Showing papers on "Wave propagation published in 1999"
TL;DR: In this article, a third-generation spectral wave model for small-scale, coastal regions with shallow water, (barrier) islands, tidal flats, local wind, and ambient currents is verified in stationary mode with measurements in five real field cases.
Abstract: A third-generation spectral wave model (Simulating Waves Nearshore (SWAN)) for small-scale, coastal regions with shallow water, (barrier) islands, tidal flats, local wind, and ambient currents is verified in stationary mode with measurements in five real field cases. These verification cases represent an increasing complexity in two- dimensional bathymetry and added presence of currents. In the most complex of these cases, the waves propagate through a tidal gap between two barrier islands into a bathymetry of channels and shoals with tidal currents where the waves are regenerated by a local wind. The wave fields were highly variable with up to 3 orders of magnitude difference in energy scale in individual cases. The model accounts for shoaling, refraction, generation by wind, whitecapping, triad and quadruplet wave-wave interactions, and bottom and depth-induced wave breaking. The effect of alternative formulations of these processes is shown. In all cases a relatively large number of wave observations is available, including observations of wave directions. The average rms error in the computed significant wave height and mean wave period is 0.30 m and 0.7 s, respectively, which is 10% of the incident values for both.
1,082 citations
TL;DR: In this article, the operation principle of resonant channel add-drop filters based on degenerate symmetric and antisymmetric standing-wave modes has been described using group theoretical arguments.
Abstract: The operation principle of resonant channel add-drop filters based on degenerate symmetric and antisymmetric standing-wave modes has been described elsewhere using group theoretical arguments. In this paper, the analysis is carried out using coupling of modes in time. A possible implementation of such a filter is a four-port system utilizing a pair of identical single-mode standing wave resonators. The analysis allows a simple derivation of the constraints imposed on the design parameters in order to establish degeneracy. Numerical simulations of wave propagation through such a filter are also shown, as idealized by a two-dimensional geometry.
635 citations
TL;DR: The theory of exact boundary conditions for constant coefficient time-dependent problems is developed in detail, with many examples from physical applications as discussed by the authors, and an illustrative numerical example is given.
Abstract: We consider the efficient evaluation of accurate radiation boundary conditions for time domain simulations of wave propagation on unbounded spatial domains. This issue has long been a primary stumbling block for the reliable solution of this important class of problems. In recent years, a number of new approaches have been introduced which have radically changed the situation. These include methods for the fast evaluation of the exact nonlocal operators in special geometries, novel sponge layers with reflectionless interfaces, and improved techniques for applying sequences of approximate conditions to higher order. For the primary isotropic, constant coefficient equations of wave theory, these new developments provide an essentially complete solution of the numerical radiation condition problem. In this paper the theory of exact boundary conditions for constant coefficient time-dependent problems is developed in detail, with many examples from physical applications. The theory is used to motivate various approximations and to establish error estimates. Complexity estimates are also derived to compare different accurate treatments, and an illustrative numerical example is given. We close with a discussion of some important problems that remain open.
413 citations
27 May 1999
TL;DR: In this paper, the author sets up the foundations of the modern theory of conservation laws, describing the physical models and mathematical methods, leading to the Glimm scheme, and then takes the reader to the current state of knowledge in the subject.
Abstract: Systems of conservation laws arise naturally in physics and chemistry. To understand them and their consequences (shock waves, finite velocity wave propagation) properly in mathematical terms requires, however, knowledge of a broad range of topics. This book sets up the foundations of the modern theory of conservation laws, describing the physical models and mathematical methods, leading to the Glimm scheme. Building on this the author then takes the reader to the current state of knowledge in the subject.The maximum principle is considered from the viewpoint of numerical schemes and also in terms of viscous approximation. Small waves are studied using geometrical optics methods. Finally, the initial-boundary problem is considered in depth.Throughout, the presentation is reasonably self-contained, with large numbers of exercises and full discussion of all the ideas. This will make it ideal as a text for graduate courses in the area of partial differential equations.
405 citations
TL;DR: In this paper, wave transmission properties in one dimensional nonlinear lattices are discussed and the results from the theory of dynamical systems are used to investigate various aspects of wave transmission and wave localization.
362 citations
TL;DR: In this article, a heuristic model of irradiance fluctuations for a propagating optical wave in a weakly inhomogeneous medium is developed under the assumption that small-scale irradiance fluctuation fluctuations are modulated by large-scale fluctuations of the wave.
Abstract: A heuristic model of irradiance fluctuations for a propagating optical wave in a weakly inhomogeneous medium is developed under the assumption that small-scale irradiance fluctuations are modulated by large-scale irradiance fluctuations of the wave. The upper bound for small turbulent cells is defined by the smallest cell size between the Fresnel zone and the transverse spatial coherence radius of the optical wave. A lower bound for large turbulent cells is defined by the largest cell size between the Fresnel zone and the scattering disk. In moderate-to-strong irradiance fluctuations, cell sizes between those defined by the spatial coherence radius and the scattering disk are eliminated through spatial-frequency filtering as a consequence of the propagation process. The resulting scintillation index from this theory has the form σI2=σx2+σy2+σx2σy2, where σx2 denotes large-scale scintillation and σy2 denotes small-scale scintillation. By means of a modification of the Rytov method that incorporates an amplitude spatial-frequency filter function under strong-fluctuation conditions, tractable expressions are developed for the scintillation index of a plane wave and a spherical wave that are valid under moderate-to-strong irradiance fluctuations. In many cases the models also compare well with conventional results in weak-fluctuation regimes. Inner-scale effects are taken into account by use of a modified atmospheric spectrum that exhibits a bump at large spatial frequencies. Quantitative values predicted by these models agree well with experimental and simulation data previously published. In addition to the scintillation index, expressions are also developed for the irradiance covariance function of a plane wave and a spherical wave, both of which have the form BI(ρ)=Bx(ρ)+By(ρ)+Bx(ρ)By(ρ), where Bx(ρ) is the covariance function associated with large-scale fluctuations and By(ρ) is the covariance function associated with small-scale fluctuations. In strong turbulence the derived covariance shows the characteristic two-scale behavior, in which the correlation length is determined by the spatial coherence radius of the field and the width of the long residual correlation tail is determined by the scattering disk.
331 citations
TL;DR: In this article, the bifurcation, stability, and evolution of gravity and capillary-gravity waves are discussed. And the importance of surface tension effects on steep waves is studied.
Abstract: This review deals primarily with the bifurcation, stability, and evolution of gravity and capillary-gravity waves. Recent results on the bifurcation of various types of capillary-gravity waves, including two-dimensional solitary waves at the minimum of the dispersion curve, are reviewed. A survey of various mechanisms (including the most recent ones) to explain the frequency downshift phenomenon is provided. Recent significant results are given on “horseshoe” patterns, which are three-dimensional structures observable on the sea surface under the action of wind or in wave tank experiments. The so-called short-crested waves are then discussed. Finally, the importance of surface tension effects on steep waves is studied.
306 citations
TL;DR: The dispersion and dissipation properties of the discontinuous Galerkin method are investigated with a view to simulating wave propagation phenomena and are verified by the results from full numerical solutions of the simple scalar advection equation and the Euler equations.
274 citations
TL;DR: In this paper, a new method is developed to generate specific wave trains by using designed mass source functions for the equation of mass conservation, i.e., ∂ui∂xi = f(x, t), in the internal flow region.
Abstract: The flow motion of incompressible fluid can be described by Navier-Stokes equations with the continuity equation, which requires zero divergence of the velocity vector (i.e., ∂ui/∂xi = 0). A new method is developed to generate specific wave trains by using designed mass source functions for the equation of mass conservation, i.e., ∂ui∂xi = f(x, t), in the internal flow region. The new method removes the difficulty in specifying incident waves through an inflow boundary with the presence of strong wave reflection. Instead, only the open (radiation) boundary condition is needed in the simulation. By using different source functions, the writers are able to generate various wave trains, including the linear monochromatic wave, irregular wave, Stokes wave, solitary wave, and cnoidal wave. By comparing numerical results with analytical solutions, the writers have shown that the proposed method can accurately generate not only small amplitude waves but also nonlinear waves in both intermediate and shallow water...
273 citations
TL;DR: In this article, a model for the propagation of vibration in the ground from a stationary oscillating load applied via a railway track structure is presented, which includes the track as an infinite layered beam structure resting on a ground made up of infinite parallel homogeneous elastic layers.
207 citations
TL;DR: In this paper, the authors compared techniques for calculating broadband time histories of ground motion in the near field of a finite fault by comparing synthetics with the strong-motion data set for the 1994 Northridge earthquake.
Abstract: This article compares techniques for calculating broadband time histories of ground motion in the near field of a finite fault by comparing synthetics with the strong-motion data set for the 1994 Northridge earthquake. Based on this comparison, a preferred methodology is presented. Ground-motion-simulation techniques are divided into two general methods: kinematic- and composite-fault models. Green's functions of three types are evaluated: stochastic, empirical, and theoretical. A hybrid scheme is found to give the best fit to the Northridge data. Low frequencies ( 1 Hz) are calculated using a composite-fault model with a fractal subevent size distribution and stochastic, bandlimited, white-noise Green's functions. At frequencies below 1 Hz, theoretical elastic-wave-propagation synthetics introduce proper seismic-phase arrivals of body waves and surface waves. The 3D velocity structure more accurately reproduces record durations for the deep sedimentary basin structures found in the Los Angeles region. At frequencies above 1 Hz, scattering effects become important and wave propagation is more accurately represented by stochastic Green's functions. A fractal subevent size distribution for the composite fault model ensures an ω−2 spectral shape over the entire frequency band considered (0.1-20 Hz).
TL;DR: In this article, a compact and accurate approximation to the deceleration term, standing for the frictional effect, allows the retention of the concept of harmonics and separation of the time and space variations.
Abstract: The hydrodynamics of rivers affected by tides is dominated by the damping and the distortion induced by quadratic bottom friction. A compact and accurate approximation to the deceleration term, standing for the frictional effect, allows the retention of the concept of harmonics and separation of the time and space variations. It then becomes possible to explain, in terms of basic physics, the transformation of the tide from the estuary, to the zone where it becomes extinct. The theoretical reasoning is supported by pertinent observations collected in the Saint Lawrence river; numerical relations are derived to demonstrate the existence of non-linear effects and to quantitatively link various relevant physical parameters. This analysis, in turn, helps outline approaches to improve the tide predictions in such rivers which happen to have such great economic and strategic importance.
TL;DR: In this article, the dynamics of a viscous accretion disc subject to a slowly varying warp of large amplitude is considered, and the equations of fluid dynamics are derived in a coordinate system that follows the principal warping motion of the disc, and reduced using asymptotic methods for thin discs, and solved to extract the equation governing the warp.
Abstract: The dynamics of a viscous accretion disc subject to a slowly varying warp of large amplitude is considered. Attention is restricted to discs in which self-gravitation is negligible, and to the generic case in which the resonant wave propagation found in inviscid Keplerian discs does not occur. The equations of fluid dynamics are derived in a coordinate system that follows the principal warping motion of the disc. They are reduced using asymptotic methods for thin discs, and solved to extract the equation governing the warp. In general, this is a wave equation of parabolic type with non-linear dispersion and diffusion, which describes fully non-linear bending waves. This method generalizes the linear theory of Papaloizou & Pringle to allow for an arbitrary rotation law, and extends it into the non-linear domain, where it connects with a generalized version of the theory of Pringle. The astrophysical implications of this analysis are discussed briefly.
TL;DR: Both theoretical and experimental measurements show that the directivity pattern of a point source vibrator presents two very strong lobes for an angle around 35/spl deg/.
Abstract: For the last 10 years, interest has grown in low frequency shear waves that propagate in the human body. However, the generation of shear waves by acoustic vibrators is a relatively complex problem, and the directivity patterns of shear waves produced by the usual vibrators are more complicated than those obtained for longitudinal ultrasonic transducers. To extract shear modulus parameters from the shear wave propagation in soft tissues, it is important to understand and to optimize the directivity pattern of shear wave vibrators. This paper is devoted to a careful study of the theoretical and the experimental directivity pattern produced by a point source in soft tissues. Both theoretical and experimental measurements show that the directivity pattern of a point source vibrator presents two very strong lobes for an angle around 35/spl deg/. This paper also points out the impact of the near field in the problem of shear wave generation.
TL;DR: In this paper, the acoustical behavior of a 1D model of granular medium, which is a chain of identical spherical beads, is discussed, and the authors compare the predictions of the different models to experimental results that concern linear sound wave propagation in the chain submitted to a static force, and nonlinear solitary wave propagating in an unconstrained chain.
Abstract: We discuss the acoustical behavior of a 1D model of granular medium, which is a chain of identical spherical beads. In this geometry, we are able to test quantitatively alternative models to the Hertz theory of contact between elastic solids. We compare the predictions of the different models to experimental results that concern linear sound wave propagation in the chain submitted to a static force, and nonlinear solitary wave propagation in an unconstrained chain. We use elastic, elastic-plastic and brittle materials, the beads roughness extends on one order of magnitude, and we also use oxidized metallic beads. We demonstrate experimentally that at low static forces, for all types of beads, the linear acoustic waves propagate in the system as predicted by Hertz's theory. At larger forces, after onset of permanent plastic deformation at the contacts, the brass beads exhibit non Hertzian behavior, and hysteresis. Except in the case of brass beads, the nonlinear waves follow the predictions of Hertz theory.
TL;DR: In this article, the role of planetary waves in stratosphere-troposphere coupled variability is investigated using an extended singular value decomposition analysis of zonal-mean zonal wind and the vertical component of the Eliassen-Palm (E-P) flux for the winters from 1979/80 to 1995/96.
Abstract: The role of planetary waves in stratosphere-troposphere coupled variability is investigated using an extended singular value decomposition analysis of zonal-mean zonal wind and the vertical component of the Eliassen-Palm (E-P) flux for the winters from 1979/80 to 1995/96. The results suggest a close relationship between anomalies of zonal-mean zonal wind and the convergence zone of E-P flux, which together shift poleward and downward from the stratosphere to the troposphere as time advances. Following enhanced vertical propagation of waves into the stratosphere, the Arctic Oscillation (AO) pattern is seen in the 500 hPa geopotential height field in association with an increased poleward propagation of tropospheric waves.
TL;DR: In this article, the authors present strong evidence based on 2(1/2)D particle-in-cell simulations of the interaction of ultrashort, high-intensity laser pulses with underdense plasmas, of the formation of long-lived, slowly moving $(0.1c)$, low-frequency solitonlike electromagnetic waves.
Abstract: We present strong evidence, based on 2(1/2)D particle-in-cell simulations of the interaction of ultrashort, high-intensity laser pulses with underdense plasmas, of the formation of long-lived, slowly moving $(0.1c)$, low-frequency solitonlike electromagnetic waves. These nonlinear waves consist of electron-density depressions and intense cylindrical electromagnetic field concentrations with a larger amplitude and a lower frequency than those of the laser pulse.
TL;DR: A new and very fast ray-tracing method using a ray tube tree, which is based on uniform geometrical theory of diffraction (UTD) and can solve some of the problems that other ray- Tracing methods have.
Abstract: In this paper, we present a new and very fast ray-tracing method using a ray tube tree, which is based on uniform geometrical theory of diffraction (UTD) and can solve some of the problems that other ray-tracing methods have. It is developed for quasi three-dimensional (3-D) environments and can be applied to any complex propagation environment composed of arbitrary-shaped buildings and streets. It finds all propagation paths from a transmitter to a receiver extensively with very high computation efficiency. It is fundamentally a point-to-point tracing method, so reception tests are not required and it guarantees high accuracy. To validate our ray-tracing method, signal path loss and root mean square (rms) delay spread were computed in the downtown core of Ottawa, Canada, and they were also compared with the published measurements. The results of the proposed method in this paper show good agreement with the measurements. The computation time required to obtain a path loss map in the site is revealed to be very short in comparison with other methods.
TL;DR: In this article, a detailed study of the propagation properties of cosh-Gaussian (ChG) beams has been made, where the passage of ChG beams through a first-order paraxial optical ABCD system has been expressed in closed forms for both unapertured and apertured cases.
TL;DR: In this paper, the performance of high-frequency (HF) radars based on ground-wave propagation is used for remotely sensing ocean surface currents and gravity waves for some 20 years a number of systems have been developed taking advantage of improved electronics and computer techniques.
TL;DR: In this article, a method to measure the nonlinear effect of ultrasonic waves is suggested as a new approach for the effective evaluation of material degradation, which can be interpreted as the generation of higher order harmonic waves.
TL;DR: In this article, a semi-infinite photonic crystal can support electromagnetic wave propagation at its surface by using the supercell method, and the authors studied the properties of these (nonradiative) modes in crystals of two-dimensional periodicity constituted by parallel rods of square cross section.
Abstract: A semi-infinite photonic crystal can support electromagnetic wave propagation at its surface By using the supercell method, we studied in detail the properties of these (nonradiative) modes in crystals of two-dimensional periodicity constituted by parallel rods of square cross section The rods cut the plane of periodicity (001) at the sites of a square lattice, and the sides of the rods have the same orientation as the lattice We have performed calculations for crystals of air cylinders in a dielectric background The Bloch-type surface waves are assumed to propagate at the (100) surface in the [010] direction For both transverse electric and transverse magnetic polarizations, we found that the dispersion curves of the surface modes and their field confinements at the surface are strongly dependent on the crystal termination, that is, on the position of the cut plane through the rods We also found that the degree of localization of the fields at the surface depends on the position of the mode within the band gap Plots of the field intensity show that the TM waves are more strongly localized than the TE waves
TL;DR: In this paper, a discrete-time wave-propagation method was proposed to calculate the seismic response of multistory buildings, founded on layered soil media and subjected to vertically propagating shear waves.
Abstract: This paper presents a discrete-time wave-propagation method to calculate the seismic response of multistory buildings, founded on layered soil media and subjected to vertically propagating shear waves. Buildings are modeled as an extension of the layered soil media by considering each story as another layer in the wave-propagation path. The seismic response is expressed in terms of wave travel times between the layers and wave reflection and transmission coefficients at layer interfaces. The method accounts for the filtering effects of the concentrated foundation and floor masses. Compared with commonly used vibration formulation, the wave-propagation formulation provides several advantages, including simplicity, improved accuracy, better representation of damping, the ability to incorporate the soil layers under the foundation, and providing better tools for identification and damage detection from seismic records. Examples are presented to show the versatility and the superiority of the method.
TL;DR: In this paper, the dynamics of planar frames and trusses are analyzed in terms of the propagation of axial (longitudinal) and flexural (transverse) stress waves being structural members, and scattering coefficients representing the reflection and transmission of both types of waves at each joint are derived from the dynamics and compatibility conditions of the joint.
Abstract: The dynamics of planar frames and trusses is analyzed in terms of the propagation of axial (longitudinal) and flexural (transverse) stress waves being structural members. The waves are multiscattered at the joints, and scattering coefficients representing the reflection and transmission of both types of waves at each joint are derived from the dynamics and compatibility conditions of the joint. The complex multireflected waves within the structure are evaluated in the frequency domain by a newly developed reverberation matrix, which is formulated from scattering coefficients and propagating phase factors. Transient waves are then analyzed by Fourier synthesis and evaluated by a fast Fourier transform algorithm. Transient responses for the axial and bending strains in all structural members are calculated over a long duration for a model truss with rigid joints. Comparison to experimental data of the model truss under a step loading shows good agreement for the early as well as considerably long time responses.
TL;DR: In this article, the one-dimensional wave propagation in a functionally graded elastic slab is considered, where the stiffness and density of the medium vary continuously in thickness direction and it is initially at rest and stress-free.
TL;DR: In this article, the authors reported experiments on the scattering of surface-elastic waves by a periodic array of cylindrical holes in a marble quarry by using honeycomb and triangular lattices.
Abstract: In this paper, we report experiments on the scattering of surface-elastic waves by a periodic array of cylindrical holes. The experiments were performed in a marble quarry by drilling cylindrical holes in two different configurations: honeycomb and triangular lattices. The attenuation spectra of the surface waves show the existence of absolute band gaps for elastic waves in these semi-infinite two-dimensional crystals. Results are compared with theoretical calculations based on a scalar-wave approach. The scaling property of the underlying theory has led us to explore the possible application of the results obtained to the attenuation of surface waves in seismic movements. @S0163-1829~99!07419-6#
TL;DR: In this article, two different attenuated total-internal reflection prism configurations are used to explore the excitation of surface electromagnetic waves on one-dimensional (1-D) photonic bandgap (PBG) arrays.
Abstract: Two different attenuated total-internal reflection prism configurations are used to explore the excitation of surface electromagnetic waves on one-dimensional (1-D) photonic bandgap (PBG) arrays. The effect of surface termination of the photonic crystal is shown to have a significant effect on the dispersion of the surface modes excited at that interface. The results show that it is possible to engineer the position of the surface mode within the forbidden bandgap. Modes that are located close to the center of the bandgap are shown to be more localized, leading to significantly higher surface electromagnetic fields than modes located near the band edge. The existence of surface modes can have an effect on many of the proposed applications for PBG materials. The modes are also of interest in their own right for use in applications such as sensors and modulators.
TL;DR: In this paper, surface gravity waves shoaling between 8m water depth and the shoreline on a barred beach indicate that breaking results in an increase in the directional spread of wave energy, in contrast to the directional narrowing with decreasing depth predicted by refraction theory (Snell's law).
Abstract: Observations of surface gravity waves shoaling between 8-m water depth and the shoreline on a barred beach indicate that breaking results in an increase in the directional spread of wave energy, in contrast to the directional narrowing with decreasing depth predicted by refraction theory (Snell's law). During low-energy wave conditions, when breaking-induced wave energy losses over the instrumented transect are small, the observed mean propagation direction and spread about the mean both decrease with decreasing depth, consistent with the expected effects of refraction. Nonlinearity causes high-frequency components of the spectrum to become directionally aligned with the dominant incident waves. During high-energy wave conditions with significant wave breaking on the sand bar, the observed mean directions still decrease with decreasing depth. However, the observed directional spreads increase sharply (nominally a factor of 2 for values integrated over the swell-sea frequency range) between the outer edge of the surf zone and the crest of the sand bar, followed by a decrease toward the shoreline. Observations on a nonbarred beach also show directional broadening, with spreads increasing monotonically from the outer edge of the surf zone to a maximum value near the shoreline. Although the mechanism is not understood, these spatial patterns of directional broadening suggest that wave breaking causes significant scattering of incident wave energy into obliquely propagating components.
TL;DR: In this paper, the authors investigated passive noise control by flush-mounted panels in an otherwise rigid duct and found that the wave dissipation by panel materials like rubber could outperform typical fibrous duct lining, and the combination of wave reflection, dissipation, and slowing down allows broadband, low-frequency noise reduction over a short distance.
Abstract: Theoretical exploration is undertaken for passive noise control by flush-mounted panels in an otherwise rigid duct. For a plane sound wave traveling in the flexible segment, the wall compliance renders a wave speed less than the isentropic speed of sound in air. Scattering and reflection occur at the upstream edge of the panel while the energy flux of the transmitted wave is partitioned between the wall flexural waves and the sound in air. For a lossless panel these waves are scattered and reflected again by the downstream edge forming standing waves responsible for the undesirable passbands. For panels with substantial structural damping, however, both flexural and sound waves diminish with distance, eliminating the passbands. It is estimated that the wave dissipation by panel materials like rubber could outperform typical fibrous duct lining. The combination of wave reflection, dissipation, and slowing down allows broadband, low-frequency noise reduction over a short distance.