Showing papers on "Wave propagation published in 1983"

The applied dynamics of ocean surface waves

Abstract: The aim of this book is to present selected theoretical topics on ocean wave dynamics, including basic principles and applications in coastal and offshore engineering, all from the deterministic point of view. The bulk of the material deals with the linearized theory.

Seismic Wave Propagation in Stratified Media

Abstract: Publisher Summary This chapter focuses on elastic wave propagation in stratified media. The development of the theory of elastic wave propagation in stratified media has been strongly influenced by the problems of seismic wave propagation and the nature of the seismograms recorded from earthquakes. For purely analytic developments of elastic wave propagation, the level of manageable algebraic complexity is reached in a model with one or two uniform layers overlying a uniform half space. This chapter shows how the excitation of elastic waves, within a horizontally stratified structure, can be conveniently developed in terms of reflection and transmission matrices. This procedure has allowed the construction of the full response of the medium or approximations with desired properties so that theoretical seismograms may be calculated for realistic distributions of elastic parameters. Although this development has been for isotropic media, nearly all the results apply directly to the case of full anisotropy if 3 × 3 reflection and transmission matrices allowing coupling between all wave types are employed. This development of the wavefield for both source and receiver within the stratification may be used for other classes of wave propagation.

Wave propagation in a magnetic cylinder

Abstract: The nature of oscillations in a magnetic cylinder embedded in a magnetic environment is investigated. It is shown that the standard slender flux tube analysis of a kink mode in a cylinder excludes the possibility of a second mode, which arises under photospheric conditions. Under coronal conditions, two widely separated classes of oscillation can be freely sustained, one on an acoustic time-scale and the other on an Alfvenic time-scale. The acoustic-type oscillations are always present, but the much shorter period, Alfvenic-type, oscillations arise only in high density (strictly, low Alfven velocity) loops. An application to waves in fibrils is also given, and suggests (following Wentzel, 1979) that they are fast kink waves propagating in a density enhancement.

A Compressible Model for the Simulation of Moist Mountain Waves

Abstract: A two-dimensional, nonlinear, nonhydrostatic model is described which allows the calculation of moist airflow in mountainous terrain. The model is compressible, uses a terrain-following coordinate system, and employs lateral and upper boundary conditions which minimize wave reflections. The model's accuracy and sensitivity are examined. These tests suggest that in numerical simulations of vertically propagating, highly nonlinear mountain waves, a wave absorbing layer does not accurately mimic the effects of wave breakdown and dissipation at high levels in the atmosphere. In order to obtain a correct simulation, the region in which the waves are physically absorbed must generally be included in the computational domain (a nonreflective upper boundary condition should be used as well). The utility of the model is demonstrated in two examples (linear waves in a uniform atmosphere and the Jan. 11, 1972 Boulder windstorm) which illustrate how the presence of moisture can influence propagating waves. In both cases, the addition of moisture to the upstream flow greatly reduces the wave response.

Sampling Theory and Wave Propagation

Abstract: In the seismic reflection method, the seismic signal does vary in amplitude, shape, frequency and phase versus the propagation time

Wave Propagation in the Split Hopkinson Pressure Bar

Abstract: Elastic wave propagation in the split Hopkinson pressure bar (SHPB) is discussed with an emphasis on the origin and nature of the oscillations that often trail the leading edge of the pressure wave. The authors show that in the conditions of the SHPB test the pressure bars vibrate in the fundamental mode and that elastic wave progapation can be fully described mathematically. Excellent agreement is found between experimental results and predictions of the mathematical treatment. This suggests that dispersion effects in the pressure bars can be removed from the strain gage records, which reduces the magnitude of the oscillations in the resulting stress strain curve. 12 references, 11 figures, 1 table.

Dynamics of magnetosphere-ionosphere coupling including turbulent transport

Abstract: The dynamics of magnetosphere-ionosphere coupling has been investigated by means of a two-dimensional two-fluid MHD model including anomalous resistivity. When field-aligned current is generated on auroral field lines, the disturbance propagates toward the ionosphere in the form of a kinetic Alfven wave. When the current exceeds a critical value, microscopic turbulence is produced, which modifies the propagation of the Alfven wave. This process is modeled by a nonlinear collision frequency, which increases with the excess of the drift velocity over the critical value. The system evolves toward an electrostatic structure, with the perpendicular electric field having a shorter scale than the field-aligned current. The approach to a steady state is strongly dependent on the presence or absence of the turbulence and on the boundary conditions imposed in the generator. As current is increased or scale size is decreased, the turbulent region reflects and absorbs most of the Alfven wave energy, decoupling the generator from the ionosphere.

Theory of hydromagnetic waves in the magnetosphere

Abstract: Many of the significant theoretical advances in understanding the origin and behaviour of low frequency hydromagnetic waves originating in the magnetosphere in the last decade are reviewed. Topics covered include wave generation mechanisms, wave damping, effects of inhomogeneity, signal behaviour in the ionosphere and atmosphere.

Review of elastic and electromagnetic wave propagation in horizontally layered media

Abstract: The objective of this paper is to provide a unified treatment of elastic and electromagnetic (EM) wave propagation in horizontally layered media for which the parameters in the partial differential equations are piece‐wise continuous functions of only one spatial variable. By applying a combination of Fourier, Laplace, and Bessel transforms to the partial differential equations describing the elastic or EM wave propagation I obtain a system of 2n linear ordinary differential equations. The 2n×2n coefficient matrix is partitioned into 4n×n submatrices. By a proper choice of variables, the diagonal submatrices are zero and the off‐diagonal submatrices are symmetric. All the results in the paper are derived from the symmetry properties of this general equation. In the appendices it is shown that three‐dimensional elastic waves, cylindrical P‐SV waves, acoustic waves, and electromagnetic waves in isotropic layered media can all be represented by an equation with the same properties. The symmetry properties of...

The apparent attenuation of a scattering medium

Abstract: We report the results of some numerical experiments that bring out the lowpass characteristics of a purely elastic medium with a heterogeneous velocity structure. Although the typical fluctuation is spatially confined within less than a wavelength, waves propagating over a sufficiently long path suffer major cumulative effects. We summarize the removal of high frequencies during transmission by a frequency-independent apparent Q, and show that attenuation by intrinsic friction and scattering are approximately additive. We propose some diagnostics that might help to distinguish the presence of velocity fluctuations and resultant scattering from the presence of anelasticity and true dissipation. When scattering dominates over intrinsic friction: (1) the coda of a transmitted wave contains relatively higher frequencies than the initial pulse; (2) the attenuation deduced from the power spectrum of the transmitted wave is greater than that deduced from the phase spectrum; (3) compressional and shear wave apparent Q's are approximately equal; and (4) estimates of apparent Q made from reflected coda vary with frequency, while estimates made from the transmitted waves do not. We also outline several topics in the theory of wave propagation that will be relevant in a satisfactory interpretation of short-period observations, if the amplitude of such signals is affected by scattering.

Multiple phase-screen calculation of the temporal behavior of stochastic waves

Abstract: An analytical/numerical technique is presented that provides a solution to the parabolic wave equation and allows for direct calculation of the received time-domain signal after propagation of a wide-bandwidth waveform through a turbulent ionized medium. The results are applicable to the case of satellite communication or to radar observation through a frequency-selective transionospheric propagation channel. A number of examples of the application of multiple phase-screen (MPS) techniques are given that enhance intuitive understanding of wave propagation. Numerical predictions of scattering through a striated barium cloud are compared to experimental observations. Good agreement is also shown between MPS calculations and theoretical results for cases in both weak and strong scattering regimes.

Plasma rest frame frequencies and polarizations of the low-frequency upstream waves: ISEE 1 and 2 Observations

Abstract: The plasma rest frame frequencies and polarizations of the large amplitude low frequency (0.03 Hz) upstream waves are investigated using magnetic field data from the dual ISEE 1 and 2 spacecraft. The monochromatic sinusoidal waves associated with intermediate ion fluxes are propagating in both the Alfven and magnetosonic modes, in both cases with typical frequencies approximately 0.1 times the local proton gyrofrequency and wavelengths of approximately 1 R(E). It is shown that the generation of the magnetosonic mode can be explained by the cyclotron resonance mechanism driven by narrow reflected ion beams, but the concurrent observation of Alfven mode waves appears to require wave generation by the more isotropic diffuse ion distributions as well.

The interaction of waves and a turbulent current: waves propagating against the current

Abstract: The results of an experimental study of the interaction between waves and a current propagating in the same direction, have been reported by Kemp & Simons (1982). This paper describes the second part of the study, and considers the case of waves propagating against the current. Tests were performed in a laboratory flume with smooth and rough beds, and velocity measurements were made with a directionally sensitive laser anemometer as described in the previous paper. Analysis, including ensemble averaging of velocities and surface elevation, was performed by an on-line computer. Results indicate that the rate of wave attenuation is greatly increased by the addition of an opposing current, and reduced by a following current. Wave profiles remain closely described by Stokes second-order theory; orbital velocities are also found to be in agreement with a second-order wave theory modified to take account of the presence of the current. Certain results described occur regardless of the relative directions of current and wave. Mean velocities in the upper flow increase in the direction of the wave generator for increasing wave height. This suggests that the current is enhancing the wave-induced mass transport. Near the bed the velocity profiles so change that above the rough bed the current is retarded by the wave motion. In the logarithmic layer over the smooth bed velocities are increased with increasing wave height. However, all changes to velocity profiles have to be carefully interpreted, as the sidewall boundary layer decreases in thickness with even the smallest wave superimposed on the current. Turbulence intensities and Reynolds stresses near the rough bed are increased by the presence of the waves, most strongly in a layer two roughness heights above bed level, where fluctuations are periodic and effected by vortices ejected from the roughness troughs. Above this level, and over the smooth bed, turbulence levels are similar to those for the currents alone.

Kelvin:Helmholtz Instability at the magnetopause: Solution for compressible plasmas

Abstract: The Kelvin-Helmholtz (K-H) instability of a tangential discontinuity in a compressible plasma is reexamined in the linear magnetohydrodynamic (MHD) approximation. For fixed plasma conditions, two different kinds of surface waves (labeled F for fast and S for slow) may exist simultaneously with different tangential wave vectors k/sub t/. The surface waves can be excited only for a limited range of U, the relative flow speed of the plasmas on the two sides of the interface. Thus the instability requires U/sub c/m or approx. =U/sub i/, but the slow wave growth rate is small in comparison with both epsilon/sub F/ and epsilon/sub i/. Consequently, plasma compressibility is relatively ineffective in reducing the critical velocity for surface wave growth below that for an incompressible plasma.

Transverse elastic waves in periodically layered infinite and semi-infinite media

Abstract: The propagation of transverse elastic waves both perpendicular and parallel to the laminations of infinite and semi-infinite periodically layered media is studied. The displacement fields and the dispersion relations for such waves are obtained analytically, and the latter are solved numerically to yield the corresponding dispersion curves. It is shown that a semi-infinite medium layered periodically parallel to its stress-free surface can support shear horizontal surface acoustic waves that have no counterpart in a homogeneous medium. Finally, the dynamical elastic Green's function for a semi-infinite medium layered periodically parallel to its stress-free surface is obtained, and its possible application to Brillouin scattering studies of the surface acoustic waves on such a medium is discussed.

Weakly nonlinear high frequency waves

Abstract: : In this paper we derive a method for finding small amplitude high frequency solutions to hyperbolic systems of quasilinear partial differential equations. Our solution is the sum of two parts: (i) a superposition of small amplitude high frequency waves; (ii) a slowly varying 'mean solution'. Each high frequency wave displays nonlinear distortion of the wave profile and shocks may form. Shock conditions are derived for conservative systems. Different high frequency waves do not interact provided the frequencies and wave numbers of two waves are not linearly related to those of a third. The mean solution is found by solving a linear partial differential equation. This method generalizes Whitham's nonlinearization technique 9 for single waves, to problems where many waves are present. We obtain these results by generalizing a scheme first proposed by Choquet-Bruhat 1 which employs the method of multiple scales. (Author)

Waves observed upstream of interplanetary shocks

Abstract: The properties of the waves that are present upstream of interplanetary, collisionless, quasi-parallel shocks are described. Two types of such waves have been detected, a higher frequency whistler mode wave and a lower frequency fast mode MHD wave. Both are typically circular or elliptically polarized right-hand waves which propagate along the ambient magnetic field with a 15 deg angle cone. The high frequency waves have sufficient group velocities to outrun the shock, and may be generated by cyclotron resonance with 100 eV to 1 keV shock electrons. The lower frequency waves must be generated locally by particles upstream of the shock, probably by 1-10 keV ions flowing away from the shock. Distinct changes in the spectra of upstream waves as a function of distance from the shock have been noted.

Beam propagation in uniaxial anisotropic media

Abstract: Paraxial wave equations are derived for the propagation of beams in uniform uniaxial anisotropic media. The equations are generalized to the case of nonuniform media with weakly varying refractive indices. An ordinary wave beam is governed by a standard paraxial equation, whereas an extraordinary wave beam is governed by a paraxial wave equation, which involves both a displacement relative to the position of an ordinary wave beam and a rescaling of one transverse coordinate. The solution to the latter equation for a propagating Gaussian beam displays a distortion of both shape and phase front. Numerical results for diffraction by a uniformly illuminated circular aperture in a calcite medium display various anomalies ascribable to a loss of circular symmetry.

Analysis of anisotropic dielectric gratings

Abstract: A method for analyzing slanted anisotropic gratings is presented. The propagation of electromagnetic waves in the periodic anisotropic media is described by coupled-wave equations in a unified matrix form expressing the coupling of the space harmonics in the grating region. The solution of the equations is reduced to an eigenvalue problem of this coupling matrix. Through introduction of the concepts of transmission and boundary matrices, the diffraction properties of general slanted gratings are obtained rigorously by systematic matrix calculations that are easily implemented on a computer. The calculated results indicate that not only TE–TE or TM–TM but also TE–TM diffractions take place in general slanted gratings.

The rate of occurrence of dayside Pc 3,4 pulsations: The L‐value dependence of the IMF cone angle effect

Abstract: When the angle of the IMF to the earth sun line is 15 deg or less, the occurrence rate of dayside Pc 3,4 pulsations in 7-8 times the average at L values of 2.4-2.8, and 2.2-3.5 times the average at L of 4-4.3. These waves disappear when the IMF is nearly at right angles to the sun-earth line. Such observations are consistent with a source originating in the waves upstream of the subsolar bow shock, which are transported by convection to the magnetopause. There, they couple to oscillations of magnetospheric field lines. Because the magnetospheric plasma's index of refraction decreases with radial distance except at the plasmapause, inwardly propagating waves should be refracted away from the radial direction. To reach low L values, the waves should therefore couple near the stagnation point and propagate nearly radially inwards. The streamline geometry and its connection to the foreshock region is illustrated for various IMF orientations, using a simple approximation to the magnetosheath flow field.

Oblique incidence of a strong electromagnetic wave on a cold inhomogeneous electron plasma. Relativistic effects

Abstract: A method which simplifies the investigation of the form of an obliquely incident wave on a plane parallel layered plasma by reducing it to the case where the wave is normally incident is presented. The resonance at N0=Nc (critical density) is discussed. Another resonance at N0=4Nc is described.

Differential methods in inverse scattering

Abstract: This paper discusses a new set of differential methods for solving the inverse scattering problem associated to the propagation of waves in an inhomogeneous medium. By writing the medium equations in the form of a two-component system describing the interaction of rightward and leftward propagating waves, the causality of the propagation phenomena is exploited in order to identify the medium layer by layer. The recursive procedure that we obtain constitutes a continuous version of an algorithm first derived by Schur in order to test for the boundedness of functions analytic inside the unit circle. It recovers the local reflectivity function of the medium. Using similar ideas, some other differential methods can also be derived to reconstruct alternative parametrizations of the layered medium in terms of the local impedance or of the potential function.The differential inverse scattering methods turn out to be very efficient since, in some sense, they let the medium perform the inversion by itself and thus...

On the origin of plasmaspheric hiss: Ray path integrated amplification

Abstract: An investigation has been made of processes responsible for the growth, damping, and propagation characteristics of whistler mode emissions within the earth's plasmasphere. Three-dimensional ray path calculations of the integrated wave gain in a realistic model plasmasphere have provided an explicit confirmation of the anisotropic electron cyclotron resonant generation mechanism for the maintenance of plasmaspheric hiss. Peak wave amplification occurs for field-aligned waves in the outer plasmasphere. The majority of unstable low-frequency waves follow ray trajectories that internally reflect at the plasmapause and are thus trapped within the plasmasphere. This reflection allows waves to subsequently propagate into the locally stable inner and middle plasmasphere and also migrate substantially in longitude. The combination of internal reflection at the plasmapause and magnetospheric reflection at high latitude provide an important class of wave trajectories that are recycled back to the equatorial growth region with sufficiently small wave normal angles to allow further cyclotron resonant amplification. It is unlikely that wave growth can occur from the natural incoherent emissivity level within the plasmasphere since the required gains (≈100 dB) would mandate unreasonably high energetic electron flux. An alternate, as yet unidentified, embryonic source is therefore required to initiate the growth process. But once established the observed spectrum of broad band plasmaspheric hiss can be maintained by the modest net gains anticipated along ray trajectories that are recycled back to the favorable equatorial growth region. A simulation of the spectral properties of waves arriving at selected observation points following several equatorial transits shows that the largest accumulated gain occurs for recycled waves that reflect from the plasmapause following each equatorial crossing. Furthermore, the peak gain is relatively insensitive to the location of the observation point, and waves are expected to arrive over a broad solid angle in k space consistant with observations. The ability of waves to gain access to regions far from the source is a direct result of the relatively weaker Landau damping of oblique waves along the high latitude portion of the recycled ray path in comparison to the equatorial cyclotron resonant growth. The hiss upper frequency cutoff can result from the limited anisotropy of the cyclotron resonant electrons, the more severe Landau damping at higher frequencies, or in part, from the decreased ability of the higher frequency waves to recycle and thus experience multitransit growth. The characteristic lower frequency cutoff can be due to either the decrease in flux of energetic electrons that cyclotron resonate with the lower frequency waves or from thermal electron Landau damping should the plasmaspheric electron temperature exceed several electron volts.

Linear and nonlinear modified electron-acoustic waves

Abstract: It is shown that a modified electron-acoustic wave exists in a plasma with distinct hot and cold electron components. The frequency of this wave depends strongly on the cold electron number density. Solitons associated with the modified electron-acoustic waves are also discussed.

Modulational instability of finite amplitude dispersive Alfvén waves

Abstract: The stability of a finite amplitude plane monochromatic circularly polarized Alfven wave is studied by using an approximate two-fluid model obtained by performing an amplitude and dual time scale expansion in which temporal changes, observed when moving with the wave, are assumed slow. The lowest order dispersive effects and coupling terms to sound waves are of the same order. A large-amplitude Alfven wave obeying an approximate dispersion relation is an exact solution of the resulting model equations. Small perturbations of this solution consisting of two sideband Alfven waves and a sound wave are then introduced. The resulting dispersion relation, which is of fourth order, is examined analytically for small wave amplitudes of the parent wave. It reveals different regions of stability and instability in a plot of wave number k0 of the unperturbed wave versus β0, the ratio of sound speed to Alfven speed. For long wave lengths, the left-hand polarized mode is found to be stable for β0 > 1 and the right-hand polarized mode for β0 1. Decay instability is predicted near β0 = 0 and β0 = 1. Formulas for growth rates and unstable wave number bands are given.

Wave propagation through random media: Contributions from ocean acoustics

Abstract: Recent theoretical and experimental progress in understanding sound transmission through a random field of internal waves is reviewed. Some attempt is made to place this work in historical relation to similar efforts in radio-wave propagation through the ionosphere and light propagation through the atmosphere. It is emphasized that internal waves as a random medium possess several new features unfamiliar to those dealing with homogeneous isotropic turbulence. The effect of a background deterministic wave-speed variation (the ocean sound channel) is central to the theoretical treatment, which is based on a path-integral solution of the parabolic wave equation. A distinction is made between two sections of the saturated region and some emphasis is placed on the region of partial saturation. Comparison with experiment is discussed with examples from the two-point mutual coherence function of time, frequency, and vertical separation; the intensity correlation in time, frequency, and vertical separation; the spectra of phase and log intensity, pulse propagation, and the higher moments of intensity.

Steady wind- and wave-induced currents in the open ocean

Abstract: Steady wind-drift currents in a deep viscous rotating ocean are studied theoretically. The analysis is based on the Lagrangian description of motion. A mean wind-stress at the surface yields the traditional Ekman current. In addition, the wind-stress is assumed to contain a fluctuating part which transfers energy to the surface waves and compensates for loss due to viscous dissipation. The induced drift due to such waves is investigated. The wave-drift depends on the eddy viscosity as well as the earth's rotation. We assume a fully developed sea, and take the eddy viscosity to be proportional to the friction velocity times a characteristic depth. Hence the total current (Ekman current plus wave-induced current) can be expressed as functions of the wind speed. The results show that the magnitude of the total surface current lies between 3.1 and 3.4% of the wind speed at 10 m height for winds between 5 and 30 m s−1. The deflection angle away from the wind direction varies from 23 to 30° in this ran...