Showing papers on "Wave propagation published in 1987"

The runup of solitary waves

Abstract: This is a study of the runup of solitary waves on plane beaches. An approximate theory is presented for non-breaking waves and an asymptotic result is derived for the maximum runup of solitary waves. A series of laboratory experiments is described to support the theory. It is shown that the linear theory predicts the maximum runup satisfactorily, and that the nonlinear theory describes the climb of solitary waves equally well. Different runup regimes are found to exist for the runup of breaking and non-breaking waves. A breaking criterion is derived for determining whether a solitary wave will break as it climbs up a sloping beach, and a different criterion is shown to apply for determining whether a wave will break during rundown. These results are used to explain some of the existing empirical runup relationships.

Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities

Abstract: The interaction of a plane weak shock wave with a single discrete gaseous inhomogeneity is studied as a model of the mechanisms by which finite-amplitude waves in random media generate turbulence and intensify mixing. The experiments are treated as an example of the shock-induced Rayleigh-Taylor instability. or Richtmyer-Meshkov instability, with large initial distortions of the gas interfaces. The inhomogeneities are made by filling large soap bubbles and cylindrical refraction cells (5 cm diameter) whose walls are thin plastic membranes with gases both lighter and heavier than the ambient air in a square (8.9 cm side shock-tube text section. The wavefront geometry and the deformation of the gas volume are visualized by shadowgraph photography. Wave configurations predicted by geometrical acoustics, including the effects of refraction, reflection and diffraction, are compared to the observations. Departures from the predictions of acoustic theory are discussed in terms of gasdynamic nonlinearity. The pressure field on the axis of symmetry downstream of the inhomogeneity is measured by piezoelectric pressure transducers. In the case of a cylindrical or spherical volume filled with heavy low-sound-speed gas the wave which passes through the interior focuses just behind the cylinder. On the other hand, the wave which passes through the light high-sound-speed volume strongly diverges. Visualization of the wavefronts reflected from and diffracted around the inhomogeneities exhibit many features known in optical and acoustic scattering. Rayleigh-Taylor instability induced by shock acceleration deforms the initially circular cross-section of the volume. In the case of the high-sound-speed sphere, a strong vortex ring forms and separates from the main volume of gas. Measurements of the wave and gas-interface velocities are compared to values calculated for one-dimensional interactions and for a simple model of shock-induced Rayleigh-Taylor instability. The circulation and Reynolds number of the vortical structures are calculated from the measured velocities by modeling a piston vortex generator. The results of the flow visualization are also compared with contemporary numerical simulations.

Nonlinear pulse propagation in birefringent optical fibers

Abstract: Equations describing nonlinear pulse propagation in birefringent, single-mode fibers are derived. The physical meaning and technical implications of these equations are then discussed in detail. Finally, the modulational instability is studied.

Stability and Instability of Solitary Waves of Korteweg-de Vries Type

Abstract: Considered herein are the stability and instability properties of solitary-wave solutions of a general class of equations that arise as mathematical models for the unidirectional propagation of weakly nonlinear, dispersive long waves. Special cases for which our analysis is decisive include equations of the Korteweg-de Vries and Benjamin-Ono type. Necessary and sufficient conditions are formulated in terms of the linearized dispersion relation and the nonlinearity for the solitary waves to be stable.

Stability of solitons in birefringent optical fibers. I: Equal propagation amplitudes

Abstract: The effect of birefringence on soliton propagation in single-mode optical fibers is considered. Emphasis is on solitons with multipicosecond widths that are appropriate for communications applications. It is shown that while linear birefringence will lead to a substantial splitting of the two polarizations over 20 km, this effect can be eliminated by use of the Kerr nonlinearity. Above a certain amplitude threshold, the central frequency of each polarization shifts just enough to lock the two polarizations together.

Computational aspects of the choice of operator and sampling interval for numerical differentiation in large-scale simulation of wave phenomena*

Abstract: Conventional finite-difference operators for numerical differentiation become progressively inaccurate at higher frequencies and therefore require very fine computational grids. This problem is avoided when the derivatives are computed by multiplication in the Fourier domain. However, because matrix transpositions are involved, efficient application of this method is restricted to computational environments where the complete data volume required by each computational step can be kept in random access memory. To circumvent these problems a generalized numerical dispersion analysis for wave equation computations is developed. Operators for spatial differentiation can then be designed by minimizing the corresponding peak relative error in group velocity within a spatial frequency band. For specified levels of maximum relative error in group velocity ranging from 0.03% to 3%, differentiators have been designed that have the largest possible bandwidth for a given operator length. The relation between operator length and the required number of grid points per shortest wavelength, for a required accuracy, provides a useful starting point for the design of cost-effective numerical schemes. To illustrate this, different alternatives for numerical simulation of the time evolution of acoustic waves in three-dimensional inhomogeneous media are investigated. It is demonstrated that algorithms can be implemented that require fewer arithmetic and I/O operations by orders of magnitude compared to conventional second-order finite-difference schemes to yield results with a specified minimum accuracy.

The Synoptic Setting and Possible Energy Sources for Mesoscale Wave Disturbances

Abstract: Published data on 13 cases of mesoscale wave disturbances and their environment were examined to isolate common features for these cases and to determine possible energy sources for the waves. These events are characterized by either a singular wave of depression or wave packets with periods of 1-4 h, horizontal wavelengths of 50-500 km, and surface-pressure perturbation amplitudes of 0.2-7.0 mb. These wave events are shown to be associated with a distinct synoptic pattern (including the existence of a strong inversion in the lower troposphere and the propagation of a jet streak toward a ridge axis in the upper troposphere) while displaying little correlation with the presence of convective storm cells. The observed development of the waves is consistent with the hypothesis that the energy source needed to initiate and sustain the wave disturbances may be related to a geostrophic adjustment process associated with upper-tropospheric jet streaks.

Leakage from higher modes on microstrip line with application to antennas

Abstract: Some confusion in the literature is clarified regarding the properties of microstrip-line higher modes in the neighborhood of cutoff. It is shown that those modes become leaky in that range; with the aid of the steepest-descent plane, one finds that the continuous spectrum can be characterized in a highly convergent manner by essentially a single leaky mode. The leakage occurs in two forms: a surface wave and a space wave. For structures without a top cover, it is found that almost all of the leakage is in the form of a space wave, so that an efficient leaky-wave antenna of particularly simple configuration may be designed that consists of just a length of uniform microstrip line fed in its first higher mode. An accurate leaky-wave analysis is developed that explains quantitatively the performance features and the limitations of this class of antennas.

Light Propagation in Singly and Doubly Periodic Planar Waveguides

Abstract: Light propagation in singly and doubly periodic planar waveguides is investigated with respect to future applications in integrated optics. The waveguides used in our experiments reveal, in the vicinity of Bragg reflection, a strong difference between the directions of phase and group velocities, the beam steering. A clear graphical representation of the observable propagation effects is given in wave-vector diagrams, showing the directional dispersion of the elementary waves in periodic structures, the Floquet-Bloch waves. The dispersion phenomena were measured with high accuracy, using selective wave excitation. In conjunction with straight tapered transitions to smooth planar waveguides, the periodic structures show a great variety of strong frequency and direction-dependent effects such as lateral beam shifting and focusing with a frequency-variant focal length. Ray optics of Floquet-Bloch waves is used to describe these phenomena. Complex interference patterns observable in the vicinity of B...

Influence of interfacial waves in stratified gas‐liquid flows

Abstract: Interfacial stresses are calculated from new measurements of liquid height and pressure drop for fully developed horizontal stratified flow. These are related to wave properties. An improved design method is suggested.

Acoustic Absorption by Sunspots

Abstract: The paper presents the initial results of a series of observations designed to probe the nature of sunspots by detecting their influence on high-degree p-mode oscillations in the surrounding photosphere. The analysis decomposes the observed oscillations into radially propagating waves described by Hankel functions in a cylindrical coordinate system centered on the sunspot. From measurements of the differences in power between waves traveling outward and inward, it is demonstrated that sunspots appear to absorb as much as 50 percent of the incoming acoustic waves. It is found that for all three sunspots observed, the amount of absorption increases linearly with horizontal wavenumber. The effect is present in p-mode oscillations with wavelengths both significantly larger and smaller than the diameter of the sunspot umbrae. Actual absorption of acoustic energy of the magnitude observed may produce measurable decreases in the power and lifetimes of high-degree p-mode oscillations during periods of high solar activity.

Existence and dynamic stability of solitary wave solutions of equations arising in long wave propagation

Abstract: We obtain conditions for the nonlinear stability (Theorem 5.1) of solitary waves fro two classes of nonlinear dispersive equations which arise in the mathematical description of long wave propagation:(u is in general complex-valued), where the linear operator L, typically nonlocal, and the nonlinearity, are of some general class.For the case of homogeneous nonlinearities, A(u), a new variational characterization of solitary waves for I and II is presented (Theorem 3.1) and is exploited in the dynamic stability analysis. The existence of solitary waves in higher dimensions is also considered (Theorem 7.1).

a Method for Detection of Diffracted Waves on Common-Offset SECTIONS*

Abstract: A method of detection of diffracted waves on common-offset sections is proposed. The method utilizes the main kinematic and dynamic properties of the diffracted waves. The detection algorithm is defined by an automatic procedure including phase correlation of the diffracted waves and the application of certain statistical criteria. This procedure enables one to make decisions with regard to the presence of the diffracted waves and also to estimate parameters of the scattering objects. The method is applied to synthetic and field data and, even for a relatively low signal-to-noise ratio, it gives reliable results.

The effect of crustal structure on strong ground motion attenuation relations in eastern North America

Abstract: Strong ground motion attenuation relations are usually described by smoothly decreasing functions of distance. However, consideration of wave propagation in the crust suggests that attenuation relations should be more complex. Such complexity may be present in strong ground motion data for eastern North American earthquakes, which show amplitudes in the distance range of 60 to 150 km that lie above the trends at smaller and greater distances. Using a wavenumber integration method to compute Green's functions and close-in recordings of several earthquakes as empirical source functions, we have generated synthetic seismograms that are in good agreement with regional and strong-motion recordings of eastern North American earthquakes. From these synthetic seismograms, we have shown that the observed interval of relatively high amplitudes may be attributable to postcritically reflected S waves from the Moho. The presence and location of the interval of relatively high amplitudes is highly dependent on the crustal velocity structure and may therefore be expected to show regional variation. However, for any realistic structure model, there will be a transition in the attenuation relation from an interval at shorter distances (less than about 100 km) that is dominated by direct waves to an interval at greater distances that is dominated by postcritically reflected waves. The synthetic seismograms have response spectral velocities that match those of the recorded data, and their m_(bLg) values are in good agreement with observed values.

Data and theory for a new model of the horizontal structure of rain cells for propagation applications

Abstract: A large population of radar-measured ground rain cells is used to devise and assess a rain cell model for use in some of the future telecommunication applications. The model is based on cells of exponential profile (which is shown to reproduce best the point rain rate CDF); both rotational and biaxial symmetries are considered for the horizontal cross sections. Furthermore, the proposed model contains analytical expressions for the joint probability densities of the parameters which define the cell, i.e., peak rain intensity, cell size and axial ratio. Finally, an algorithm is given for adapting the model to the characteristics of any given site: this algorithm requires as input the local cumulative distribution of point rainfall and provides the spatial number densities (i.e., the average number of cells per square kilometer and per unit range of the parameters) which this distribution would produce. The model offers the possibility of predicting the statistics of many propagation parameters (such as attenuation or interference by rain scattering) which are determined by the rain cell characteristics and their frequency of occurrence.

Optical transmission in disordered media.

Abstract: The scale dependence of transmission in wedged random media containing titania microstructures is measured. The diffusion coefficient and absorption length are determined from the total transmission versus thickness. These parameters are observed to determine the scale dependence of the correlation frequency of fluctuations in intensity within the transmitted speckle pattern as the laser frequency is scanned. Mean free paths as short as 1.4 and 0.35 \ensuremath{\mu}m are observed.

Inhomogeneous wave generation and propagation in lossy anisotropic solids. Application to the characterization of viscoelastic composite materials

Abstract: This article develops a method for investigating some anisotropic media, such as composites, by the use of ultrasonic waves transmitted through a plate‐shaped sample immersed in water. The discussion begins with Christoffel’s equations for plane linear anelastic waves under the assumptions that for small angles of incidence the wave modes are plane and inhomogeneous and that the anisotropy is representable by hexagonal symmetry. The water–sample interface is treated using the law of Snell–Descartes for nonabsorbing media and takes into account mode conversion and the generation of acoustic surface waves. The method produces viscoelastic constants and relative attenuation coefficients as a function of the angle of refraction. The experimental measurement apparatus is described and data are given for the 25‐layer unidirectional Gr/epoxy composite. Results are presented in terms of slowness, damping vector, and attenuation curves. The results are significant in that they demonstrate the anisotropy both for t...

Numerical study of ribbon-induced transition in Blasius flow

Abstract: The early three-dimensional stages of transition in the Blasius boundary layer are studied by numerical solution of the Navier-Stokes equations. A finite-amplitude two-dimensional wave and low-amplitude three-dimensional random disturbances are introduced. Rapid amplification of the three-dimensional components is observed and leads to transition. For intermediate amplitudes of the two-dimensional wave the breakdown is of subharmonic type, and the dominant spanwise wavenumber increases with the amplitude. For high amplitudes the energy of the fundamental mode is comparable to the energy of the subharmonic mode, but never dominates it; the breakdown is of mixed type. Visualizations, energy histories, and spectra are presented. The sensitivity of the results to various physical and numerical parameters is studied. The agreement with experimental and theoretical results is discussed.

Applied seismic wave theory

Abstract: Introduction. I. Capita Selecta from Vector Analysis. Scalar product, gradient, curl and divergence. Theorem of Stokes, theorem of Gauss and Green's theorem. II. One-Dimensional Discrete Spectral Analysis. The delta pulse and discrete functions. Fourier series of periodic time functions. Fourier integral of transients. Relationship between the discrete property and periodicity. Sampling and aliasing in time and frequency. Matrix formulations. Decomposition of a broad band experiment into monochromatic simulations. III. Multi-Dimensional Discrete Spectral Analysis. Basic theory. Spatial aliasing. Two-dimensional spectral analysis and plane wave decomposition. Extensions to three dimensions. IV. Vibrations. Basic concepts. Free vibrations. Forced vibrations. Coupled systems. From vibrations to waves. V. Acoustic Waves. Derivation of the acoustic wave equation. One-way versions of the acoustic wave equation. Plane waves. Spherical waves. Cylindrical waves. Principle of numerical modeling with the acoustic wave equation. VI. Elastic Waves. Compressional waves in homogeneous isotropic solids. Shear waves in homogeneous isotropic solids. Derivation of the elastic wave equation. One-way versions of the elastic wave equation. Principle of numerical modeling with the elastic wave equation. VII. Boundary Conditions. Reflection and transmission coefficients for acoustic boundaries. Reflection in terms of convolution. The fluid-solid boundary. Reflection and transmission coefficients for elastic boundaries. Summary. VIII. Kirchhoff and Rayleigh Integrals. Derivation of the Kirchhoff integral for homogeneous media. Derivation of the Rayleigh integrals for homogeneous media. Rayleigh integrals in terms of convolution. Transformation of Rayleigh integrals to the wave number domain. Kirchhoff and Rayleigh integrals for inhomogeneous fluid-like media. Rayleigh integrals as one-way versions of the Kirchhoff integral. Discrete version of the Kirchhoff integral. Discrete versions of the Rayleigh integrals. Summary. IX. Directivity Properties of Wave Fields. Fraunhofer approximations in terms of the Fourier integral. Directivity patterns. Far field expressions of scattered wave fields. Summary. X. Forward and Inverse Problems. Principle of one-way forward wave field extrapolation. Principle of one-way inverse wave field extrapolation. Principle of two-way techniques. Example. Summary. (Each chapter includes an introduction and references). Appendices. Subject Index.

Linear plane waves in dissipative relativistic fluids.

Abstract: This paper analyzes the dispersion relations for linear plane waves in the Eckart and the Israel-Stewart theories of dissipative relativistic hydrodynamics. We show that in the long-wavelength (compared to a typical mean-free-path-length) limit the complicated dynamical structure of the Israel-Stewart theory reduces to the familiar dynamics of classical fluids: 9 of the 14 modes of an Israel-Stewart fluid are strongly damped in this limit, two propagate at the adiabatic sound speed (with appropriate viscous and thermal damping), two transverse shear modes decay at the classical viscous damping rate, and the final longitudinal mode is damped at the classical thermal diffusion rate. The short-wavelength limit of these dispersion relations is also examined. We demonstrate that the phase and group velocities of these waves must approach the characteristic velocities in the short-wavelength limit. Finally, we show how some of the perturbations of an Eckart fluid violate causality.

A dynamical-chemical model of wave-driven fluctuations in the OH nightglow

Abstract: Wave-induced temporal fluctuations in the intensity of the OH nightglow are related to the temperature oscillations of the wave field by a model that incorporates a five-reaction photochemical scheme and the complete dynamics of linearized acoustic-gravity waves in an isothermal, motionless atmosphere. The intensity I and rotational temperature T oscillations, δI and δT, are conveniently related by the ratio, where the overbar refers to time-averaged quantities. The ratio η is a complex quantity that depends on the properties of the basic state atmosphere (temperature, thermodynamic parameters, major constituent O2, N2 and minor constituent O, O3, OH, H, HO2 concentrations, and scale heights), chemical reaction rate constants, wave period, horizontal wavelength, and direction of wave energy propagation (upward or downward). The intensity-temperature oscillation ratio η is evaluated for a nominal case corresponding to an altitude of about 83 km in a nightside model atmosphere with an atomic oxygen scale height of −2.8 km; horizontal wavelength λx is 100 km, and wave energy propagation is upward. Over a broad range of acoustic periods |η| varies between 7 and 8, and η is approximately in phase with the temperature fluctuations. At gravity wave periods, |η| decreases with increasing period from a maximum value of about 7.0; at a period of about 3 hours, |η| is about 1.8. The phase of η and δT are within 45° in the gravity wave regime. The main effect of order of magnitude changes in λx is the modification of the location and width (in period) of evanescent regions. At hour periods, |η| increases as the magnitude of atomic oxygen scale height decreases; at periods of several hours, |η| is about 1/3 greater for an atomic oxygen scale height of −2 km than for the nominal scale height. The amplitude of η is essentially independent of the direction of wave energy propagation, but the phase of η relative to that of δT depends on the upward or downward sense of energy propagation at periods in close proximity to the evanescent regime. The magnitude of η at gravity wave periods can depend sensitively on the altitude of the OH emission layer; higher OH emission heights give smaller values of |η| at 10-min periods, providing the O3 scale height is not too great. Neglect of minor constituent photochemistry in computing η is a tolerable approximation at acoustic wave periods, but it is entirely inadequate at gravity wave periods. Inclusion of dynamical effects is absolutely essential for a valid assessment of η at any period.

Electromagnetic shock waves from transmission lines.

Abstract: We have observed subpicosecond electrical pulses to propagate on 5-\ensuremath{\mu}m coplanar transmission lines at velocities faster than the phase velocity in the underlying dielectric. This situation produces an electromagnetic shock wave in a manner similar to Cherenkov radiation and electro-optic Cherenkov radiation. Using time-domain spectroscopy we have measured the strong frequency-dependent loss of energy in the propagating electrical pulse due to this radiation.

Instantaneous and time-averaged energy transfer in acoustic fields

Abstract: The fundamentals of energy transfer in an acoustic field are addressed and it is shown that describing the flux of energy in an acoustic field with the active intensity alone is inaccurate. A single active intensity vector describes only the time‐average energy flux at a point in space, but not where the energy came from nor where it is going. Consequently, the instantaneous intensity must be used to properly describe energy flux as a time‐dependent process. The phenomenon of the acoustic vortex is examined and, from the perspective of active intensity, it is seen to represent a resultant wave rotating around a zero pressure line or point at which the pressure phase is discontinuous. It is shown that this resultant wave travels with a phase speed cp, which is generally different than the plane‐wave phase speed c. The instantaneous intensity, however, shows that energy is flowing through the vortex and not with the resultant waves. Although the complex intensity vector is normally separated into the active...

Experimental Study of Instability Modes in a Three-dimensional Boundary Layer.

Abstract: Travelling waves in an unstable three-dimensional boundary layer are studied experimentally with the use of hot-wire anemometry. For the sake of realistic comparisons with stability theory, the tests were performed on a swept flat plate where infinite swept-wing conditions were approximated by means of contoured end plates. The required pressure gradient was imposed by a displacement body. The Reynolds number for the first appearance of travelling waves is roughly the same as that of stationary vortices. The frequencies of the most amplified waves depend on the Reynolds number. It is shown with the aid of a twin probe that in a more strongly amplified state, the travelling waves propagate in a direction different from that of the mean flow. Further upstream, where stationary waves first become visible in the oil-flow pattern, a uniform direction could not be identified. Under certain conditions, travelling waves of two frequency ranges are amplified that propagate in different directions. The present work is part of the transition experiment started at the DFVLR. It is closely connected to the theoretical work by Dallmann and Bieler.

Steepened magnetosonic waves at Comet Giacobini-Zinner

Abstract: Intense MHD waves at Comet Giacobini-Zinner were examined to investigate the mode and direction of wave propagation and thereby to provide important constraints on potential mechanisms for the wave origin in the vicinity of the comet. From observations of steepened wave forms, it is found that the waves must be propagating toward the sun but are blown back across the ICE spacecraft. The correlation between magnetic field magnitude and electron density enhancements indicates that these waves are fast magnetosonic mode emissions. The sense of rotation of the partial rotations are left-hand circularly polarized in the spacecraft frame, consistent with anomalously Doppler-shifted right-hand waves.