Showing papers on "Wave propagation published in 1977"

Electromagnetic propagation in periodic stratified media. I. General theory

Abstract: The propagation of electromagnetic radiation in periodically stratified media is considered. Media of finite, semi-infinite, and infinite extent are treated. A diagonalization of the unit cell translation operator is used to obtain exact solutions for the Bloch waves, the dispersion relations, and the band structure of the medium. Some new phenomena with applications to integrated optics and laser technology are presented.

Phase transitions under shock-wave loading

Abstract: First-order polymorphic, second-order, melting, and freezing transitions induced by shock-wave loading are reviewed. Comprehensive tabulations of the experimental observations are presented and materials that have been subjected to in-depth study are reviewed in more detail. Theories of the mechanics, thermodynamics, kinetics, and shear strength of shock-loaded materials are described and experimental techniques are briefly reviewed.

Generation of time-reversed wave fronts by nonlinear refraction*

Abstract: We describe a nonlinear method for generating, nearly instantaneously, a time-reversed replica of any monochromatic-beam wave pattern The method employs the interaction of the incident beam, of arbitrary wave front, with counter-propagating plane “pump” waves in a homogeneous, transparent, nonlinear medium Media are shown to exist in which time-reversed waves can be generated with high efficiency using available laser pump sources

On two-dimensional packets of capillary-gravity waves

Abstract: The motion of a two-dimensional packet of capillary-gravity waves on water of finite depth is studied. The evolution of a packet is described by two partial differential equations: the nonlinear Schroedinger equation with a forcing term and a linear equation, which is of either elliptic or hyperbolic type depending on whether the group velocity of the capillary-gravity wave is less than or greater than the velocity of long gravity waves. These equations are used to examine the stability of the Stokes capillary-gravity wave train. The analysis reveals the existence of a resonant interaction between a capillary-gravity wave and a long gravity wave. The interaction requires that the liquid depth be small in comparison with the wavelength of the (long) gravity waves and the evolution equations describing the dynamics of this interaction are derived.

Nonlinear deep-water waves: theory and experiment. Part 2. Evolution of a continuous wave train

Abstract: Results of an experimental investigation of the evolution of a nonlinear wave train on deep water are reported. The initial stage of evolution is found to be characterized by exponential growth of a modulational instability, as was first discovered by Benjamin ' Feir. At later stages of evolution it is found that the instability does not lead to wave-train disintegration or loss of coherence. Instead, the modulation periodically increases and decreases, and the wave train exhibits the Fermi–Pasta–Ulam recurrence phenomenon. Results of an earlier study of nonlinear wave packets by Yuen ' Lake, in which solutions of the nonlinear Schrodinger equation were shown to provide quantitatively correct descriptions of the properties of nonlinear wave packets, are applied to describe the experimentally observed wave-train phenomena. A comparison between the laboratory data and numerical solutions of the nonlinear Schrodinger equation for the long-time evolution of nonlinear wave trains is given.

Wave-speed limitation on expiratory flow-a unifying concept.

Abstract: The mechanism limiting forced expiratory flow is explained on the basis that a local flow velocity reaches the local speed of wave propagation at a point, called the choke point, in intrathoracic a...

Steep gravity waves in water of arbitrary uniform depth

Abstract: Modern applications of water-wave studies, as well as some recent theoretical developments, have shown the need for a systematic and accurate calculation of the characteristics of steady, progressive gravity waves of finite amplitude in water of arbitrary uniform depth. In this paper the speed, momentum, energy and other integral properties are calculated accurately by means of series expansions in terms of a perturbation parameter whose range is known precisely and encompasses waves from the lowest to the highest possible. The series are extended to high order and summed with Pade approximants. For any given wavelength and depth it is found that the highest wave is not the fastest. Moreover the energy, momentum and their fluxes are found to be greatest for waves lower than the highest. This confirms and extends the results found previously for solitary and deep-water waves. By calculating the profile of deep-water waves we show that the profile of the almost-steepest wave, which has a sharp curvature at the crest, intersects that of a slightly less-steep wave near the crest and hence is lower over most of the wavelength. An integration along the wave profile cross-checks the Pade-approximant results and confirms the intermediate energy maximum. Values of the speed, energy and other integral properties are tabulated in the appendix for the complete range of wave steepnesses and for various ratios of depth to wavelength, from deep to very shallow water.

Interstellar Scattering and Scintillation of Radio Waves

Abstract: A review is presented of interstellar scattering and scintillation observations in the light of modern theory for extended, spatially homogeneous, power law inhomogenieties. Formulas are presented for the experimentally observable quantities and are compared with data. A general discussion of the model is given. (GHT)

Momentum and energy transport by waves in the solar atmosphere and solar wind.

Abstract: The fluid equations for the solar wind are presented in a form which includes the momentum and energy flux of waves in a general and consistent way. The concept of conservation of wave action is introduced and is used to derive expressions for the wave energy density as a function of heliocentric distance. The explicit form of the terms due to waves in both the momentum and energy equations are given for radially propagating acoustic, Alfven, and fast mode waves. The effect of waves as a source of momentum is explored by examining the critical points of the momentum equation for isothermal spherically symmetric flow. We find that the principal effect of waves on the solutions is to bring the critical point closer to the sun's surface and to increase the Mach number at the critical point. When a simple model of dissipation is included for acoustic waves, in some cases there are multiple critical points.

Path integrals for waves in random media

Abstract: The problem of wave propagation in a random medium is formulated in terms of Feynman’s path integral. It turns out to be a powerful calculational tool. The emphasis is on propagation conditions where the rms (multiple) scattering angle is small but the log‐intensity fluctuations are of order unity—the so‐called saturated regime. It is shown that the intensity distribution is then approximately Rayleigh with calculable corrections. In an isotropic medium, the local or Markov approximation which is commonly used to compute first and second (at arbitrary space–time separation) moments of the wave field is explicitly shown to be valid whenever the rms multiple scattering angle is small. It is then shown that in the saturated regime the third and higher moments can be obtained from the first two by the rules of Gaussian statistics. There are small calculable corrections to the Gaussian law leading to ’’coherence tails.’’ Correlations between waves of different frequencies and the physics of pulse propagation are studied in detail. Finally it is shown that the phenomenon of saturation is physically due to the appearance of many Fermat paths satisfying a perturbed ray equation. For clarity of presentation much of the paper deals with an idealized medium which is statistically homogeneous and isotropic and is characterized by fluctuations of a single typical scale size. However, the extension to inhomogneous, anisotropic, and multiple scale media is given. The main results are summarized at the beginning of the paper.

Importance of physical dispersion in surface wave and free oscillation problems: Review

Abstract: Physical dispersion resulting from anelasticity is investigated from the point of view of linear viscoelastic models and causality relations. It is concluded that inasmuch as Q in the earth's mantle is nearly independent of frequency, at least in the seismic frequency band, a dispersion relation in the form of C(ω) = C(ω_r)[1 + (1/πQ_m) In (ω/ω_r)] must be used for correcting the effect of physical dispersion arising from anelasticity. (Here C(ω) is the phase velocity of either body waves, surface waves, or free oscillations, ω is the angular frequency, ωr is the reference angular frequency, and Q_m is the path average Q for body waves or Q of a surface wave or a mode of angular frequency ω; for surface waves and free oscillations, C(ω_r) should be understood as the phase velocity at ω computed by using the elastic moduli at ω = ω_r.) The values of Q outside the seismic frequency band affect mainly the absolute value of the phase velocity but do not affect significantly the relative dispersion within the seismic frequency band. Even if the microscopic mechanism of attenuation is nonlinear, this dispersion relation can be used if departure from elasticity is relatively small, so that the signal can be approximated by a superposition of propagating harmonic waves. Since surface wave and free oscillation Q is 100–500 for fundamental modes, a correction of 0.5–1.5% must be made for joint interpretation of body wave and surface wave data. This correction is nearly 1 order of magnitude larger than the uncertainties associated with these data and are therefore very significant. When this correction is made, the discrepancy between the observed surface wave phase velocities and free oscillation periods and those predicted by the Jeffreys or Gutenberg model becomes much smaller than has previously been considered.

Electromagnetic propagation in periodic stratified media. II. Birefringence, phase matching, and x-ray lasers *

Abstract: The theory of electromagnetic Bloch waves in periodic stratified media is applied to the problems of birefringence and group velocity in these media. The relevance of periodic media to phase matching in nonlinear mixing experiments and to laser action in the x-ray region is discussed.

Theory and application of wave propagation and scattering in random media

Abstract: This paper presents a review of basic theories and recent advances in the studies of wave propagation and scattering in random media. Examples of the random media include the atmosphere, the ocean, and biological media whose characteristics are randomly varying in time and space. The study of electromagnetic, optical, and acoustic waves in such media has become increasingly important in recent years in the areas of communication, detection, and remote-sensing. Topics covered in this paper are divided into "waves in randomly distributed scatterers," "waves in random continua," and "remote-sensing of random media." Transport theory with various approximate solutions and multiple scattering theories are discussed and their relationships are clarified. Included in the analyses are propagation characteristics of intensities, wave fluctuations, pulse propagation and scattering, coherence bandwidth, and coherence time of communication channels through random media. Remote-sensing techniques include recent advances in the use of inversion techniques to deal with ill-posed problems.

The Born approximation in the theory of the scattering of elastic waves by flaws

Abstract: We used the integral equation formulation of the scattering of elastic waves to generate an approximate solution analogous to the Born approximation in quantum mechanics. This solution is attractive because of the ease with which it may be applied to scatterers of complicated shapes. We investigated the validity of the approximation by comparing it with exact results for spherical scatterers. Our conclusion for voids in elastic media is that the approximation describes well the scattering when the wavelength of the incident wave is approximately an order of magnitude larger than the scatterer and when the scattering is viewed in the backscattered directions. For many applications this range of validity is experimentally accessible. For elastic inclusions, however, where the properties of defect and host differed by 20–40%, the Born approximation is surprisingly good for all angles and even at short wavelengths.

A review of the effects of anisotropic layering on the propagation of seismic waves

Abstract: Summary. This paper reviews recent work, much of it unpub~shed, on the effects of anisotropy on seismic waves, and lays the theoretical background for some of the other papers in this number of the Geophysical Journal. The propagation of both body and surface waves in anisotropic media is fundamentally different from their propagation in isotropic media, although the differences in behaviour may be comparatively subtle and difficult to observe. One of the most diagnostic of these anomalies, which has been observed on. some surface-wave trains, and should be evident in body-wave arrivals, is generalized, three-dimensional polarization, where the Rayleigh motion is coupled to the Love, and the P and SV motion is coupled to the SH. This coupling introduces polarization anomalies which may be used to investigate anisotropy within the Earth. 1 Introduction A material displaying velocity anisotropy must have its effective elastic constants arranged in some form of crystalline symmetry. The behaviour of both body and surface waves in such anisotropic structures differs from that in isotropic structures, and the variation of velocity with direction is only one of the anomalies which may occur, where we use anomaly to mean differences in behaviour from that expected in isotropic material. Within an anisotropic material three body waves propagate in any direction, having different and varying velocity, and different and varying polarization. Away from directions of crystal symmetry there may be anomalous phases, body and surface waves will have anomalous polarizations, and energy propagation of body and surface waves will not be parallel to the propagation vector. It appears intuitively that many of the anomalies can be attributed to the subtle interplay of the three varying body waves, making the variations of these anomalies difficult to predict. Similarly, smd differences in the structure, such as the thickness of the layer, can make radical changes in the anomalous behaviour. In this paper, we shall describe the type of phenomena to be expected in seismic waves from the presence of a layer of anisotropy within the Earth. A more complete treatment of the mathematics for the general problem of a plane layered structure containing a layer of anisotropy can be found in Keith (1975) for body waves, and Crampin (1970) and Taylor & Crampin (1977) for surface waves.

Seismic body waves in anisotropic media: Reflection and refraction at a plane interface

Abstract: Summary. A formulation is derived for calculating the energy division among waves generated by plane waves incident on a boundary between generally anisotropic media. A comprehensive account is presented for P, SV and SH waves incident from an isotropic half-space on an orthorhombic olivine half-space, where the interface is parallel to a plane of elastic symmetry. For comparison, a less anisotropic medium having transverse isotropy with a horizontal axis of symmetry is also considered. The particle motion polarizations of waves in anisotropic medium differ greatly from the polarizations in isotropic media, and are an important diagnostic of the presence of anisotropy. Incident P and SV waves generate quasi-SH waves, and incident SH waves generate quasi-P and quasi-SV waves, often of considerable relative magnitude. The direction of energy transport diverges from the propagation direction.

Mode Conversion of the Fast Magnetosonic Wave in a Deuterium-Hydrogen Tokamak Plasma

Abstract: Model conversion from the fast magnetosonic wave to a slow wave near the two-ion hybrid resonance is shown to explain recent experimental fast-wave damping results. A model for tunneling and mode conversion of the fast wave in the two-ion resonance zone incorporating k/sub parallel/ and plasma-density and magnetic-field profiles is used to explain the observations. The strong dependence of the absorption on k/sub parallel/ and the species concentration which is obtained has important consequences for major plasma-heating programs which are planned for tokamaks.

Shallow Wave Propagation in Open Channel Flow

Abstract: The propagation characteristics of various types of shallow water waves in open channel flow are calculated on the basis of linear stability theory. The celerity and attenuation functions of kinematic, diffusion, convective dynamic, dynamic and gravity waves, are derived. For the most general case, i.e., the dynamic wave model, the propagation characteristics are expressed as a function of the steady uniform flow Froude number and the dimensionless wave number of the unsteady component of the motion. For the dynamic model, the wave number spectrum is divided into three bands: 1)A gravity band corresponding to large wave number, where the wave celerity is the gravity wave celerity; 2)a kinematic band corresponding to a small wave number where the wave celerity is the kinematic wave celerity; and 3)a dynamic band corresponding to mid-spectrum values of the wave number, where the wave celerity falls between the gravity and kinematic celerity values.

Two-dimensional self-modulation of a whistler wave propagating along the magnetic field in a plasma

Abstract: Two-dimensional nonlinear self-modulations of a high-frequency whistler wave propagating along an applied magnetic field in a plasma are investigated. We derive new, fairly broad, regions of modulational instabilities in directions oblique to the initial wave propagation with growth rates much greater than in the case of ‘parallel’ self-modulation. The largest growth rate appears to be for the angles corresponding to the parametric instabilities. Nonlinear solutions describing the envelope solitons propagating obliquely to the initial wave are also discussed. Our results are in qualitative agreement with recent experiments.

Stochastic closure for nonlinear Rossby waves

Abstract: An extension of the turbulence ‘test-field model’ (Kraichnan 1971 a) is given for two-dimensional flow with Rossby-wave propagation. Such a unified treatment of waves and turbulence is necessary for flows in which the relative strength of nonlinear terms depends upon the length scale considered. We treat the geophysically interesting case in which long, fast Rossby waves propagate substantially without interaction while short Rossby waves are thoroughly dominated by advection. We recover the observations of Rhines (1975) that the tendency of two-dimensional flow to organize energy into larger scales of motion is inhibited by Rossby waves and that an initially isotropic flow develops anisotropy preferring zonal motion. The anisotropy evolves to an equilibrium functional dependence on the isotropic part of the flow spectrum. Theoretical results are found to be in quantitative agreement with numerical flow simulations.

Reflection and refraction of type-II S waves in elastic and anelastic media

Abstract: The general theory of viscoelasticity, which accounts for elastic as well as anelastic linear behavior of materials, predicts that two types of S waves propagate in anelastic earth materials. The particle motion for an inhomogeneous plane S wave of type I is elliptical in the plane defined by the directions of propagation and attenuation, while the particle motion for an inhomogeneous plane S wave of type II is linear perpendicular to this plane. The general theory predicts that an S -wave incident upon a plane boundary perpendicular to the plane defined by the directions of propagation and attenuation generates S waves only of the same type. General characteristics of the type-II S waves reflected and refracted at plane anelastic boundaries are: 1. (a) velocities and maximum attenuations which depend on the angle of incidence and frequency, 2. (b) maximum energy flow at a different velocity and in a different direction than phase propagation, 3. (c) energy flow across the boundary due to interaction of the incident and reflected waves. The general theory predicts these characteristics for the waves whenever a plane type-II S wave interacts with a plane anelastic boundary such as a soil-bedrock, crust-mantle, or core-mantle interface. None of these characteristics are predicted for the plane SH waves described by elasticity theory.

The Mean Forces Exerted by Waves on Floating or Submerged Bodies with Applications to Sand Bars and Wave Power Machines

Abstract: Water waves transport both energy and momentum, and any solid body which absorbs or reflects wave energy must absorb or reflect horizontal momentum also. Hence the body is subject to a mean horizontal force. In low waves, the force may be calculated immediately when the incident, reflected and transmitted wave amplitudes are known. For wave power devices the mean force can be large, so that anchoring presents practical problems. Experiments with models of the Cockerell wave-raft and the Salter ‘duck’ accurately confirm the predicted magnitude of the force at low wave amplitudes. For steeper waves, however, the magnitude of the force can be less than that given by linear theory. By experiments with submerged cylinders, it is shown that this is due partly to the presence of a free second harmonic on the down-wave side. In breaking waves, it is confirmed that the mean force on submerged bodies is sometimes reduced, and even reversed. An explanation is suggested in terms of the ‘wave set-up’ produced by breaking waves. Submerged cylinders act as a kind of double beach. A negative mean force arises from an asymmetry in the breaking waves, associated with a time-delay in the response to the change in depth. Similar arguments apply to submerged reefs and sand bars. Experiments with a model bar show that long low waves propel the bar towards the shore, whereas steep, breaking waves propel it seawards. This is similar to the observed behaviour of off-shore sand bars. The existence of a horizontal momentum flux (or radiation stress) in water waves is demonstrated by using it to propel a small craft.

Theoretical seismograms of core phases calculated by frequency‐dependent full wave theory, and their interpretation

Abstract: Summary. A frequency-dependent full wave theory is successfully employed to synthesize long-period seismograms of the core phases SmKS (m= 1, 2, …) in the distance range 100°–125°. Body-wave displacements are calculated by numerically integrating in the complex ray parameter plane. Langer's method is employed to obtain a uniformly asymptotic approximation to the vertical wave functions. Plane-wave reflection and transmission coefficients are adequately corrected for the effect of the curvature at the core -mantle discontinuity by the use of generalized cosines. Results are presented in the time domain, after a numerical Fourier (inverse) transform. The computed seismograms exhibit many non-ray effects that the SmKS incur upon interacting with the core- -mantle boundary. For SKS, the amplitude, group delay and phase delay are very strong functions of frequency at less than 0.5 Hz, both because of the frequency dependence of the reflection/transmission coefficients at the core—mantle boundary, and because of the presence of diffracted energy, called SP(diff)KS, perturbing the waveform. The diffracted energy of the type that perturbs SKS may also interact with shear waves to give rise to a precursor to the body-wave ScS, called SP(diff)S. The major complication in synthesizing the portion of the seismogram containing SmKS for m≥ 2 is that the arrival time of each successively higher order reflection is within the waveform of previous lower order reflections. It is found that a summation of body-wave displacements from S2KS to S15KS gives an adequate seismogram in the distance range 100°–125°. Each individual reflection has an amplitude spectrum, group delay and phase delay which are strongly frequency-dependent at less than 0.2 Hz. It is shown that arrival times for SmKS, m≥ 2, cannot be picked accurately by conventional methods. Furthermore, neglecting the frequency-dependence of reflection/transmission coefficients can significantly distort the interpretation of amplitude and phase data. The seismograms generated by this method agree so remarkably well with observed records that the synthetic waveforms provide a powerful test of the validity of particular earth models. In particular, we find that the waveforms of SmKS are exceedingly sensitive to velocity gradients of the upper 200-km of the outer core, and indications are that the velocities in the outer 200-km of the core are higher, but the velocity gradient is lower, than that predicted by Hales & Roberts or earth model 1066B. The pulse widths of SmKS are also used to determine some fault parameters.

Numerical solution of conservation equations arising in linear wave theory: application to aeroacoustics

Abstract: The propagation of waves in slightly inhomogeneous dispersive media is conveniently described by a geometrical or kinematic theory. In such frameworks the solution of the propagation problem is constructed by (a) deriving a dispersion relation and determining its characteristic lines and (b) solving an equation expressing the conservation of a field invariant like the wave action. This paper is concerned with the implementation of the last step under general field and boundary conditions. The method presented is based on the derivation of a variational system of differential equations for the geodesic elements of the wave front. The elementary cross-section of the wave front is obtained by integration and the principle of conservation of the field invariant directly yields the field amplitude. In addition, suitable jump conditions are derived for treating specular reflexions at solid boundaries. The method is illustrated by specific problems of interest in aeroacoustics.

Stochastic acceleration by an electrostatic wave near ion cyclotron harmonics

Abstract: A nonlinear effect of a large amplitude electrostatic wave propagating perpendicularly to a static magnetic field on the motion of an ion is studied. The case where the frequency of the wave w is sufficiently close to a multiple of the ion cyclotron frequency is considered. It is found that the trapping motion is influenced by periodic forces. These forces lead to randomization of the trapping motion near the separatrix, and ions are expected to be stochastically accelerated. In order to confirm the results, numerical calculations are carried out.

High Velocity Impact Calculations in Three Dimensions

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