Sound scattering at fluid-fluid rough surface

Extinction theorem was used to deduce the first order scattering cross-section including the double scattering effects for the fluid-fluid rough surface. If the double scattering effects are neglected in the present method, the scattering cross-section agrees with the result obtained by the perturbation method based on Rayleigh hypothesis. Calculations of scattering strength were carried out, and comparisons with the first-order perturbation method based on Rayleigh hypothesis were also done. The results show that double scattering effects are obvious with the increase of the root mean square of surface height and the grazing angle when the valid condition k ₁ h < 1 is satisfied. Supported by the National Basic Research Program of China (Grant No. 2005CB422307)     

Acoustic transmission across a roughened fluid-fluid interface

A set of tank experiments was performed to investigate acoustic transmission across a roughened fluid-fluid interface with the intention to test heuristic Bragg scattering predictions used to explain observations of anomalous transmission in field experiments. In the tank experiments, two immiscible fluids (vegetable oil floating on glycerin) formed the layers. Small polystyrene beads were floated at the interface to simulate roughness. An array of hydrophones placed in the bottom layer (glycerin) was used to measure the acoustic levels transmitted across the interface. This array was also employed as a beamformer to determine the apparent angle and sound speed of the scattered signals. Data were acquired at subcritical grazing angles in the frequency range of 100-200 kHz for three different bead diameters and for various configurations in which the locations of the beads floating on the interface were varied. Results of these measurements demonstrated that a significant amount of acoustic energy can be scattered into the bottom layer by beads floating at the interface. The scattered levels increased with increasing bead diameter. However, discrepancies occurred between observed propagation properties and the Bragg predictions. By comparing the processed tank data to a computer simulation of the same it was determined that these discrepancies are a consequence of near-field reception of the scattering by the bead array and ignoring the directionality of the scattering by the beads. Consequences to observations made in field experiments are discussed.     

Small-slope approximation for electromagnetic wave scattering at a rough interface of two dielectric half-spaces

Abstract

The small-slope approximation (SSA) for wave scattering at the rough interface of two homogeneous half-spaces is developed. This method bridges the gap between two classical approaches to the problem: the method of small perturbations and the Kirchhoff (or quasi-classical) approximation. In contrast to these theories, the SSA is applicable irrespective of the wavelength of radiation, provided that the slopes of roughness are small compared with the angles of incidence and scattering.

The resulting expressions for the SSA are given for the entries of an S-matrix that represents the scattering amplitudes of plane waves of different polarizations interacting with the rough boundary. These formulae are quite general and are valid, in fact, for waves of different origins. Apart from the shape of the boundary, some functions in these formulae are coefficients of the expansion of the S-matrix into a power series in terms of elevations. These roughness independent functions are determined by a specific scattering problem. In this paper they are calculated for the case of electromagnetic scattering at the interface of two dielectric half-spaces. In contrast to an earlier paper by the author, where only the formulae for the reflected field were presented, in this paper both reflected and transmitted fields are considered in detail.

The a priori symmetry relations that this scattering problem should obey (reciprocity and energy conservation) are formulated in terms of the S-matrix.

The statistical moments of scattering amplitudes are directly related to the mean-reflection coefficient and scattering cross sections, which are usually determined experimentally. The corresponding formulae are given here for the case of Gaussian space-homogeneous statistics of roughness.     

A theoretical study of ultrasonic wave transmission through a fluid-solid interface

This article develops a model for the study of the transient ultrasonic waves radiated by a transducer in a liquid and transmitted into a solid through a plane interface. The method is an extension to the transient case, of the angular spectrum method previously developed for the monochromatic case. It is based on the decomposition of the ultrasonic field, in impulse plane waves. The radiated waveform is calculated at any point in the field by a simple summation of these impulse plane waves, where the propagation delay and the refraction have been taken into account. These plane waves are, first of all, delayed by an amount of time corresponding to the travel time up to the considered field point. The transmission through the plane interface is taken into account by using Snell refraction laws and transmission coefficients. In the obtained results all the waves previously described by other authors are highlighted: direct wave, edge waves, head waves as well as subsurface waves with a clear resolution between compression and shear waves.     

Non-local small-slope approximation for wave scattering from rough surfaces

A new general analytical approach to solving the problems of wave scattering from rough surfaces, referred to as the non-local small-slope approximation (NLSSA), is suggested. It is formulated in the general form both for vector and scalar waves. This approach is valid for an arbitrary wavelength of radiation provided that the slopes of the undulations are small enough. The NLSSA represents a generalization of the small-slope approximation to situations where double scattering (in the optical sense) appears. It is demonstrated that with appropriate approximations the NLSSA of the lowest order reduces to the small-slope approximation of the second order.     

弹性波在固体自由粗糙平界面上的散射

利用散射幅度矩阵的概念来处理弹性波在粗糙界面弹性介质中的散射问题。利用微扰近似解边界方程,对散射幅度进行求解,得到了散射幅度的0阶、1阶和2阶解。同时分析了粗糙起伏高度符合高斯分布时,散射幅度的数学期望值和方差,它们分别代表平均场和声场在偏离镜面方向的起伏。最后进行了实验。     

A finite element approach for scattering from inhomogeneous media with a rough interface

Electromagnetic scattering from an inhomogeneous medium with a one-dimensional rough interface is analysed. The proposed procedure combines the finite element method (FEM), to model the electromagnetic field in the inhomogeneous region, with a perturbative technique to account for the contributions due to the rough interface. Backscattering and bistatic scattering coefficients are computed and plotted for both plane wave and Gaussian beam incident fields in the case of TM_z polarization.     

Theory of radio wave scattering at a rough sea surface

The problem of the reflection of a plane single-frequency electromagnetic wave from a statistically rough dielectric boundary with arbitrary is solved in the perturbation approximation. The statistical characteristics (scattering cross section, change of polarization, and frequency spectrum) of a radar signal reflected from a rough sea surface are investigated. The model used for the surface—a small ripple superimposed on large waves—enables the perturbation theory approach to be extended to the decimeter and centimeter wave band.Izvestiya VUZ. Radiofizika, Vol. 9, No. 5, pp. 876–887, 1966     

Low-frequency sound transmission through a gas-solid interface

Sound transmission through gas-solid interfaces is usually very weak because of the large contrast in wave impedances at the interface. Here, it is shown that diffraction effects can lead to a dramatic increase in the transparency of gas-solid interfaces at low frequencies, resulting in the bulk of energy emitted by compact sources within a solid being radiated into a gas. The anomalous transparency is made possible by power fluxes in evanescent body waves and by excitation of interface waves. Sound transmission into gas is found to be highly sensitive to absorption of elastic waves within a solid.     

Low-frequency sound transmission through a gas-liquid interface

Typically, sound speed in gases is smaller and mass density is much smaller than in liquids, resulting in a very strong acoustic impedance contrast at a gas-liquid interface. Sound transmission through a boundary with a strong impedance contrast is normally very weak. This paper studies the power output of localized sound sources and acoustic power fluxes through a plane gas-liquid interface in a layered medium. It is shown that, for low-frequency sound, a phenomenon of anomalous transparency can occur where most of the acoustic power generated by a source in a liquid half-space can be radiated into a gas half-space. The main physical mechanism responsible for anomalous transparency is found to be an acoustic power transfer by inhomogeneous (evanescent) waves in the plane-wave decomposition of the acoustic field in the liquid. The effects of a liquid's stratification and of guided sound propagation in the liquid on the anomalous transparency of the gas-liquid interface are considered. Geophysical and biological implications of anomalous transparency of water-air interface to infrasound are indicated.     

Enhanced transmission through randomly rough surfaces

We present an experimental and theoretical study of two enhancement effects that occur in the transmission of light through a thin metal film whose illuminated surface is a one-dimensional random surface while its back surface is planar. The first is a well defined peak in the antispecular direction in the angular distribution of the intensity of the incoherent component of the transmitted light (enhanced transmission). The second is an additionally well defined peak in the forward direction in the angular distribution of the intensity of the incoherent component of the transmitted light, when the illuminated surface is not only randomly rough but has even symmetry as well (enhanced refraction). A fully automated bidirectional reflectometer has been used to measure the intensity of the incoherent component of He-Ne laser light transmitted through gold and silver films of these two types and the results are compared with the predictions of theoretical calculations of the enhancement effects.     

Enhanced transmission through randomly rough surfaces

Abstract

We present an experimental and theoretical study of two enhancement effects that occur in the transmission of light through a thin metal film whose illuminated surface is a one-dimensional random surface while its back surface is planar. The first is a well defined peak in the antispecular direction in the angular distribution of the intensity of the incoherent component of the transmitted light (enhanced transmission). The second is an additionally well defined peak in the forward direction in the angular distribution of the intensity of the incoherent component of the transmitted light, when the illuminated surface is not only randomly rough but has even symmetry as well (enhanced refraction). A fully automated bidirectional reflectometer has been used to measure the intensity of the incoherent component of He-Ne laser light transmitted through gold and silver films of these two types and the results are compared with the predictions of theoretical calculations of the enhancement effects.     

Electromagnetic wave diffraction by a rough interface of homogeneous isotropic media

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 32, No. 4, pp. 451–460, April, 1989.     

指数型分层介质粗糙面电磁波透射系数的特征

根据瑞利假设,运用微扰法近似,将透射场按平面波展开,对坐标进行傅里叶变换,研究了平面波入射时的透射散射现象,避免了繁琐的推导和证明;采用指数型粗糙面模拟实际的介质粗糙面,结合其功率谱导出了透射系数计算公式。数值计算结果表明:中间介质介电常数的实部越大,透射系数越大,虚部越大,透射系数越小;中间介质厚度越大,透射系数越小;粗糙面均方根越大,透射系数越大;粗糙面相关长度越大,透射系数越大;透射系数随入射波频率振荡地增大。     

指数型分层介质粗糙面电磁波透射系数的特征

根据瑞利假设,运用微扰法近似,将透射场按平面波展开,对坐标进行傅里叶变换,研究了平面波入射时的透射散射现象,避免了繁琐的推导和证明;采用指数型粗糙面模拟实际的介质粗糙面,结合其功率谱导出了透射系数计算公式。数值计算结果表明:中间介质介电常数的实部越大,透射系数越大,虚部越大,透射系数越小;中间介质厚度越大,透射系数越小;粗糙面均方根越大,透射系数越大;粗糙面相关长度越大,透射系数越大;透射系数随入射波频率振荡地增大。     

Electric and magnetic susceptibilities for a fluid-fluid interface; The ellipsometric coefficient

Formulae for the electro-magnetic constitutive coefficients are derived in terms of the interfacial position autocorrelation function. Explicit expressions for these coefficients are then found in terms of e.g. the surface tension and the capillary length. The ellipsometric coefficient is expressed in these constitutive coefficients and a comparison with recent experiments by Beaglehole is made.     

高斯分层介质粗糙面光波透射问题的微扰法研究

运用微扰法研究平面波入射分层介质粗糙面的光波透射问题,推出了不同极化状态的透射光波散射系数公式。采用高斯粗糙面来模拟实际的分层介质粗糙面,结合高斯粗糙面的功率谱导出了平面波入射高斯分层介质粗糙面的透射系数计算公式。通过数值计算得到HH极化透射系数随透射光波散射角变化的曲线,讨论底层介质介电常数、中间介质介电常数和厚度、粗糙面参数及入射光波长对透射系数的影响。数值计算结果表明：底层介质介电常数、中间介质介电常数和厚度、粗糙面参数及入射光波长对透射系数的影响是非常复杂的。     

Electric and magnetic susceptibilities for a fluid-fluid interface: II. Critical behaviour

Formulae for the electromagnetic constitutive coefficients derived in a previous paper are used to analyse the critical behaviour of the reflectivities at normal and oblique incidence as well as the ellipsometric coefficient at the Brewster angle. Contributions due to correlations, which are neglected if one uses the average profile, are taken into account. Thus we e.g. calculate the energy losses due to scattering at the interface. We find that the ellipsometric coefficient contains the intrinsic thickness of the profile rather than the thickness of the average profile. For cyclohexane-aniline a comparison is made with recent experiments by Beaglehole.     

Numerical simulation of continuum models for fluid-fluid interface dynamics

This paper is concerned with numerical methods for two-phase incompressible flows assuming a sharp interface model for interfacial stresses. Standard continuum models for the fluid dynamics in the bulk phases, for mass transport of a solute between the phases and for surfactant transport on the interface are given. We review some recently developed finite element methods for the appropriate discretization of such models, e.?g., a pressure extended finite element (XFE) space which is suitable to represent the pressure jump, a space-time extended finite element discretization for the mass transport equation of a solute and a surface finite element method (SurFEM) for surfactant transport. Numerical experiments based on level set interface capturing and adaptive multilevel finite element discretization are presented for rising droplets with a clean interface model and a spherical droplet in a Poisseuille flow with a Boussinesq-Scriven interface model.