into flat-topped, frequency-broadened, and positively chirped 20psec output pulses with self-steepened fall times of less than 2 psec was observed.
Abstract: The predictions of the nonlinear Schrodinger equation have been tested by passing 5.5-psec optical pulses through a 70-m single-mode optical fiber. With use of a precise cross correlation technique based on pulse compressions, dramatic reshaping of the input pulses into flat-topped, frequency-broadened, and positively chirped 20-psec output pulses with self-steepened fall times of less than 2 psec was observed. The observations are in good agreement with theory.
265 citations
TL;DR: In this paper, the streamwise and perpendicular components of the velocity field were investigated, in the mid-span plane of a two-dimensional mixing layer, with a 6:1 velocity ratio.
Abstract: Using digital image processing of particle streak photography, the streamwise and perpendicular components of the velocity field were investigated, in the mid‐span plane of a two‐dimensional mixing layer, with a 6:1 velocity ratio. The Reynolds number of the flow, based on the local vorticity thickness and the velocity difference across the layer, ranged from 1360 to 2520, in the plane of observation. The significant result of this experiment was that the region of vorticity bearing fluid is confined to a small fraction of the flow. A second finding, consistent with the small regions of concentrated vorticity, was the observation of instantaneous streamwise velocity reversal, in the laboratory frame, in small regions of the flow.
94 citations
TL;DR: In this paper, the authors investigated the body force equivalents for a seismic dislocation occurring in an anisotropic source medium and study radiation patterns of seismic body waves resulting from them.
Abstract: We investigate body force equivalents for a seismic dislocation occurring in an anisotropic source medium and study radiation patterns of seismic body waves resulting from them. The point source representation of the equivalent body forces is obtained following a result of Kosevich (1962, 1965). Green9s tensor for an anisotropic medium is calculated using a far-field approximate method by Kosevich and Natsik (1964). Radiation patterns of seismic body waves are obtained by a straightforward convolution operation on the equivalent forces with the approximate Green9s tensor. The seismic dislocation occurring in an anisotropic source medium is equivalent in general to the sum of three orthogonal dipole forces with different magnitudes, for which the seismic moment tensor has a nonzero trace. Because of the third dipole force which never appears for an isotropic medium, a significant distortion of the radiation patterns occurs in a direction near the null vector. Nodal lines of P -wave radiation patterns are separated into isolated loops and/or secondary nodal lines appear. In directions where group velocity differs from the corresponding phase velocity, the effect of the medium transfer response on the polarities of body waves seems to be larger than that in other directions. The combination of the effects of source forces and medium transfer response distorts the radiation pattern.
65 citations
TL;DR: In this paper, the effect of diffraction on velocity and attenuation measurements for the case of circular, axially concentric transmitting and receiving transducers of the same radius are also presented.
Abstract: Publisher Summary This chapter describes the ultrasonic wave velocity and attenuation measurements. The measurement of the velocity and attenuation of ultrasonic waves have been the basis of evaluation of a wide variety of physical properties of gases, liquids, and solids. In some cases, the measurements have been made with great precision and accuracy. In other cases, the ready availability of the result was more important than extreme precision. A number of sources of error need to be considered if one is measuring velocity and attenuation. In the first place, error is associated with the measurement of such quantities as time and distance. The measurement of velocity involves measurement, either of the time required for the ultrasonic wave to travel a known distance or of the wavelength and frequency. An insidious source of error in velocity measurements in solids is the effect of the transducer producing the ultrasonic waves and of the bond coupling the transducer to the sample. The investigations of the effect of diffraction on velocity and attenuation measurements for the case of circular, axially concentric transmitting and receiving transducers of the same radius are also presented.
60 citations
TL;DR: In this article, the authors measured surface wave group velocities across central India using multiple-filter technique and found that the wave paths from Koyna earthquakes to Bokaro cross purely through the Peninsular Plateau.
Abstract: Surface wave group velocities across central India are measured from computer plots of frequency-time analysis using multiple-filter technique. Periods range from 5 to 56 sec for fundamental mode Rayleigh wave, 5 to 16 sec for first higher mode Rayleigh wave, and 5 to 49 sec for fundamental mode Love wave. The wave paths from Koyna earthquakes to Bokaro cross purely through the Peninsular Plateau. The group velocities for these paths are found to be similar to those of surface waves recorded at Poona from earthquake which lie to the northeast of Bokaro in sub-Himalayan regions. From this, it is concluded that the shield structure of the peninsula extends to the sub-Himalayan regions to northeast of the Peninsular Plateu with a negligible part of sedimentary layer. Group velocities of fundamental mode Rayleigh and Love waves are also obtained for the paths from Koyna earthquakes to Shillong and are found to be similar to the above-mentioned group velocities except at very low periods where group velocities are affected by the small part of each path through thick sedimentary layer of Bengal Basin. Northern limit of this basin sedimentary layer has been identified. Mean and standard deviation of observed group velocity at each period are obtained for each of Rayleigh fundamental, Rayleigh first higher, and Love fundamental modes. The group velocities closely agree with those obtained earlier for the path between New Delhi and Kodaikanal and are also found to be similar to those observed in some shield regions. Monte Carlo inversion method is applied and crust and upper mantle structure of the Indian Shield across central India is obtained. Crustal structure obtained shows a marked resemblance to the results obtained earlier through body wave study.
57 citations
TL;DR: In this paper, numerical simulations of transient equatorial waves in the quasi-biennial oscillation are presented, showing that the upper atmospheric mean flow acceleration is very sensitive to the precise magnitude and distribution of the damping mechanisms.
Abstract: Vertically propagating internal waves give rise to mean flow accelerations in an atmosphere due to the effects of wave transience resulting from compressibility and vertical group velocity feedback. Such accelerations appear to culminate in the spontaneous formation and descent of regions of strong mean wind shear. Both analytical and numerical solutions are obtained in an approximate quasi-linear model which describes this effect. The numerical solutions display mean flow accelerations due to Kelvin waves in the equatorial stratosphere. Wave absorption alters the transience mechanism in some significant respects, particularly in causing the upper atmospheric mean flow acceleration to be very sensitive to the precise magnitude and distribution of the damping mechanisms. Part II of this series discusses numerical simulations of transient equatorial waves in the quasi-biennial oscillation. These results are of sufficient qualitative interest to merit attention in this paper, and this is done with t...
57 citations
TL;DR: In this article, the mean and turbulence velocities of the jets for which strong peaks are evident were examined, and contour plots of the mean velocity fields were presented for both analog and digital analysis, allowing extensive correlations to be made.
Abstract: Turbulent jet flows from rectangular nozzles exhibit "saddle-backed" velocity profiles that are related to the upstream shaping of the nozzles. These velocity peaks are as much as 20% greater than the centerline velocity. The peaks appear to merge downstream. The present study includes examination of the mean and turbulence velocities of the jets for which strong peaks are evident. Contour plots of the mean velocity fields are presented. Outputs from two hot-wire anemometers have been subjected to both analog and digital analysis, allowing extensive correlations to be made. Coherence measurements are also presented.
54 citations
TL;DR: In this paper, a real-valued generalization of Hamilton's equations for media with moderate absorption is proposed, based on a dispersion equation with complex coefficients, on Sommerfeld-Runge's and Whitham's laws for the real parts of k, ω, on Connor and Felsen's condition for the imaginary part of k and on the expression Re (∂ ω/∂k) for the velocity of a wave packet.
Abstract: For lossless media, Hamilton's equations of geometrical optics can be derived from the dispersion equation either by the method of characteristics or by its combination with Sommerfeld-Runge's refraction law, Whitham's conservation law, and the expression ∂ω / ∂ k for the group velocity. The formal generalization to media with absorption leads to characteristics with complex space-time coordinates due to the now complex coefficients of the dispersion equation. For media with moderate absorption a real-valued generalization of Hamilton's equations is proposed. It is based on a dispersion equation with complex coefficients, on Sommerfeld-Runge's and Whitham's laws for the real parts of k, ω, on Connor and Felsen's condition for the imaginary part of k, and on the expression Re (∂ ω/∂k) for the velocity of a wave packet. These real-valued equations have been shown to hold in homogeneous media with moderate absorption.
51 citations
TL;DR: In this paper, it was shown that the measured curves of area vs. distance are governed by a combination of friction and gravity, and longitudinal bending and tension forces, which produce standing waves of area superposed upon the mean gradients.
Abstract: Theories are developed to explain the experimental observations of steady, supercritical flow in compliant, partially collapsed tubes, presented in the companion paper (part 1). It is shown that the measured curves of area vs . distance are governed by a combination of (i) friction and gravity, which produce mean gradients of area, and (ii) longitudinal bending and tension forces, which produce standing waves of area superposed upon the mean gradients. The experiments confirm the one-dimensional theory for the mean gradients: (i) in the absence of gravity, friction causes a pressure rise and a positive mean gradient of area; (ii) a downward slope can cancel gravity and lead asymptotically to a uniform state having zero gradients of pressure and area. The inviscid dispersion relationship for area waves due to longitudinal bending and tension is developed, based on a simple, approximate model for the mechanics of the tube. The phase velocity increases as the wavelength decreases, hence the group velocity exceeds the phase velocity. Consequently, in steady flows that are supercritical with respect to the infinite-wavelength phase velocity, energy can propagate upstream and standing waves of area may appear. In the experiments of part 1, longitudinal tension predominated over longitudinal bending. The measured wavelengths of standing waves were found to be in general agreement with the dispersion relationship for tension-induced area waves. The observed streamwise growth of standing area waves is interpreted physically as the attenuation of waves radiating upstream from a source of disturbance such as a shock-like rapid increase of area. The rate of wave attenuation indicates that the skin-friction coefficient has a large out-of-phase oscillatory component. The observed steepness of shock transitions agrees with an approximate theory based on treating the forward portion of the shock as the rearward part of the standing wave train that the shock drives upstream.
01 Jan 1981
TL;DR: In this paper, a turbulent hydrogen diffusion flame in a co-flowing stream with accelerating and decelerating pressure gradients is studied, where the light-scatter signal obtained from the seeded nozzle fluid is used as a measure of hydrogen element concentration, and is processed to derive records of density and mixture fraction which are correlated in digitized form with the simultaneously recorded streamwise velocity component.
Abstract: Simultaneous measurements of scattered light intensity and axial velocity have been made in a turbulent hydrogen diffusion flame in a co-flowing stream with accelerating and decelerating pressure gradients. The light-scatter signal obtained from the seeded nozzle fluid is used as a measure of hydrogen element concentration, and is processed to derive records of density and mixture fraction which are correlated in digitized form with the simultaneously recorded streamwise velocity component. Results reported here include the mean and r.m.s. fluctuation of the streamwise velocity component and the density and correlations of the streamwise velocity component with the mixture fraction and the density as well as other correlations and Favre or density weighted averages. It is shown that the density velocity correlation is only large enough to make a few percent difference between the Favre and conventional mean velocities but that such correlations are important in the determination of the excess momentum flux. Correlations between velocity and mixture fraction are comparable with those found in isothermal flow but change sign where the excess velocity changes sign. The correlation between density and velocity shows similar behaviour and is shown to have a significant effect on the turbulent kinetic energy balance.
TL;DR: In this paper, the time of flight of polaritons in the forbidden, mixed and allowed modes of propagation was studied in the presence of excited states of the A exciton and the n = 1 state of the B exciton.
10 Jun 1981
TL;DR: In this paper, the authors proposed tuning the source to the wavelength where the group velocity dispersion passes through zero to avoid pulse broadening in low-loss silica glass fibers, where the effect of the inevitable dispersion, acting alone, is always to broaden such pulses.
Abstract: The propagation of ultrashort (picosecond) pulses in optical fibers is a matter of considerable contemporary interest, both to communications and to pure science. The effect of the inevitable dispersion, acting alone, is always to broaden such pulses. Thus at first there would appear to be only one way to avoid pulse broadening: to tune the source to the wavelength (for low-loss silica glass fibers, typically in the neighborhood of 1.3 µm) where the (group velocity) dispersion passes through zero.
TL;DR: In this article, the propagation of zero-sound pulses near a collective-mode attenuation peak in /sup 3/He-B was observed and it was shown that above a threshold input level, the sound pulse propagates as a soliton.
Abstract: We report observations of nonlinear phenomena in the propagation of zero-sound pulses near a collective-mode attenuation peak in /sup 3/He-B. These include saturation of the sound absorption, amplitude dependence of the group velocity, and pulse breadup. Our data show effects similar to those observed in nonlinear optical systems. We suggest that above a threshold input level, the sound pulse propagates as a soliton.
TL;DR: In this article, an analysis is presented which describes the slow-time evolution of an internal gravity wave in an arbitrarily specified stratification, and a coupled pair of nonlinear partial differential equations governing the evolution of both the short-wave and the long-wave modes.
Abstract: An analysis is presented which describes the slow-time evolution of an internal gravity wave in an arbitrarily specified stratification. The weakly nonlinear description of a single-wave mode, governed by the nonlinear Schrodinger equation, breaks down when certain resonant conditions are satisfied. One such condition occurs when the group velocity of the wavetrain is equal to the phase velocity of a higher-mode long wave of the system. The resonant interaction occurs on a faster time scale and is described by a coupled pair of nonlinear partial differential equations governing the evolution of both the short-wave and the long-wave modes. This long-wave/short-wave interaction is pursued further in an experimental investigation by measuring the modal interchange of energy between two internal waves of disparate length and time scales. The resulting data are compared with numerical solutions of the long-wave/short-wave resonant interaction equations. In general, the agreement between the theory and the experiment is reasonably good in the range of operating conditions for which the theory is valid.
01 Jan 1981
TL;DR: In this article, group velocity data in the region of the Ionian Sea have been inverted using the Hedgehog procedure, and the range of acceptable solutions shows that only a crustal thickness exceeding 30 km is consistent with the data.
Abstract: Group velocity data in the region of the Ionian Sea have been inverted using the Hedgehog procedure. The range of acceptable solutions shows that only a crustal thickness exceeding 30 km is consistent with the data. Furthermore, the obtained models indicate a clearly defined velocity layering, including velocity inversions, within the crust, as well as a crust-mantle transition zone in place of a sharp Moho discontinuity.
TL;DR: In this article, a convenient and efficient numerical technique is presented for determining modal properties of an optical fiber or planar waveguide. But this technique is not suitable for single mode fibres.
Abstract: A convenient and efficient numerical technique is presented for determining modal properties of an optical fibre or planar waveguide. A simple recurrence relation, suitable for programming on only a pocket calculator, leads to parameters such as group velocity and cutoff wavelengths. The method is particularly useful for analysing single mode fibres, and an example of current interest is given.
TL;DR: In this article, a turbulent round jet diffusion flame is modeled as a convective wavelet and a probability density function, correlation, spatial scale, and convective velocity are obtained with the object of getting a better understanding of the structure of the turbulent diffusion flame.
TL;DR: In this paper, the dual wave to the de Broglie wave is introduced with a group velocity of the deBroglie Wave, and the physical consequences of the hypothesis are discussed.
TL;DR: In this article, the wave energy flux associated with wave motion due to a transient source was analyzed for a simple constant-parameter atmosphere, where the source was taken to be a transient fluctuation of the lower boundary, (modeling convective overshoot) which was located at the level τ5000=0.08 in the solar atmosphere.
Abstract: This paper deals with a rather general class of magnetoatmospheres — media for which the restoring forces of buoyancy, compressibility and magnetic tension/pressure are important in sustaining wave motion. The magnetic field has the general form (B
0(z), 0,0) and there is also an aligned shear flow (U
0(z), 0, 0) present. After discussion of the equilibrium and stability of such systems, and certain mathematical properties of a particular system (an isothermal atmosphere with uniform magnetic field, of interest in solar physics), theory is developed which enables expressions to be written down for the mechanical wave energy flux associated with wave motion due to a transient source. These analytic expressions are very general and contain contributions from the continuous and discrete frequency spectra, corresponding respectively to freely propagating and trapped (or surface) waves. These fluxes are evaluated for various ranges of magnetic field, horizontal wavenumber, characteristic source times and frequency, for a simple constant-parameter atmosphere. The source is taken to be a transient fluctuation of the lower boundary, (modelling convective overshoot) which is taken to be located at the level τ5000=0.08 in the solar atmosphere. The relative distribution of wave energy flux in the various modes is discussed in the context of solar physics parameters. The possible significance of ‘leaky’ modes arising from supergranular or other flow, for the local flux balance in the solar chromosphere is outlined.
01 Oct 1981
TL;DR: In this paper, a linearized model of the vehicle motion is used to identify and model three physical effects that influence the measurements of a freely sinking velocity profiler, and the corrected measurements are in good agreement with simultaneous velocity measurements from an instrument whose performance in the band of comparison does not depend on vehicle motion.
Abstract: For most freely sinking instruments that measure horizontal velocity, it is necessary to understand the response of the vehicle to the flow properly to interpret the measurements. Three physical effects that influence the measurements are identified and modeled. First, the vehicle tends to follow the low vertical wave number variability in the velocity profile. A linearized model of the vehicle motion shows that the horizontal velocity of the vehicle is the low pass of the true current profile, while relative velocity measured by a velocity sensor on the vehicle is the high pass. The filter has a single pole at a wave number that does not depend on the sinking rate. Second, when there is a horizontal velocity sensor on the vehicle and the sensor is displaced from the vehicle's center of mass, there is a phase difference between the measured profile and the vehicle motion that is accounted for. This phase difference significantly increases the apparent energy in low vertical wave number velocity fluctuations. The third effect arises when the drag on the vehicle is distributed along the length of the vehicle and cannot be modeled adequately as a point force. The effect of the distributed drag force is only significant for high vertical wave number variations. The above results are applied in correcting measurements from a freely sinking velocity profiler. The corrected measurements are in good agreement with simultaneous velocity measurements from an instrument whose performance in the band of comparison does not depend on the vehicle motion.
TL;DR: In this paper, a complex Fourier analysis is made of simulated and observed stationary waves to explain why the Aleutian high stands out in the winter stratosphere, and it is found that in the troposphere the envelope of the time mean geopotential height consisting of wavenumbers 1 ∼ 3 attains its major and minor maxima in the Pacific and Atlantic, respectively.
Abstract: In order to explain why the Aleutian high stands out in the winter stratosphere, a complex Fourier analysis is made of simulated and observed stationary waves. It is found that in the troposphere the envelope of the time mean geopotential height consisting of wavenumbers 1 ∼ 3 attains its major and minor maxima in the Pacific and Atlantic, respectively. The major maximum is dominated by wavenumbers 1 ∼ 2 and shifts eastward with height in the stratosphere in the approximate direction of the group velocity and strengthens the Aleutian high. The minor maximum is dominated by wavenumber 3 and is confined in the troposphere.
TL;DR: In this article, a parallel intense photon (laser, microwave, etc.) beams?0,k0 and?1,k1 shone on a plasma with frequency separation equal to the plasma frequency?p is capable of accelerating plasma electrons to high energies in large flux.
Abstract: Parallel intense photon (laser, microwave, etc.) beams ?0,k0 and ?1,k1 shone on a plasma with frequency separation equal to the plasma frequency ?p is capable of accelerating plasma electrons to high energies in large flux. The photon beat excites through the forward Raman scattering large amplitude plasmons whose phase velocity is equal to (?0-?1)/(k0-k1), close to c in an underdense plasma. The plasmon electrostatic fields trap electrons and carry them to high energies: Maximum electron energy Wmax = 2mc2[1-(?0-?1)2/c2(k0-k1)2]-1~2mc2(?0/?p)2. The multiple forward Raman instability produces smaller and smaller frequency and group velocity of photons; thus the photons slow down in the plasma by emitting accelerated electrons (inverse Cherenkov process).
TL;DR: In this paper, the effects of linear (Rayleigh) friction on free internal waves in the equatorial wayeguide were studied, and it was shown that the meridional scale becomes significantly larger than the inviscid value only when the frequency is much less than the friction coefficient.
Abstract: We study theoretically the effects of linear (Rayleigh) friction on free internal waves in the equatorial wayeguide. The waves may be vertically propagating or in standing vertical modes. Analytic solutions on a beta-plane show that the meridional scale of the wayeguide becomes significantly larger than the inviscid value only when the frequency is much less than the friction coefficient. In the limit of zero frequency, the meridional scale grows without bound. The amount of zonal damping depends on the wave type. Kelvin, high-frequency Yanai (mixed Rossby-gravity), inertial-gravity and low-wavenumber (non-dispersive) Rossby waves decay relatively slowly while low-frequency Yanai and high-wavenumber (short) Rossby waves are much more strongly attenuated. With friction, transitions to evanescence are spread over frequency bands; waves that had zero group velocity without friction are zonally evanescent with friction. Off the equator, friction changes amplitude nodes into non-zero minima and smooth...
TL;DR: In this paper, the structure of fully developed turbulence in a smooth circular tube has been studied for a Reynolds number of 69000 (based on centreline velocity and radius) and at a distance from the wall of y+ − 70.
Abstract: The structure of fully developed turbulence in a smooth circular tube has been studied for a Reynolds number of 69000 (based on centre-line velocity and radius) and at a distance from the wall of y+ — 70. The data were taken as correlations of the longitudinal component of turbulence in narrow frequency bands, the longitudinal and transverse separations being varied simultaneously. Fourier transformation of these correlations defines power spectral density functions with frequency ω and longit-dinal and transverse wavenumbers kx and kzas the independent variables. In this form the data show the distribution of convection velocity among waves of different size and inclination as well as defining the coherence lengths associated with such wave packets. Essential features of a geometrically similar wave description of the turbulence are discussed, such a model allowing considerable simplification in the description of the turbulence both for two-point and three-point space-time correlations of the velocity field. Morrison & Kronauer (1969) predicted that the wave convection velocity should depend only on total wavenumber k in a specific manner related to the mean velocity profile. The experimentally determined convection velocities contradict this prediction. An alternative formulation for convection velocity involving an additional empirical function of frequency S(ω), fits the data for the range of experimentation. Unfortunately the results provide no information on the functional dependence (if any) of convection velocity on distance from the wall.