Problem Of Wave Reflection Research Articles

Reciprocity in the wave reflection and transmission problem

Matrices of reflection and transmission coefficients of plane waves in media or normal waves in waveguides are, in general case, not symmetric. When all the waves are of the propagating type, the matrix can be symmetrized by normalizing the wave amplitudes with the wave power flow. For evanescent (inhomogeneous) waves this is not valid because of their zero power flow. This difficulty is overcome in the present paper. The main result is that a reflection and transmission matrix becomes symmetric if the wave amplitudes are normalized with the certain energy‐like quantity that coincides with the power flow in the case of propagating waves. The result is valid for all types of waves (including those with complex wave numbers) and for all media and waveguides where the classical reciprocity theorem is valid. All symmetry relations, known in the literature for reflection and transmission coefficients follow from the result as particular cases. The result is useful in analysis of multimodal sound fields in composite media. It is illustrated in examples with inhomogeneous waves in fluids and solid waveguides.

Impact of a Digital Filter as a Weak Constraint in MM5 4DVAR: An Observing System Simulation Experiment

In this study, a digital filter is introduced into the fifth-generation Pennsylvania State University‐National Center for Atmospheric Research Mesoscale Model (MM5) four-dimensional variational data assimilation (4DVAR) system as a weak constraint to control high-frequency oscillations, which negatively affect assimilation performance. To assess the impact of the digital filter and to understand how the digital-filter 4DVAR functions, a series of observing system simulation experiments are conducted with the assimilation of global positioning system (GPS) refractivity soundings for a cyclogenesis case over the Antarctic region. It is shown that the use of a digital filter, centered at the midpoint of the assimilation period, is effective in suppressing the highfrequency waves. The imbalance during the early period of assimilation is further reduced by utilizing an additional short-span filter, starting at the beginning of the assimilation period. The filtering of the wind field is found to be the most effective in suppressing high-frequency oscillations. It is also revealed that the imposed weak constraint significantly reduces the wave-reflection problem caused by imperfect upper boundary conditions. It is concluded that the weakly constrained 4DVAR with digital filters not only reduces dynamic imbalance, but also significantly improves the qualities of analysis and forecast. Without projecting its solution onto the highfrequency waves, which diminish rapidly with forecast time, the constrained 4DVAR is able to yield additional improvement in the model initial condition in the larger-scale range and hence utilizes the available observations more effectively when compared with the unconstrained 4DVAR.

REFLECTION OF GENERALIZED THERMOELASTIC WAVES FROM THE BOUNDARY OF A HALF-SPACE

We investigated the problem of thermoelastic wave reflection from the insulated and isothermal stress-free as well as rigidly fixed boundaries of homogeneous isotropic solid half-spaces in the context of various linear theories of thermoelasticity, namely, Lord-Shulman, Green-Lindsay, Green-Nagdhi, coupled thermoelasticity, and uncoupled thermoelasticity. The ratios of reflection coefficients to that of incident coefficients are obtained for P- and SV-wave incidence cases. The results for partition of the energy for various values of the angle of incidence are computed numerically and presented graphically for aluminum-epoxy composite material in case of incident P- and SV-waves from the stress-free and rigidly fixed thermally insulated boundaries. The results obtained are discussed and compared in various models of thermoelasticity.

Solving exterior problems of wave propagation based on an iterative variation of local DtN operators

This paper discusses the problem of wave reflection from the fictitious boundary, with particular regard to the higher harmonic modes. This problem occurs when solving the wave equation in exterior domains using an asymptotic local low-order Dirichlet-to-Neumann (DtN) map for computational procedures applied to a finite domain. We demonstrate that the amplitudes of the reflected fictitious harmonics depend on the wave number, the location of the fictitious boundary, as well as on the local DtN operator used in the computations. Moreover, we show that a constant value of the asymptotic local low-order operator cannot sufficiently eliminate the amplitudes of all reflected waves, and that the results are poor especially for higher harmonics. We propose therefore an iterative method, which varies the tangential dependence of the local operator in each computational step. We only discuss some logical and interesting choices for the operators although this method permits several possibilities on how to vary the operator. The method is simple to apply and the presented examples demonstrate that the accuracy is considerably improved by iterations.

Reciprocity in the wave reflection and transmission problem: Part 1. Symmetry of the matrices of reflection coefficients

The reciprocity theorem in Lyamshev’s formulation is used to derive a general symmetry relationship for the matrices of reflection coefficients in homogeneous media and one-dimensional waveguides. This relationship is shown to be equivalent to the normalization of the amplitudes by the cross power flux of the forward and backward waves. The relationship is valid for both propagating and evanescent waves, and all the symmetry relationships known from the literature represent its particular cases.

Influence of ionospheric conductivity on parameters of a radio wave at a reflection point

A generalized solution of the problem of radio wave reflection in a linear conductive layer indicates the following: (1) the height of radio wave reflection depends on the value of the conductivity gradient; (2) only a fraction of the energy of an incident wave is propagating downwards from a reflection point; (3) Doppler frequency depends critically on temporary changes of layer conductivity; (4) the angle of incidence is not equal to the reflection angle at the height of radio wave reflection.

Acoustic Properties of Continuous and Discrete Models in Fluid Dynamics

The article investigates the propagation of small perturbations in fluids whose dynamics is described by Euler and Navier–Stokes equations or by a quasi-fluid-dynamic system derived from the difference approximation of the Boltzmann equation. The problem of wave reflection from the artificial boundaries of the numerical region is solved using various boundary conditions. The analysis is repeated for difference approximations of fluid-dynamic equations. The procedure is tested for viscous subsonic flow past a plate.

617 解適合非構造格子法による超音速流の数値シミュレーション(O.S.6-4 熱流体の数値計算2)(オーガナイズドセッション6 熱流体・燃焼の数値計算)

Our solution-adaptive scheme for the unstructured grid using the edge algorithm was applied to the reflection problem of oblique shock waves with conditions of Mach number 2.0 and deviation angle about 11 degrees. The result shows that our adaptation scheme captures the regular reflection on both the upper and the lower walls and the expansion fan more clearly. Therefor the applicability of our scheme was confirmed.

A method for solving the functional equation with variable delay

Mathematical simulation of physical conditions at a moving boundary in problems of wave reflection leads to a finite-difference equation with variable delay. If the reflector velocity is smaller than the wave-propagation velocity, the existence and uniqueness of the equation solution is proved using the principle of contraction maps and the method of successive approximations. It is shown that the solution can be expressed as a function of the composite argument that depends on one variable. The required accuracy of numerical calculations is ensured by partial sums when the argument is represented by an infinite converging series.

The scattering of general SH plane wave by interface crack between two dissimilar viscoelastic bodies

The scattering of general SH plane wave by an interface crack between two dissimilar viscoelastic bodies is studied and the dynamic stress intensity factor at the crack-tip is computed. The scattering problem can be decomposed into two problems: one is the reflection and refraction problem of general SH plane waves at perfect interface (with no crack); another is the scattering problem due to the existence of crack. For the first problem, the viscoelastic wave equation, displacement and stress continuity conditions across the interface are used to obtain the shear stress distribution at the interface. For the second problem, the integral transformation method is used to reduce the scattering problem into dual integral equations. Then, the dual integral equations are transformed into the Cauchy singular integral equation of first kind by introduction of the crack dislocation density function. Finally, the singular integral equation is solved by Kurtz's piecewise continuous function method. As a consequence, the crack opening displacement and dynamic stress intensity factor are obtained. At the end of the paper, a numerical example is given. The effects of incident angle, incident frequency and viscoelastic material parameters are analyzed. It is found that there is a frequency region for viscoelastic material within which the viscoelastic effects cannot be ignored.

Transfer Relations for Electromagnetic Wave Scattering From Periodic Dielectric One-Dimensional Interface: Te Polarization

Some general statements for theory of wave multiple scattering in a three-dimensional inhomogeneous layered dielectric medium are established using the composition rule of the scattering (T-matrix) operators to show that the problem of wave scattering from dielectric interface may be studied similar to the problem of volume wave scattering. The medium is thought as being a stack of n layers, each of them is confined by perpendicular to the z axis planes and consists of a three-dimensional discrete or continuous inhomogeneous medium. The layers do not intersect between them and are embedded into a homogeneous background. A result of the paper is a mixed system of exact operator equations (transfer relations) for the operator wave reflection and transmission coefficients of the medium and the operator wave amplitudes of waves in splits between layers. It is shown that the transfer relations lead to a separate recurrent system of operator equations, which describe the incremental change of the operator wave reflection and transmission coefficients of stack of n - 1 layers upon attachment of a n's layer to the stack. We derive from this recurrent equations a generalized Riccati equation for the operator wave reflection coefficient of the medium and an corresponding equation for the operator wave transmission coefficient of the medium, the coefficients of the Riccati equation and the corresponding equation being expressed in terms of the operator wave reflection and transmission coefficients of a thin slice of the medium and embedding parameter being taken along the z axis. The derived Riccati equation is applied to the problem of electromagnetic wave reflection from a periodic one-dimensional interface of two dielectric half-spaces, the interface being varied in the x axis direction and the wave electric field vector being parallel to the y axis. A solution to the Riccati equation for this problem is found numerically, taking into account with the aid of the Bloch (Floquet) theorem both the propagating and evanescent waves and not invoking the Rayleigh hypothesis. A resonant effect related to the Wood anomalies is discussed.

Radiative transfer in a layer of magnetized plasma with random irregularities

The problem of radio wave reflection from an optically thick plane uniform layer of magnetized plasma is considered in the present work. The plasma electron density irregularities are described by a spatial spectrum of arbitrary form. The small-angle scattering approximation in invariant ray coordinates is proposed as a technique for the analytical investigation of the radiation transfer equation. The approximate solution describing the spatial and angular distribution of radiation reflected from a plasma layer is obtained. The solution obtained is investigated numerically for the case of ionospheric radio wave propagation. Two effects occur as a consequence of multiple scattering: a change in the reflected signal intensity and an anomalous refraction.

Principles for capturing the upstream effects of deep sills in low resolution ocean models

Principles for incorporating the upstream effects of deep sills into numerical ocean circulation models using nonlinear analytical hydraulic models are discussed within the context of reduced gravity flow. A method is developed allowing the upstream influence of a numerically unresolvable deep sill or width contraction to be reproduced. The method consists of placing an artificial boundary in the numerical model's overflowing layer at some distance upstream of the actual sill or width contraction of the deep strait. Given the model state at time t, the dependent flow variables are then predicted at the artificial boundary at time t + Δt by using the method of characteristics in combination with quasi-steady hydraulic laws. The calculation requires the use of Riemann invariants and examples are given for a simple nonrotating flow and for rotating channel flow with uniform potential vorticity. The computation is considerably simplified by linearizing the relevant equations in the vicinity of the artificial boundary, resulting in a linear wave reflection problem. The reflection coefficients for the two cases are calculated and these can be used directly to numerically satisfy the boundary condition in a straightforward way.

Separation Of Incident And Reflected Spectra In Wave Flumes

In wave flumes or basins, when simulating sea waves in physical models with reflective structures, there frequently arrive, on the wave maker paddle, important reflected waves, due to the structure, which affect the incident waves. So that the waves generated by the paddle movement are not perturbed, the paddle movement must be compensated in order that the reflected waves be absorbed and have no effect For this, the incident and the reflected spectra have to be separated. There exist several methods for separating incident and reflected spectra both in the time and the frequency domain. The methods considered in this paper belong to the last group. Basically, these methods consist in deducing the incident and reflected wave spectra from the observed wave spectra at two or more points located along a line parallel to the wave propagation direction. Besides separating the spectra, the model is also able to produce numerically simulated data with given characteristics of wave spectra and physical constraints. It can also be tested by both numerically simulated data and real data recorded by the different wave gages operating in the wave flume. Comparing the so-called two-gage method and the N-gage method in terms of the ability to reconstruct the incident and reflected wave spectra, and according to the numerical and physical tests already carried out, the N-gage method seems to produce more rigorous results than the two-gage method. For the work presented in this paper these two methods were implemented in computer for a bi-dimensional flume and numerical simulation procedures able to verify the methods were established. The results of the numerical simulations developed to test these two methods proved both methods to be quite accurate. The two methods were then applied to physical flume waves with satisfactory results. From the work reported in this paper a first version of a software package able to address the problem of unwanted wave reflection in wave flumes was developed. Transactions on the Built Environment vol 27, © 1997 WIT Press, www.witpress.com, ISSN 1743-3509

Restoration of the parameters of a stratified medium

An analytical solution is found for the frequency domain in the inverse problem of wave reflection at an absorbing layer on a homogeneous half-space in the case of normal incidence. The method of solution uses the data on the real part of the reflectivity in a limited frequency range. The minimum size of this range is discussed.

Nonlinear bulk acoustic waves in anisotropic solids: Propagation, generation, and reflection

In this article, we address the nonlinear properties of bulk acoustic waves in anisotropic solids. While ordinary driving waves are obtained by means of the quasiwave mode concept in the discussion on propagation problems, we focus our analysis on the driving wave satisfying the resonant condition which exhibits the characteristics of three-dimensional spatial accumulation. Then a theory as the basis for solving nonlinear boundary value problems is developed. The novel analysis is presented for nonlinear reflection of bulk acoustic waves at a free surface of a generally anisotropic solid, which reveals that the surface may generate freely propagating second-harmonic waves, and that the reflective second-harmonic waves increase two dimensionally in the bulk. This technique can also be applied to wave reflection problems at other kinds of planar boundaries. Some numerical calculation is carried out for the case in an isotropic solid.

A uniformly valid far field asymptotic expansion of the green function for two-dimensional propagation above a homogeneous impedance plane

Abstract A generalized asymptotic expansion in the far field for the problem of cylindrical wave reflection at a homogeneous impedance plane is derived. The expansion is shown to be uniformly valid over all angles of incidence and values of surface impedance, including the limiting cases of zero and infinite impedance. The technique used is a rigorous application of the modified steepest descent method of Ott [1].

Reflection of Waves at the Free Edge of a Laminated Circular Cylinder

A wave function expansion method is employed to solve the reflection problem of time-harmonic elastic waves incident upon the free edge of a semi-infinite laminated circular cylinder. Wave functions are obtained using a propagator matrix approach for laminated isotropic cylinders and by a Rayleigh-Ritz type approximation for laminated composite cylinders. The least-square technique as well as the variational method are employed to evaluate the complex amplitudes and the energy flux associated with the reflected waves. To validate the solutions and present algorithm, results are compared with analytical solutions whenever available. Examples include free-end reflection of waves in an isotropic solid rod, a two-layered isotropic cylinder, and a four-ply [ + 15/ −15/ +15/ −15] graphite/epoxy cylinder. Numerical experimentation shows that the least-square method provides poor results for the laminated anisotropic cylinder compared to those obtained through the variational technique.

Propagation and reflection of one-dimensional waves in ferroelectric ceramics

Employing a linearized version of the general constitutive equations for a homogeneous deformable dielectric material body with memory, we study problems of wave propagation and reflection. We formulate these problems so as to correspond to certain well-defined experiments appearing in the literature and involving the application of time-dependent mechanical loads or prescribed voltage differences. Employing asymptotic procedures based upon geometrical optics we are able to solve problems of reflection hitherto unsolved, produce numerical results in an efficient manner, and elicit some important implications of the theory that appear not to have been noted before.

Duality transformations for general bi-isotropic (nonreciprocal chiral) media

The transformation is defined to leave a given bi-isotropic medium invariant, whence it is self-dual in this transformation. It is shown that duality transformations always exist in pairs, labeled as left-hand and right-hand transformations. Self-dual fields are seen to be generalizations of the wave fields E+or- applied in the analysis of reciprocal chiral media. It is demonstrated that plane wave propagation and reflection problems in bi-isotropic media can be solved easily in terms of self-dual field decompositions. Nonreciprocity is seen to give rise to effects like polarization rotation in reflection, which cannot be interpreted in terms of reciprocal chiral media.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>