Showing papers on "Plane wave published in 1985"

Effective equations for wave propagation in bubbly liquids

Abstract: We derive a system of effective equations for wave propagation in a bubbly liquid. Starting from a microscopic description, we obtain the effective equations by using Foldy's approximation in a nonlinear setting. We discuss in detail the range of validity of the effective equations as well as some of their properties.

Wave generation by an oscillating surface-pressure and its application in wave-energy extraction

Abstract: A two-dimensional analysis, based on linear surface-wave theory, is developed for an oscillating-water-column wave-energy device in water of arbitrary constant depth. The immersed part of the structure is assumed of shallow draught except for a submerged vertical reflecting wall. Both the cases of linear and nonlinear power take-off are considered. The results show that air compressibility can be important in practice, and its effects may in general be satisfactorily represented by linearization. The analysis indicates that using a turbine whose characteristic exhibits a phase difference between pressure and flow rate may be a method of strongly reducing the chamber length and turbine size with little change in the capability of energy extraction from regular waves. It was found in two examples of devices with strongly nonlinear power take-off that the maximum efficiency is only marginally inferior to what can be achieved in the linear case.

Plane waves in linear elastic materials with voids

Abstract: The behavior of plane harmonic waves in a linear elastic material with voids is analyzed. There are two dilational waves in this theory, one is predominantly the dilational wave of classical linear elasticity and the other is predominantly a wave carrying a change in the void volume fraction. Both waves are found to attenuate in their direction of propagation, to be dispersive and dissipative. At large frequencies the predominantly elastic wave propagates with the classical elastic dilational wave speed, but at low frequencies it propagates at a speed less than the classical speed. It makes a smooth but relatively distinct transition between these wave speeds in a relatively narrow range of frequency, the same range of frequency in which the specific loss has a relatively sharp peak. Dispersion curves and graphs of specific loss are given for four particular, but hypothetical, materials, corresponding to four cases of the solution.

Acoustic radiation potential on a sphere in plane, cylindrical, and spherical standing wave fields

Abstract: The method of Gor'kov is applied for deriving the acoustic radiation potential on a sphere in an arbitrary sound field. Generalized potential and force expressions are derived for arbitrary standing wave modes in rectangular, cylindrical, and spherical geometries for the case where the sphere radius is much smaller than the wavelength. Criteria for determining radiation-potential minima are derived and examples of characteristic spatial radiation-potential profiles are presented. Single modes that can sustain stable positioning are discussed for each geometry. The localizing force strengths for representative standing wave modes in the three geometries are also compared. The positioning of samples due to acoustic forces only are considered. However, the method developed is general and is extended to include gravity or other external forces.

Plane-wave Q deconvolution

Abstract: Often the information content of measured signals from distance sources is hidden, because the signal distorts, weakens, and loses resolution as it propagates. For seismic energy traveling in the earth, these propagation effects can be approximated by the constant (frequency-independent) Q model for attenuation and dispersion. For a propagating plane wave, this model leads to a spatial attenuation factor that is an unbounded function of frequency. Consequently, the broadband inverse of the constant-Q filter does not exist. For a fixed distance between the source and receiver the effects of the propagation path can be deconvolved (removed) within the seismic band by reversing the propagation of the plane wave. This propagation reversal is done by a time reversal with Q replaced by -Q, thereby changing absorption to gain in the complex wavenumber.Normally, measured seismic traces contain returns from a variety of depths. The interference of waves with different amounts of attenuation complicates the inversion process. From a superposition of plane waves with reversed propagation, a general inverse to an attenuation earth filter is proposed. To account for the increased attenuation with depth, the plane-wave inverse filter is now time-varying. This time-varying inverse filter has a simple Fourier integral representation where the wavenumber is complex, and the direction of propagation is chosen such that the wave is growing rather than attenuating with distance. To control the wavelet side lobes a frequency-domain window function (Hanning window) is applied to the trace. This two-step plane-wave deconvolution scheme was demonstrated to be superior to conventional deconvolution procedures. Tests with field data indicate the method is effective in removing attenuation effects from both VSP (Vertical Seismic Profile) and surface measurements. Phase distortions are eliminated and interference between events is reduced within the seismic band.This inverse is nearly exact for events where the time-bandwidth (propagation time-signal bandwidth) product is less than the effective Q. For depths where the time-bandwidth product is greater than Q eff large wavelet side lobes appear. The wavelet side lobes can be partially suppressed by tapering the edges of the spectrum. However, the large side lobes of wavelets from shallow reflectors limit the bandwidth that can be recovered from the deeper events to aproximately 2Q eff /t, where t is the propagation time to the event. Advances in the inversion algorithm (e.g., a Wiener filter could be used in place of the Hanning window to control side lobes) could probably improve upon our results, but in most cases even a small amount of measurement noise limits the reflection sequences to time-bandwidth products that are less than twice the effective Q.

Synchronous cavity mode and feedback wavelength scanning in dye laser oscillators with gratings

Abstract: A simple result of scalar diffraction theory is used to derive the round trip phase accrual of a plane wave in dye laser oscillators containing gratings. This is used to determine configurations where the standing wave condition is satisfied at the feedback wavelength throughout an angle scan. We find that at least one such exactly synchronous configuration always exists regardless of oscillator type.

A uniform GTD formulation for the diffraction by a wedge with impedance faces

Abstract: A uniform high-frequency solution is presented for the diffraction by a wedge with impedance faces illuminated by a plane wave perpendicularly incident on its edge. Arbitrary uniform isotropic impedance boundary conditions may be imposed on the faces of the wedge, and both the transverse electric (TE) and transverse magnetic (TM) cases are considered. This solution is formulated in terms of a diffraction coefficient which has the same structure as that of the uniform geometrical theory of diffraction (UTD) for a perfectly conducting wedge. Its extension to the present case is achieved by introducing suitable multiplying factors, which have been derived from an asymptotic evaluation of the exact solution given by Maliuzhinets. When the field point is located on the surface near the edge, a more accurate asymptotic evaluation is employed to obtain a high-frequency expression for the diffracted field, which is suitable for several specific applications. The formulation described in this paper may provide a useful, rigorous basis to search for a more numerically efficient but yet accurate approximation.

A general formulation of focus wave modes

Abstract: A general formulation is given for electromagnetic pulses which remain localized in a multidimensional space, and which propagate at the speed of light without dispersing (focus wave modes). It is shown that such modes necessarily have infinite electromagnetic energy in the source‐free, three‐dimensional space. Finite‐energy focus wave modes cannot exist without sources. A set of complete focus wave modes with Hermite–Gaussian transverse variation is derived. The relation of focus wave modes to the solutions of the paraxial wave equation is established.

Scattering and absorption characteristics of lossy dielectric, chiral, nonspherical objects

Abstract: A procedure based on the T-matrix method is devised to study the electromagnetic response of chiral, (lossy) dielectric, nonspherical objects exposed to an arbitrary incident field. Reductions in the method for axisymmetric objects are discussed. Using the technique thus developed, the plane wave scattering and absorption characteristics of lossy dielectric, axisymmetric scatterers (spheres as well as prolate and oblate spheroids), with and without chiral properties, are examined at frequencies above 50 GHz. The relative permittivity of the objects is assumed to be frequency dependent, whereas the chiral parameters are set to be constant in the numerical study. From the computed results, it appears that chiral spheres are the most effective objects in retarding the progress of an incident plane wave regardless of its polarization.

Circuit-Concept Approach to Externally Excited Transmission Lines

Abstract: The coupling of external electromagnetic waves to transmission lines is developed using a circuit-analysis concept. The validity of forcing terms of line equations reported in the literature is confirmed by experimental results of a wire model that is installed above a ?perfectly? conducting ground plane and excited by plane waves of parallel and perpendicular polarizations. Equivalent-circuit representations are derived from solutions of the equations. These are versatile expressions for prediction of coupling of external waves to various types of lines. Coupling, externally excited transmission line, line equations, forcing terms.

Generalized Burgers equation for plane waves

Abstract: Burgers’ equation, an equation for plane waves of finite amplitude in thermoviscous fluids, is generalized by replacing the thermoviscous term Aut’t’ (A is the thermoviscous coefficient, u particle velocity, and t’ retarded time) with an operator L(u). This operator represents the effect of attenuation and dispersion, even if known only empirically. Specific forms of L(u) are given for thermoviscous fluids, relaxing fluids, and fluids for which viscous and thermal boundary layers are important. A method for specifying L(u) when the attenuation and dispersion properties are known only empirically is described. A perturbation solution of the generalized Burgers equation is carried out to third order. An example is discussed for the case α2=2α1, where α1 and α2 are the small‐signal attenuation coefficients at the fundamental and second‐harmonic frequencies, respectively. The growth/decay curve of the second harmonic component is given both with and without the inclusion of dispersion. Dispersion causes a sma...

Absorbing boundary conditions for acoustic media

Abstract: By decomposing the acoustic wave equation into incoming and outgoing components, an absorbing boundary condition can be derived to eliminate reflections from plane waves according to their direction of propagation. This boundary condition is characterized by a first‐order differential operator. The differential operator, or absorbing boundary operator, is the basic element from which more complicated boundary conditions can be constructed. The absorbing boundary operator can be designed to absorb perfectly plane waves traveling in any two directions. By combining two or more absorption operators, boundary conditions can be created which absorb plane waves propagating in any number of directions. Absorbing boundary operators simplify the task of designing boundary conditions to reduce the detrimental effects of outgoing waves in many wave propagation problems.

Anomalous polarization of elastic waves in transversely isotropic media

Abstract: The behavior of transversely isotropic elastic media is analyzed from both the kinematic (slowness surface) and dynamic (particle displacement) point of view. The relations for the slowness surfaces and wave front surfaces are derived in polar coordinates. Examination of the eigenvectors of the displacement equations of motion gives the relation for the polarization of the displacement vector associated with any plane wave. It is shown that the polarization of plane quasi‐P and quasi‐SV waves depends strongly on the sign of a particular elastic modulus, call it A, whereas the shape of the slowness surface is independent of the sign of A. When A is positive, which is the usual case, the particle displacement vector rotates in the same sense as the slowness vector. When A is negative, which is the “anomalous” case, the sense of rotation of the particle displacement vector is opposite to that of the slowness vector. Thus there is a direction in the medium for which the displacement vector associated with the...

Investigation of a surface field phase perturbation technique for scattering from rough surfaces

Abstract: We present initial results from the investigation of a surface field phase perturbation method for the calculation of the wave field scattered by a rough surface. This technique is based on the extinction theorem and uses a perturbation expansion of a function closely related to the complex phase of the surface field. This approach was suggested earlier, but we use the expansion in a different way. In the present work we consider only deterministic periodic surfaces, rough in one dimension, on which the total field is zero. We find that, for surfaces with modest slope and curvature, this technique can be used to calculate scattered fields even when surface relief is significant compared to the wavelength of the incident radiation.

Instability and wave over-reflection in stably stratified shear flow

Abstract: We reexamine the related problems of instability of parallel shear flows and over-reflection of internal waves at a critical level, concentrating on the stratified case. Our primary aim is to delineate the specific aspects of a flow that permit overreflection and instability. A related and partly realized aim is to develop a mechanistic ‘picture’ of how over-reflection and instability work. In the course of this study we have also uncovered some new results concerning the instability of stratified shear flows – showing how regions of enhanced static stability and enhanced damping can destabilize otherwise stable flows.For the scattering of steady plane waves, we show that, of the conditions found by Lindzen & Tung (1978), in the unstratified case, only the existence of wave-propagation regions above and below the critical level is always necessary for over-reflection (at least in the absence of damping), although a trapping region around the critical level and a reflecting surface bounding the upper wave region may play crucial roles in some cases. Our results suggest that the role of the upper wave region may be to allow a wave flux through the critical level. Moreover, we show numerically that the effect of an upper wave region can be mimicked by a region of localized damping which leads to over-reflection as well.We also consider an initial-value problem, using numerical methods. When a wave is incident on the incident level, the reflection and transmission coefficients grow smoothly to their final values. The rate of growth depends on the flow parameters, but there is some evidence to suggest there is a characteristic timescale involved that depends only on the shear (and not on wave travel time). This fits a mechanistic picture of over-reflection and instability that we describe, in which the essential part is a kinematic interaction between wave and mean flow at the critical level, depending only on shear.

Resonances of plates and cylinders: Guided waves

Abstract: The study of the normal diffusion of an ultrasonic plane wave by cylinders and plates imbedded in the water shows resonances which are the natural modes of vibration. When a natural mode of an elastic target is excited, the energy which is stored during the forced excitation is emitted after the end of the forced excitation. The observation of backscattered spectra obtained by the Resonance Isolation and Identification Method (RIIM) from an aluminum cylinder shows supplementary resonances. The directivity pattern of the transducer is the cause of these supplementary resonances. The behavior of these resonances is analogous to the resonances of the plate. This leads us to study the natural modes of the cylinder. All the resonances which are experimentally detected may be considered as normal modes of the target. The results obtained on plates and cylinders have a common point: the generation of a guided wave by the excitation of a resonance.

Nonlinear propagation of electromagnetic ion‐cyclotron Alfvén waves

Abstract: The nonlinear interaction of an electron‐ion plasma with an electromagnetic ion‐cyclotron Alfven wave propagating along an external magnetic field is considered. It is found that the radiation pressure of the electromagnetic wave can excite field‐aligned electrostatic density perturbations. Localized wave packets are shown to exist. The relevance of our investigation to laboratory and astrophysical plasmas is discussed.

Diffuse elastic waves at a free surface

Abstract: For a diffusely vibrating elastic body, the participation of the surface in the general disturbance is evaluated. It is shown that in the vicinity of a free surface a diffuse acoustic field may legitimately be regarded as a sum of incoherent isotropic and homogeneous independent plane waves incident upon the surface together with their respective outgoing reflected consequences. The work contributes to a conceptual basis for the study of acoustic emission signals on time scales large compared to acoustic travel times across the structure.

A transport theory of millimeter wave propagation in woods and forests

Abstract: : A theory of mm wave propagation in woods and forests is presented which models the vegetation environment as a statistically homogeneous random medium of scatterers characterized by a scatter function (phase function) with a narrow forward lobe and an omnidirectional background The model describes the medium in terms of four overall theoretical parameters whose numerical values can be determined in principle by comparison of analytical results and experimental data The scalar transport theory is used to determine the coherent and incoherent field intensities in the forest medium; the problem solved is that of a vegetation halfspace illuminated by a plane wave Formulas and graphs are presented on the range dependence of the coherent and incoherent intensities, and on the angular spectrum (beam broadening) of the incoherent intensity Comparison with experimental results obtained by an independent investigation has shown good qualitative agreement of calculated and measured results Originator-supplied keywords include: Millimeter wave propagation, RF propagation in woods/forests, terrain effects on millimeter wave transmission, Transport theory, Random media, Coherent and incoherent field components, and Range dependence and beambroadening of millimeter waves in vegetation

The scattering of ultrasonic waves in polycrystalline materials with texture

Abstract: The theory of ultrasonic propagation in polycrystals with independent and uniformly distributed orientations of the grains presented in previous papers [J. Acoust. Soc. Am. 72, 1021–1031 (1982); 73, 1160–1163 (1983)] is generalized to calculate the scattering coefficients and the phase and group velocities of plane compressional and shear waves in textured polycrystals. The calculation was done for plane waves in polycrystals of cubic symmetry with rolling texture in second‐order perturbation theory using the assumption that the changes in the material constants from grain to grain are small. In the limit texture equal to zero the analytical results are exactly the same as those for untextured polycrystals previously presented. Numerical calculations are carried out for some examples.

A numerical study of nonlinear Alfvén waves and solitons

Abstract: Finite‐amplitude Alfven waves can be modeled by a nonlinear wave equation termed the derivative nonlinear Schrodinger equation. A computer program has been developed that solves the derivative nonlinear Schrodinger equation via the ‘‘split‐step’’ Fourier method. This program has been used to investigate a number of topics in the area of nonlinear Alfven waves. When analytic envelope solitons are used as initial conditions, the wave packets propagate without distortion and with the expected speed–amplitude relation. When an arbitrary, amplitude‐modulated wave is used as an initial condition, the results depend strongly on the β of the plasma and the polarization of the wave. For a left circularly polarized wave in a β 1, a collapse instability has been observed in which the wave amplitude increases and modulation scale decreases. For other combinations of polarization and value of β, the wave packet tends to broaden, eliminating the initial modulation.

Phase conjugation and symmetries with wave fields in free space containing evanescent components

Abstract: Several theorems are known concerning symmetry relations between monochromatic wave fields that propagate either into the same half-space (z > 0) or into complementary half-spaces (z > 0 and z < 0) and that are complex conjugates of each other in some cross-sectional plane z = constant. The theorems derived up to now apply only to wave fields that do not contain inhomogeneous (evanescent) components. In the present paper two of the main theorems are generalized to a wider class of fields. It is found that homogeneous and inhomogeneous components of a wave field have quite different symmetry properties under phase conjugation. The results are illustrated by a discussion of the behavior of plane waves, both homogeneous and evanescent ones, which undergo phase conjugation followed by transmission or by reflection.

General solutions of the narrow strip (and slot) integral equations

Abstract: Analytic solutions of the integral equations for the current induced on a narrow conducting strip are obtained by two methods. One method follows from an expansion of the strip current in a series of Chebyshev polynomials while the other is based on a special power series expansion. In the former, Fourier-type coefficients, depending on integrals of the excitation, are derived while in the latter the coefficients depend upon derivatives of the excitation. From knowledge of the strip current simple expressions for the far-zone scattered field are derived. Explicit results are given for plane wave excitation. The solution methods apply to the equations for the narrow slot in a planar conducting screen.

Effect of rotation and relaxation times on plane waves in generalised thermo-elasticity

Abstract: The propagation of harmonically time-dependent thermo-elastic plane waves of assigned frequency in infinite rotating media is studied using the theory of thermo-elasticity recently proposed by Green and Lindsay. A more general dispersion equation is deduced to determine the effect of rotation and relaxation times on the phase velocity of the coupled waves. The solutions for the phase velocity and the attenuation coefficient are obtained for small thermo-elastic coupling by a perturbation technique. Cases of low and high frequencies are also studied to determine the effect of rotation, the relaxation parameters and thermo-elastic coupling on the phase velocity and the attenuation coefficient of the waves.

Accuracy of the Born and Rytov approximations for reflection and refraction at a plane interface

Abstract: How good are the Born and Rytov approximations for the case of refraction and reflection at a plane interface? Here, we show the following results: For the reflected field, the Born approximation gives a plane wave at the correct reflection angle but approximates the true reflection coefficient by an expression linear in the scattering strength, which in this case involves both the velocity perturbation across the interface and the cosine of the incident angle. The Rytov approximation, on the other hand, can be interpreted as giving an infinite series of reflected plane waves in which the first term is just the Born approximation to the true reflected wave. Both approximations, however, are uniformly valid for the field above the interface. In contrast, the Born approximation to the transmitted field is not a plane wave and is not uniformly valid since it contains a secular term that grows linearly with distance from the interface. The Rytov approximation to the transmitted field is uniformly valid; in fact, the Rytov approximation gives a transmitted plane wave that satisfies a modified form of Snell’s law. Numerical examples indicate that the Rytov approximation to the transmitted field is surprisingly accurate. For velocity contrasts less than 40% and incident angles less than 30°, the Rytov approximation to the transmitted angle and transmission coefficient is never more than 20% in error.

A general analysis of transonic states in an anisotropic elastic body

Abstract: The basic characteristics of surface-wave propagation in an anisotropic elastic body depend crucially on the transonic states, defined by the sets of parallel tangents to a centred section of the slowness surface. The number of tangents parallel to a given direction in the plane of the section is at least 3 and at most 15 and, according to the number of points of contact and the number of branches of the slowness section to which they belong, there are 6 types of transonic states. The homogeneous plane wave represented by a point of contact is called a limiting wave and a transonic state is said to be exceptional when each of its limiting waves leaves free of traction the planes orthogonal to the tangent. For an elastic material of general anisotropy with positive definite linear elasticity tensor it is shown that at most 2 transonic states can be exceptional and that precisely 4 combinations of exceptional transonic states can occur, involving only 3 of the 6 types. Necessary and sufficient conditions for the existence of each of the possible combinations are given. As an application of the general results a complete characterization of exceptional transonic states in elastic materials with hexagonal symmetry is obtained.

Prestack inversion with plane-layer point source modeling

Abstract: Prestack inversion with point-source plane-layer modeling has many advantages over poststack or normal incidence inversion. For example, it permits the determination of absolute compressional and shear velocities, density variations, and the accurate accounting of interbed and surface multiples. I neglect shear effects in this paper by assuming that they are adequately suppressed by velocity filtering. In the forward modeling step, a spherical wave expansion into plane waves is used to account for the point source. The plane-wave reflection response for a set of plane layers is extended to the nonnormal incidence case. I use a Hankel transform to account for cylindrical symmetry. Generalized linear inversion is used because the fast recursive approaches available for normal incidence inversion are no longer applicable. I provide the derivation for the required derivative matrix, and I take into account the band-limited nature of the data in frequency, time, and space. I demonstrate that moveout of events on realistic simulated prestack data enables the determination of absolute compressional velocity in the velocity-depth profile, even though the data are band-limited in frequency. I assume that preprocessing has adequately removed the shear and surface effects and that density is constant. Low frequencies in the velocity profile may be obtained more accurately than with velocity analysis used for stacking, because interbed multiples and other modeling phenomena are accounted for in the computation. Autoregressive modeling procedures that predict into the low frequencies of the velocity profile are also less accurate and cannot generate absolute velocity. I suggest future research leading to cost-effective inversion of real data.

Diffraction of a plane wave by a thick strip grating

Abstract: The diffraction of a plane electromagnetic wave by a thick strip grating is solved rigorously by the Wiener-Hopf technique. The solution contains an infinite number of unknowns, which are shown to satisfy a certain infinite set of equations. By applying the modified residue calculus technique, this set of equations is solved and the approximate solution is derived. Representative numerical examples are given and the transmission characteristics of the grating are discussed. >