Showing papers on "Wave propagation published in 1980"
TL;DR: Using theoretical results from the physics of nonlinear waves, it is shown that the internal waves are solitons and their interactions with surface waves are described.
Abstract: The solitary wave is a localized hydrodynamic phenomenon that can occur because of a balance between nonlinear cohesive and linear dispersive forces in a fluid. It has been shown theoretically, and observed experimentally, that some solitary waves have properties analogous to those of elementary particles, and the waves have therefore been named solitons. During a measurement program in the Andaman Sea near northern Sumatra, large-amplitude, long internal waves were observed with associated surface waves called tide rips. Using theoretical results from the physics of nonlinear waves, it is shown that the internal waves are solitons and their interactions with surface waves are described.
699 citations
TL;DR: In this article, the amplitudes of S and coda waves were measured simultaneously for 900 local earthquakes in the central Japan for various frequency bands, and the data were interpreted using the S to S single-scattering theory for coda wave.
Abstract: Recent measurements of Qβ−1 of S waves in the lithosphere for frequency range from 0.02 to 25 Hz show a remarkable frequency dependence and systematic variation from place to place depending on the current tectonic activity. In order to test the hypothesis that the attenuation of S waves may be caused by the loss of energy by scattering due to heterogeneity, the amplitudes of S and coda waves were measured simultaneously for 900 local earthquakes in the central Japan for various frequency bands. The data were interpreted using the S to S single-scattering theory for coda waves, which is now supported by the observed agreement between Q of coda and Qβ, and also by the observed identical local site effect on coda and S waves. The result shows that the loss of energy from S waves required to explain coda amplitudes agrees with the attenuation of S waves within the uncertainty of measurements. This conclusion is supported by several recent studies on Q of coda, Q of Lg, Qβ, and coda excitation by other workers.
445 citations
TL;DR: In this article, a head-on collision between two solitary waves on the surface of an inviscid homogeneous fluid was considered, and a perturbation method was used to calculate the effects of the collision.
Abstract: We consider a head-on collision between two solitary waves on the surface of an inviscid homogeneous fluid. A perturbation method which in principle can generate an asymptotic series of all orders, is used to calculate the effects of the collision. We find that the waves emerging from (i.e. long after) the collision preserve their original identities to the third order of accuracy we have calculated. However a collision does leave imprints on the colliding waves with phase shifts and shedding of secondary waves. Each secondary wave group trails behind its primary, a solitary wave. The amplitude of the wave group diminishes in time because of dispersion. We have also calculated the maximum run-up amplitude of two colliding waves. The result checks with existing experiments.
326 citations
TL;DR: The spectral analysis is made highly accurate by the use of line-shape fitting techniques and mode group delays can be determined to a precision of +/-0.12 psec/km using a computation covering a 5-cm propagation path.
Abstract: Propagating beam solutions for optical waveguides can be made to generate such mode-related properties as propagation constants, relative mode powers, and group delays with high precision and considerable flexibility. These quantities are needed in the analysis of optical fiber dispersion. The technique requires the generation of correlation functions from the numerical solutions of a wave equation. These correlation functions are in turn Fourier-transformed with respect to axial distance z. The resulting spectra display sharp resonances corresponding to mode groups, and the positions and heights of these resonances determine the previously mentioned mode properties. The spectral analysis is made highly accurate by the use of line-shape fitting techniques. With this method, mode group delays can be determined to a precision of +/-0.12 psec/km using a computation covering a 5-cm propagation path.
319 citations
TL;DR: In this article, the problem of acoustic radiation generated by instability waves of a compressible plane turbulent shear layer is solved, and the solution provided is valid up to the acoustic far-field region.
Abstract: The problem of acoustic radiation generated by instability waves of a compressible plane turbulent shear layer is solved. The solution provided is valid up to the acoustic far-field region. It represents a significant improvement over the solution obtained by classical hydrodynamic-stability theory which is essentially a local solution with the acoustic radiation suppressed. The basic instability-wave solution which is valid in the shear layer and the near-field region is constructed in terms of an asymptotic expansion using the method of multiple scales. This solution accounts for the effects of the slightly divergent mean flow. It is shown that the multiple-scales asymptotic expansion is not uniformly valid far from the shear layer. Continuation of this solution into the entire upper half-plane is described. The extended solution enables the near- and far-field pressure fluctuations associated with the instability wave to be determined. Numerical results show that the directivity pattern of acoustic radiation into the stationary medium peaks at 20 degrees to the axis of the shear layer in the downstream direction for supersonic flows. This agrees qualitatively with the observed noise-directivity patterns of supersonic jets.
265 citations
TL;DR: In this paper, the wave energy, energy flux density, force, and acceleration of the solar wind were analyzed in terms of the Fourier amplitudes of the ingoing and outgoing waves.
Abstract: We treat, both analytically and numerically, small-amplitude, undamped, toroidal Alfven waves in a model of axisymmetric solar wind flow in which solar rotation is neglected. There is no restriction to WKB waves; the waves may have any frequency. By transforming in simple ways the equations governing the waves we are able to obtain exact formal solutions to the general time-dependent problem as well as to the Fourier-analyzed problem. We discuss the equations and their solutions in terms of coupled inward and outward propagating waves. One integral of the equations for the Fourier amplitudes is obtained; it relates the amplitudes of the ingoing and outgoing waves. The integral is a special case of a general law of conservation of wave action, which we show to hold for finite wavelengths. The statement of the conservation of wave action is shown to be analogous to the conservation of particle-antiparticle pairs in relativistic quantum theory. We obtain the condition required for WKB waves and show that it depends on the coupling of waves in a flowing medium. The solar wind problem is discussed in terms of the Fourier amplitudes. It is shown that there is a singularity in the equations, at the Alfven point, which determines physically acceptable solar wind solutions. A qualitative account of the amplitudes far from the sun is given based on an exact solution for a model with constant solar wind flow speed. A conservation equation for the wave energy is obtained, and the relations among the wave energy density, energy flux density, force, and acceleration are stated. Numerical solutions, based on realistic solar wind profiles, are given. We show that non-WKB waves with wave periods of about a day or two have somewhat greater wave energy densities, up to a factor of 2 or so, in the corona than do WKB waves with the same amplitude at 1 A.U. On the other hand, non-WKB waves of any wave period are no more effective in accelerating the plasma than are WKB waves; they are much less effective for wave periods of a day or more. We conclude that, for conditions actually existing in the corona, WKB estimates quite accurately account throughout the corona for the wave energy density, energy flux density, and wave acceleration of the plasma for Alfven waves with periods less than about 0.05, 1, and 0.01 day, respectively; the corresponding periods in the solar wind are about 1, 1, and 0.5 day.
249 citations
TL;DR: In this paper, the authors used the reflectivity algorithm and inversion of the P and S wave travel time data to obtain extremal bounds on the p and S velocity (VP and vs) profiles.
Abstract: P and converted S waves observed in refraction stations FF1, FF2, and FF4 of the 1959 Fanfare cruise of the Scripps Institution of Oceanography are analyzed by synthetic seismogram modeling of the data using the reflectivity algorithm and by inversion of the P and S wave travel time data to obtain extremal bounds on the P and S velocity (vp and vs) profiles. While the FF1 data are inadequate for detailed analysis, the FF2 and FF4 data yield vp profiles displaying rapidly increasing velocity with depth in layer 2, a small velocity discontinuity between layers 2 and 3, gently increasing velocity with depth in layer 3, and a 1-km-thick Moho transition. The vs profiles for FF2 and FF4 show rapidly increasing velocity with depth in layer 2, fairly uniform velocities in the top of layer 3, a slight low-velocity zone extending through most of layer 3, and a 1-km-thick Moho transition. Using theories of seismic wave velocities in cracked media and a laboratory velocity measurement made on a basalt sample from this site, a porosity of 18% is inferred for the top of the igneous crust at this site. A further reduction of porosity to 2% can explain the observed velocity gradients only to a depth of 0.6 km into the igneous crust. In the 0.8- to 1.5-km depth interval, Poisson's ratio appears to drop below 0.27 to a minimum of 0.24, which may indicate a zone of trondhjemites or other quartz-rich rocks at this depth or which may be related to state of fluid saturation of the rocks. Within layer 3, observed vp and vs agree well with laboratory velocity measurements of ophiolite samples from the western U.S. and from the Bay of Islands, Newfoundland. The observed velocities suggest the disappearance of hornblende and the appearance of augite and olivine with increasing depth in layer 3. There is no evidence for more than 30% serpentine anywhere within the crust or upper mantle at this site, except possibly within unresolvably thin zones or pods. Evidence is also given which suggests that velocities and velocity gradients in the shallow crust may be partly controlled by differential pressure (externally applied pressure minus pore fluid pressure) and its spatial gradients and that laboratory velocity measurements made on water-saturated basalt samples at zero differential pressure are more representative of in situ velocities in the shallow crust than lab measurements made at which are usually employed as in situ conditions, namely, elevated externally applied pressure and zero pore fluid pressure. The factors affecting the efficiency of shear wave conversion at the sea floor are investigated, and the important role of basement vp and especially vs are shown. Since basement vs is very sensitive to fracture geometry, the high lateral variability of shear wave conversion may be related to variability in the extent and character of basement porosity. A useful explosive source function for marine synthetic modeling is presented, and a nomenclature for marine seismic phases is suggested.
230 citations
TL;DR: By solving the Christoffel equations, general closed-form expressions are obtained for the phase and group velocities and displacement eigenvectors of arbitrarily directed acoustic waves in elastically anisotropic solids.
Abstract: By solving the Christoffel equations, general closed-form expressions are obtained for the phase and group velocities and displacement eigenvectors of arbitrarily directed acoustic waves in elastically anisotropic solids. The relationship of these general results to expressions that hold in symmetry directions is shown, and applications to phonon focusing and the determination of acoustic axes and extrema of the phase velocity are discussed. Methods for extracting the elastic constants and orientation of a crystal from measured sound velocities are outlined.
219 citations
196 citations
01 Nov 1980
TL;DR: In this article, the authors reviewed the recent developments on wave propagation in turbulent media, including adaptive optics, intensity scintillations, pulse propagation, atmospheric measurements at visible, IR, and millimeter wave frequencies, speckle interferometry, and other related topics.
Abstract: In 1975, we reviewed the recent developments on wave propagation in turbulent media. In this paper, we update that paper to include recent results on adaptive optics, intensity scintillations, pulse propagation, atmospheric measurements at visible, IR, and millimeter wave frequencies, speckle interferometry, and other related topics.
180 citations
TL;DR: In this paper, the interaction of solitary-wave solutions of a model equation for long waves in dispersive media is examined numerically, and two new solitary waves, having slightly different amplitudes from the original waves, together with a small dispersive tail are generated as a result of the interaction.
Abstract: The interaction of solitary‐wave solutions of a model equation for long waves in dispersive media is examined numerically. It is found that the waves do not emerge from the interaction unscathed. Instead, two new solitary waves, having slightly different amplitudes from the original waves, together with a small dispersive tail are generated as a result of the interaction.
TL;DR: In this paper, the relation between the axial distribution of the electron density observed along the plasma column and the corresponding power distribution of surface wave that produces it is investigated, and it is found that the electron densities decrease almost linearly along the column in the direction of the wave propagation.
Abstract: The propagation of electron surface waves can be used to sustain long plasma columns. The relation between the axial distribution of the electron density observed along the plasma column and the corresponding power distribution of the surface wave that produces it is investigated. It is found that the electron density decreases almost linearly along the plasma column in the direction of the wave propagation. This is explained by assuming that the number of electrons produced over a given axial length is proportional to the wave power absorbed over that same length.
TL;DR: In this paper, the response to a convected harmonic pressure is found by using Fourier transforms and the response is seen to consist of an infinite set of space harmonics whose amplitudes are found explicitly.
TL;DR: Frequency-selective optical couplers in which a periodic perturbation in refractive index induces contradirectional power transfer in parallel single-mode waveguides are analyzed and it is shown that by varying the amplitude of the periodic perturbing along he direction of propagation, the sidelobes present for the case of a uniform perturbations can be substantially reduced.
Abstract: Frequency-selective optical couplers in which a periodic perturbation in refractive index induces contradirectional power transfer in parallel single-mode waveguides are analyzed. Expressions for the spectral response are obtained by solving the coupled-mode equations. It is shown that by varying the amplitude of the periodic perturbation along he direction of propagation, the sidelobes present for the case of a uniform perturbation can be substantially reduced. Calculations are made of the mode propagation constants and coupling parameters for two rectangular-core waveguides with a periodic surface corrugation in the region between them. By using these results, design parameters and theoretical performance characteristics for a coupler with high transfer efficiency, low cross talk, and low reflection efficiency in the primary waveguide are determined.
TL;DR: In this paper, the propagation of finite-amplitude internal waves in a shear flow is considered for wavelengths that are long compared to the shear-layer thickness, and the equation governing the amplitude evolution is derived.
Abstract: The propagation of finite-amplitude internal waves in a shear flow is considered for wavelengths that are long compared to the shear-layer thickness. Both singular and regular modes are investigated, and the equation governing the amplitude evolution is derived. The theory is generalized to allow for a radiation condition when the region outside the stratified shear layer is unbounded and weakly stratified. In this case, the evolution equation contains a damping term describing energy loss by radiation which can be used to estimate the persistence of solitary waves or nonlinear wave packets in realistic environments. A continuous three-layer model is studied in detail and closed-form expressions are obtained for the phase speed and the coefficients of the nonlinear and dispersive terms in the amplitude equation as a function of Richardson number.
TL;DR: Fully nonlinear planar ion-acoustic solitary waves moving obliquely to an external magnetic field were studied in this article. But the results were limited to the case of a single wave.
Abstract: Fully nonlinear planar ion‐acoustic solitary waves moving obliquely to an external magnetic field are studied.
TL;DR: In this paper, the results of an experimental study of some quantitative features of the wave process that produces jet column fracture are presented, and the results point toward the "acceleration '' mechanism as the mode of wave production.
Abstract: The results of an experimental study of some quantitative features of the wave process that produces jet column fracture are presented. The tests were conducted in a supersonic wind tunnel at Mach 2.4-4.0 at ambient stagnation temperature and stagnation pressures of 2.7-9.5 atm with several injectants at various flow rates. Photographic observations were employed, and data describing the waves on the jet column that lead to breakup including wavelength, amplitude, frequency, and wave speed are presented. The results point toward the "acceleration '' mechanism as the mode of wave production. '
TL;DR: In this article, the structure of a general theory for acoustic wave propagation in ocean sediments is reviewed with emphasis on the determination of meaningful parameters from data in the literature, and it is shown that acoustic properties are nonlinear functions of cyclic strain amplitude and static stress level so that only a limited amount of the available data is useful for studies of acoustic propagation.
Abstract: The structure of a general theory for acoustic wave propagation in ocean sediments is reviewed with emphasis on the determination of meaningful parameters from data in the literature. It is shown that acoustic properties are nonlinear functions of cyclic strain amplitude and static stress level so that only a limited amount of the available data is useful for studies of acoustic propagation. An example of geoacoustic modeling is presented based on the theory and some new data for Stoneley wave velocities measured in situ are evaluated with the aid of the model.
TL;DR: In this article, a stability analysis which directly uses particle distribution functions determined from experiments or transport theory, rather than model distributions, is carried out, and features of distribution functions relevant to whistlers, ion cyclotron waves, including their low-frequency extensions for propagation along the magnetic field, and to ion-acoustic waves are analyzed in detail.
Abstract: A stability analysis which directly uses particle distribution functions determined from experiments or transport theory, rather than model distributions, is carried out. The features of distribution functions relevant to whistlers, ion cyclotron waves, including their low-frequency extensions for propagation along the magnetic field, and to ion-acoustic waves are analyzed in detail. The dependence of wave growth on the precise shape of the distributions and the numerical feasibility of the method is demonstrated by the use of measured solar wind distributions.
TL;DR: In this paper, the authors studied the propagation and power flow due to force and torque (moment) excitation at the driving point and in the far field of an infinite plate with a single line-stiffener.
TL;DR: Conclusions concerning pressure-dependence, age-Dependence, and muscular activation-dependency of the wave characteristics are drawn which are in accord with available experimental data.
Abstract: Propagation of small amplitude harmonic waves through a viscous incompressible fluid contained in an initially stressed elastic cylindrical tube is considered as a model of the pulse wave propagation in arteries. The nonlinearity and orthotropy of the vascular material is taken into account. Muscular activity is introduced by means of an "active" tension in circumferential direction of the vessel. The frequency equation is obtained and it is solved numerically for the parameters of a human abdominal aorta. Conclusions concerning pressure-dependence, age-dependence, and muscular activation-dependence of the wave characteristics are drawn which are in accord with available experimental data.
TL;DR: In this paper, the invariant form of the relative phase acceleration, the proper description of the viscosity of fluidized systems, and the nature of individual phase pressures are discussed.
TL;DR: In this article, the wave dispersion equation is modified and wave energy is dissipated by coupling between the waves in water and those induced in the mud layer, theoretically determined by assuming a viscoelastic mud layer.
Abstract: Soft muddy bottoms have significant effects on properties of water waves which propagate over them. The wave dispersion equation is modified and wave energy is dissipated by the coupling between the waves in water and those induced in the mud layer. These effects are theoretically determined by assuming a viscoelastic mud layer. A boundary-value problem is solved for the water-mud system with sinusoidal waves. The theoretical dissipation rates are compared favorably with field measurements.
TL;DR: In this article, whispering gallery rays are modeled as a sum of whispering galley waves, which propagate in a waveguide composed of a simple high velocity mantle lid underlain by a low velocity zone.
Abstract: Teleseismic Pn waves are modeled as a sum of whispering galley waves, which propagate in a waveguide composed of a simple high velocity mantle lid underlain by a low velocity zone. This model is able to account for those Pn wave propagation properties that are not dominated by scattering, i.e., their apparent velocity and lack of long period energy. Pn apparent velocity data constrain the P wave velocity gradient in the upper 100 km of mantle to be low; dvp/dz<0.001 s−1. The whispering gallery rays are shown to have significant amplitude (when compared to the direct P wave) and to have spectra that rapidly fall off at long periods. Yet this model cannot account for certain details of the observed Pn amplitude spectra. Most important among these is the spectral ratio of Pn to P, which the model underestimates by a factor of 10. Nevertheless, the model presents a useful framework for understanding some characteristics of Pn wave propagation and provides an estimate of the distribution of energy with depth in the Pn waves.
TL;DR: In this article, basic equations describing the macroscopic behavior of ultra-relativistic plasma (T ≫ m c 2 ) are formulated in a covariant form, and the dispersion relations for electrostatic wave, electromagnetic wave and Alfven wave propagating parallel to a constant magnetic field are shown.
Abstract: Basic equations describing a macroscopic behaviour of ultra-relativistic plasma ( T ≫ m c 2 ) are formulated in a covariant form. Waves in an electron-positron plasma are investigated in a frame of two-fluid model equation. Dispersion relations for electrostatic wave, electromagnetic wave and Alfven wave propagating parallel to a constant magnetic field are shown. In the case that both electron and positron gases have same temperature, there does not exist the slow mode which corresponds to the ion acoustic wave. Right and left circular polarized waves propagate with the same dispersion relation which is different from one of the non-relativistic electron-ion plasma.
TL;DR: In this article, general expressions for the kernels of the set of integral equations that relates the spectral matrix of the six components of a random electromagnetic wave field in a magnetoplasma to the wave distribution function for the field are derived.
Abstract: Summary. General expressions are derived for the kernels of the set of integral equations that relates the spectral matrix of the six components of a random electromagnetic wave field in a magnetoplasma to the wave distribution function for the field. The dependence of the kernels on wave-normal direction is examined, with particular reference to the propagation of very low-frequency waves in the whistler mode.
TL;DR: In this article, the theory of acoustic propagation in porous fluid-filled media developed by Biot is applied to the case where superfluid 4He is in the pores (T < 1.1 K where there is a negligible amount of normal fluid).
Abstract: The theory of acoustic propagation in porous fluid‐filled media developed by Biot is applied to the case where superfluid 4He is in the pores (T<1.1 K where there is a negligible amount of normal fluid). For a consolidated (fused) matrix Biot’s slow compressional wave is shown to be identical to the phenomenon known as fourth sound; V(slow wave/fourth sound)=V(fluid)/n. The index of refraction of fourth sound is related to the ’’structure factor’’α, of the Biot theory by n=α1/2, and so use of the superfluid provides a direct means of measuring α in a given sample. Predictions for the velocities of the fast wave, the shear wave, and the slow wave/fourth sound are made for fused gass bead samples in which Plona has previously reported seeing these three waves under the condition of water saturation.
TL;DR: In this paper, it was shown that the oceanic internal wave field is too energetic by roughly two orders of magnitude to be treated theoretically as an assemblage of weakly interacting waves, which may be seen both from recent weak wave theoretical calculations which contradict their premises and also from inspection of magnitudes of advection and wave propagation terms.
Abstract: It is shown that the oceanic internal wave field is too energetic by roughly two orders of magnitude to be treated theoretically as an assemblage of weakly interacting waves. This may be seen both from recent weak wave theoretical calculations which contradict their premises and also from inspection of magnitudes of advection and wave propagation terms. Thus, much recent discussion of results of implications of weak wave theory should be questioned critically. Scaling arguments based on buoyant turbulence are reviewed briefly. The role of vertical mass flux as distinguishing weak wave interactions from stronger turbulence is discussed. Possible progress by renormalization of wave interaction equations is considered.