Internal-wave radiation and optical measurements in stratified fluids

In many problems of considerable geophysical and industrial interest, fluid flows are characterized by the presence of a stable vertical density gradient. Under suitable conditions such fluids can support internal waves. In many aspects internal waves are similar to surface waves. Owing to small density difference across the fluid depth the effective gravity governing the dynamics of internal waves is typically by two or three orders of magnitude smaller than the terrestrial gravity. In a continuously stratified fluid the strength of gravity and viscous effects depends on the vertical density gradient, fluid viscosity, and characteristics of a wave-emitting disturbance. In the present report we focus our attention on experiments with internal waves generated by circular and rectilinear oscillations of cylinders in a uniformly stratified fluid. Quantitative measurements of internal waves are performed with the help of ‘synthetic’ schlieren technique based on computer evaluation of optical distortions in stratified fluids. The effects of the type and amplitude of oscillations on the generation of linear and nonlinear density-gradient disturbances are discussed.     

Reflection and transmission of waves from a plane interface between two microstretch solid half-spaces

In this paper, we have investigated the wave propagation and their reflection and transmission from a plane interface between two different microstretch elastic solid half-spaces in perfect contact. It is shown that there exist five waves in a linear homogeneous isotropic microstretch elastic solid, one of them travel independently, while other waves are two sets of two coupled waves. It is also shown that these waves travel with different velocities, three of which disappear below a critical frequency. Amplitude ratios and energy ratios of various reflected and transmitted waves are presented when a set of coupled longitudinal waves and a set of coupled transverse waves is made incident. It is found that the amplitude ratios of reflected and transmitted waves are functions of angle of incidence, frequency and are affected by the elastic properties of the media. Some special cases have been reduced from the present formulation.     

Existence of longitudinal waves in anisotropic poroelastic solids

In anisotropic fluid-saturated porous solids, four waves can propagate along a general phase direction. However, solid particles in different waves may not vibrate in mutually orthogonal directions. In the propagation of each of these waves, the displacement of pore–fluid particles may not be parallel to that of solid particles. The polarization for a wave is the direction of aggregate displacement of the particles of the two constituents of a porous aggregate. These polarizations, for different waves, are not mutually orthogonal. Out of the four waves in anisotropic poroelastic medium, two are termed as quasi-longitudinal waves. The prefix ‘quasi’ refers to their polarization being nearly, but not exactly, parallel to the direction of propagation. The existence of purely longitudinal waves in an anisotropic poroelastic medium is ensured by the stationary characters of two expressions. These expressions involve the elastic (stiffness and coupling) coefficients of a porous aggregate and the components of phase direction. Necessary and sufficient conditions for the existence of longitudinal waves are discussed for different anisotropic symmetries. Conditions are also discussed for the existence of the apparent longitudinal waves, i.e., the propagation of wave motion with the particle displacement parallel to the ray direction instead of the phase direction. A graphical solution of a numerical example is shown to check the existence of these apparent longitudinal waves for general directions of phase propagation.     

超声导波在管材中的传播特性

文中简要地介绍了近年来超声导波在管中的研究现状,并对导波在管中的传播特性以及管材内径与壁厚之比变化时,对导波频散特性的影响进行了分析。结果表明：管材的内径与壁厚比变化时将对管中导波的模式行为产生很大的影响。当内径与壁厚之比很大时,圆管中波的模式行为与同厚度板中波的模式行为基本相同,可看作板材中的导波进行近似的分析。     

Transmission of dipole radiation through interfaces and the phenomenon of anti-critical angles

Radiation emitted by an electric dipole consists of traveling and evanescent plane waves. Usually, only the traveling waves are observable by a measurement in the far field, since the evanescent waves die out over a length of approximately a wavelength from the source. We show that when the radiation is passed through an interface with a medium with an index of refraction larger than the index of refraction of the embedding medium of the dipole, a portion of the evanescent waves are converted into traveling waves, and they become observable in the far field. The same conclusion holds when the waves pass through a layer of finite thickness. Waves that are transmitted under an angle larger than the so-called anti-critical angle theta (1) ac are shown to originate in evanescent dipole waves. In this fashion, part of the evanescent spectrum of the radiation becomes amenable to observation in the far field. We also show that in many situations the power in the far field coming from evanescent waves greatly exceeds the power originating in traveling waves.     

Propagation and decay of acceleration waves in thermoconsolidating media

Summary The propagation of acceleration waves in a fluid-saturated porous medium is considered. The two-phase medium is the system consisting of a porous elastic solid skeleton, filled with a viscous compressible fluid. Two types of the media are taken into account: the medium composed of definite conductors and the medium composed of non-conductors. The method of singular surfaces has been used in these considerations. The acceleration waves in the medium consisting of non-conductors are not homentropic, in general. In this paper the conditions are determined which must be fulfilled to satisfy the acceleration waves to be homentropic.The propagation conditions of the waves are formulated and analysed. As usual in such a two-phase medium two longitudinal waves and one transverse wave are propagated. The growth equations of homothermal and homentropic waves are derived, and their solutions are analysed.     

Acoustic waves in bounded anisotropic media: theorems, estimations, and computations

This paper discusses some basic achievements in theoretical studies on acoustic wave propagation along boundaries in anisotropic solids. In particular, the following issues are reviewed: existence theorems for subsonic surface and interface waves, leaky surface acoustic waves (SAW) and their relation to "supersonic" SAWs and fast exceptional bulk waves, the resonance reflection of bulk waves in the vicinity of leaky wave branches. General conclusions are illustrated by numerical examples.     

Adjoint waves in round two-layer shielded waveguide

It is shown that adjoint waves can exist in a round two-layer shielded waveguide. In contrast to the normal waves propagating in guiding electrodynamic structures, the adjoint waves are characterized by a linear dependence of the field on the longitudinal coordinate.     

Quality of paraxial electromagnetic beams

The full wave theory of focused waves is developed and the radiation intensity distribution is determined. In the appropriate limit, the full wave theory correctly reproduces the paraxial beams. The limitations of paraxial beam theories are discussed. The method of treatment of full waves is presented with reference to the scalar Bessel-Gauss beam and wave. The necessary theoretical formulas for other beams and waves are also given. For the scalar Bessel-Gauss wave, the beam shape parameter can be adjusted to yield a flat-topped radiation pattern. The ratio of the power in the paraxial beam to that in the full wave is used as a parameter to measure the quality of the paraxial beam approximation. Lower-order waves are found to have better paraxial beam quality than do higher-order waves. The difference in the paraxial beam quality increases as kw0 is decreased where k is the wavenumber and w0 is the waist of the paraxial beam. The radiation patterns of waves are presented for some tightly focused waves.     

Effect of magnetic field and initial stress on the propagation of interface waves in transversely isotropic perfectly conducting media

Elasto-dynamical equations for transversely isotropic solids have been employed to investigate the general theory of transversely isotropic magneto-elastic interface waves in conducting media under initial hydrostatic tension or compression. Particular cases of interface waves such as Rayleigh, Love and Stoneley waves have been investigated in details. In all cases, the wave velocity equations have been deduced which are in complete agreement with the corresponding results of classical surface waves of the same types where magnetic fields and initial stresses are absent. Results obtained in this paper may be considered as more general and important in the sense that the corresponding results of classical surface waves due to Rayleigh, Love and Stoneley can readily be deduced from our results as special cases. Numerical calculations and graphs have been presented in the case of Love waves and conclusions are drawn.     

Fully nonlinear gravity-capillary solitary waves in a two-fluid system of finite depth

Large-amplitude waves at the interface between two laminar immisible inviscid streams of different densities and velocites, bounded together in a straight infinite channel are studied, when surface tension and gravity are both present. A long-wave approximation is used to develop a theory for fully nonlinear interfacial waves allowing amplitudes as large as the channel thickness. The result is a set of evolution equations for the interfacial shape and the velocity jump across it. Traveling waves of permanent form are studied and it is shown that solitary waves are possible for a range of physical parameters. All solitary waves can be expressed implicitly in terms of incomplete elliptic integrals of the third kind. When the upper layer has zero density, two explicit solitary-wave solutions have been found whose amplitudes are equal to h/4 or h/9, where 2h is the channel thickness. In the absence of gravity solitary waves are not possible but periodic ones are. Numerically constructed solitary waves are given for representative physical parameters.     

On the application of Biot's theory to acoustic wave propagation in snow

A fluid-saturated, elastic, porous media model is used to describe acoustic wave propagation in snow. This model predicts the existence of two dilatational waves and a shear wave. In homogeneous, isotropic snow the two dilatational waves are uncoupled from one another but involve coupled motion between the interstitial air and ice skeleton. Dilatational waves of the first kind and shear waves are slightly dispersive and attenuated with distance. Dilatational waves of the second kind are strongly dispersive and highly attenuated. The model also predicts that the wave impedance for snow is close to that of air and that snow strongly absorbs acoustic wave energy.Available experimental phase velocity, impedance and attenuation data support the calculated results. Phase velocity measurements indicate three identifiable categories: fast dilatational waves (phase velocity ? 500 m/s), slow dilatational waves (phase velocity < 500 m/s) and shear waves. Wave impedance and attenuation measurements illustrate the low impedance, highly absorbing characteristics of snow. Additional impedance, attenuation and phase velocity data are required to further test and improve the model.     

Some exact solutions for the propagation of transient electroacoustic waves. II: Plane interface between two piezoelectric media

Electroacoustic waves are coupled horizontal-shear (SH) and electromagnetic disturbances that propagate in certain types of piezoelectric media. At the interface between two semi-infinite piezoelectric media, a new type of electroacoustic surface wave, called a Maerfeld-Tournois wave, can exist that has no purely elastic wave counterpart. This article obtains exact transient solutions for the Maerfeld-Tournois and body waves generated by a dipole source on such an interface. These solutions are obtained for both conducting and nonconducting interfaces using a modification of the Lamb-Cagniard-Pekeris technique. In the quasistatic approximation, explicit results for all the waves present are given and the separated body and surface waves at the interface are discussed.     

Interfacial waves in dissimilar piezoelectric cubic crystals with an imperfect bonding

This paper studies propagation of shear waves along a weak interface of two dissimilar piezoelectric cubic crystals. Two piezoelectric cubic crystals are bonded along a specified cut direction. For an imperfect electrode interface, a dispersion relation of interfacial waves is derived explicitly. Numerical solutions are evaluated for several commonly-used piezoelectric cubic crystals. Our results show that interfacial imperfection alters the velocity of the interfacial shear waves. In particular, sometimes the interfacial shear waves may not exist for a perfect grounded interface and exist only for an imperfect electrode interface.     

Reflection and refraction of plane waves at interface between two piezoelectric media

This paper analyses reflection and refraction of plane waves at a perfect interface between two anisotropic piezoelectric media. The equations of elastic waves, quasi-static electric field, and constitutive relationships for the piezoelectric media are derived. A solution based on the inhomogeneous wave theory is developed to address the inconsistency between the numbers of independent wave modes in the media and the numbers of interfacial boundary conditions to obtain accurate reflection and refraction coefficients in case of strong piezoelectric media, where all the elastic and electric continuity conditions across the interface are satisfied simultaneously. The study shows that there exist independent and zero energy wave modes satisfying the general Snell’s law and propagating along the interface for any incident wave angle. These waves can be treated as pseudo surface waves. It is further found that all the reflection/refraction waves including the pseudo surface waves obey the energy conservation law at the interface boundary. In addition, the analysis also reveals that the reflection and refraction elastic waves can turn into pseudo surface waves at some critical incident angles.     

利用振荡管双开口结构消弱反射激波的研究

气波制冷机由于振荡管结构原因,造成激波运动到管末端产生具有一定强度的反射激波,而反射激波的存在是制约制冷效率的一个重要因素,因此,消除反射激波成为气波制冷技术研究的一个重要方向.本文分析了振荡管内激波的行为及反射激波对制冷效应的影响;对现有的几种消弱反射激波技术进行了对比及评价,在此基础上,提出了一种新的消弱反射激波的方法-采用振荡管双开口结构.实验证明,这种方法可有效消除反射激波,使制冷效率平均提高10%以上,而且大大优化了整机的结构,体积仅为原来的十分之一左右.     

T(0,1)模态导波在弯管上传播的仿真与实验

由于弯管的几何形状复杂,超声导波在弯管中的传播特性比在直管中复杂。弯管超声导波检测中,衡量其检测有效性的一个重要参数是透过率。通过有限元模拟研究了激励频率、弯曲半径、弯管角度对T(0,1)模态导波透过率的影响。发现:不同激励频率的导波在弯管上有不同的透过率,并且激励频率高的导波由于脉冲宽度小,更易产生新的波前;在不同的弯曲半径和弯曲角度的弯管中,最小透过率的T(0,1)模态导波的频率也各不一样;随弯管角度的变化,信号的透过率呈规律性变化。通过实验验证了不同激励频率下,T(0,1)模态导波透过率和激励频率的关系。在实际检测有弯管段的管道时,需采用多频率检测。     

Non-existence of solitary water waves in three dimensions

In the subject of free-surface water waves, solitary waves play an important role in the theory of two-dimensional fluid motions. These are steady solutions to the Euler equations that are localized, positively elevated above the mean fluid level and travelling at velocities with supercritical Froude number. They provide a stable mechanism in bodies of water for transport of mass, momentum and energy over long distances. In this paper, we prove that in the three- (or higher-) dimensional problem of surface water waves, there do not exist any localized steady positive solutions to the Euler equations.     

Making geometrical optics exact

Geometrical optics (GO) is widely used in studies of electromagnetic materials because of its ease of use compared to full-wave numerical simulations. Exact solutions for waves can, however, differ significantly from the GO approximation. In particular, effects that are “perfect” for waves cannot usually be derived using GO. Here, we give a method for designing materials in which GO is exact for some waves. This enables us to find interesting analytical solutions for exact wave propagation in inhomogeneous media. Two examples of the technique are given: a material in which two point sources do not interfere, and a perfect isotropic cloak for waves from a point source. We also give the form of material response required for GO to be exact for all waves.     

Thermo-acoustical waves in thermo-plastic materials

Summary The propagation velocities and the variation of the amplitudes of thermo-acoustical waves in thermo-plastic materials are theoretically investigated. The constitutive equations of anisotropic thermo-plastic materials are derived from the concept of imaginary decomposition of the deformation rate tensor into the elastic and plastic contributions and from that of the plastic potential. From generalized Vernotte's heat conduction law the propagation condition of the jumps of the velocity gradients and of the temperature rate is obtained. In isotropic materials and in the case of a normal stress vector on the wave front we have two purely mechanical transverse waves and two thermo-longitudinal coupled waves. Formulae for the velocities and amplitudes are quite similar with those for thermo-elastic materials. The variation of the amplitude is discussed. There are, in general, three effects on the variation, that is, the non-planar, heat conduction and plastic flow effects. The transverse waves are subjected only to the non-planar effect, while the thermo-longitudinal waves may grow or decay according to the above three effects.