The Difference in Turbulent Diffusion between the Active and Passive Scalars in a Thermally Stably Stratified Medium

The difference in the turbulent diffusion between the active (heat) and passive (mass) scalars in a thermally stably stratified medium is investigated. The axisymmetric problem is treated on the formation of a turbulent circulation flow above a heated disk and on the turbulent diffusion of a passive scalar (impurity) from a continuous surface source in a stably stratified medium. The results indicate that the thermal stratification causes appreciable differences in the coefficients of turbulent transfer between the active (heat) and passive (mass) scalars. This means that the assumption of the identity of the coefficient of turbulent diffusion of heat and mass, employed in conventional models of turbulence, produces significant errors in estimating the heat and mass transfer in a thermally stably stratified medium.     

Analytical investigation of stratified isotropic media

A rigorous analytical approach for investigating a stratified medium with an arbitrary finite number of homogeneous isotropic layers in a period is developed. The approach is based on the translation matrix method. It is well known that the translation matrix for a period must be found as the product of the layer matrices. It is proved that this matrix can be represented as a finite sum of trigonometric matrices, and thus the dispersion relation of a stratified medium is written in an analytical form. All final expressions are obtained in terms of the constitutive parameters. To this author's knowledge, this is the first time that the new sign function that allows us to develop the presented analytical results has been described. The condition of the existence of a wave with an arbitrary period divisible by a structure period is found in analytical form. It is proved that changing the layer arrangement within the period does not affect the structure of the transmission and absorption bands.     

Evaluation of elastic properties of 3-D (4-step) regular braided composites by a homogenisation method

In this article a homogenisation method that considers the internal interface condition of a heterogeneous medium is established. The relevant formulae are developed based on a specific stratified medium with plane interfaces, but they can be obtained for more general cases in which curved interfaces are considered. A 3-D 4-step regular braid is studied, and its elastic properties are evaluated in terms of the homogenisation scheme. The present theoretical prediction shows a good agreement with experimental data.     

Wall boundary layer in a stratified medium

An algebraic model of turbulence in a stratified medium is constructed using equations of second-order moments within the framework of a two-layer scheme.     

Coherence theory of electromagnetic wave propagation through stratified N-layer media

The theory of second-order coherence in connection with wave propagation through a stratified N-layer (SNL) medium is developed. Especially, the influence of the SNL medium on the propagation of the coherence generated by a given state of coherence at the entrance plane of the medium is considered. The generalization of the van Cittert-Zernike theorem is obtained, and the propagation of the second-order coherence from a quasi-homogeneous surface distribution or a rough surface is calculated. Furthermore, the influence of SNL media on the coherence properties of a pulse is calculated.     

平面波与层状多孔介质海底的反射和透射

针对典型的海底介质结构情况,研究了从海水入射到含有非固结沉积层的层状流体饱和多孔介质海底的平面波的反射和透射问题,分析了沉积层和基岩中纵、横波速度和衰减的频散变化特点,在沉积层厚度和频率变化时,对海水-海底界面上的位移势函数反射系数进行了计算和分析。研究结果表明：在沉积层厚度一定的情况下,较高频率时,沉积层对海水中声场的影响较大,而频率较低时,基岩对海水中声场的影响较大。在以不同的掠射角入射时,由于沉积层中质点的法向共振,广义位移势函数反射系数随频厚积的变化曲线会出现一系列的共振峰,随着掠射角的减小,共振峰个数减少,但共振峰的幅度会增加。     

Freely convective mass transport in a stratified fluid

Experimental and computed results are presented for the freely convective mass transport from a vertical salt surface in a stratified medium.     

变分法求波的路径和介质速度分布的反演

介绍了一种用变分原理进行射线追踪和反演的方法。根据欧拉方程对于连续性层状介质进行了方程推导，得出一个波的射线路径公式，公式形式尤其简单。在背景速度场为深度的单调函数时，利用代数重建技术反演了速度分布。数值模拟结果表明所给方法行之有效。     

An Alternative Characteristic Matrix Using Abelés' Matrix Notation

Abstract

Abelés' matrix notation for modelling the propagation of light through a stratified medium is written in terms of characteristic matrices similar to Herpin's notation.     

Eddy current solutions applicable to the problem of nondestructive inspection of flat and cylindrical surface layer

Nondestructive inspection of flat and long cylindrical metallic-surface layers is conveniently dealt with using the results of wave propagations in a one-dimensionally stratified medium. Analytical solutions for some special profiles are obtained, and perturbation technique is used to obtain results for more frequently encountered profiles.     

On Perturbations of Geostrophic Flow Determined by Volume Sources of Buoyancy and Momentum

Journal of Engineering Physics and Thermophysics - Consideration has been given to a linear analytical model of perturbations of geostrophic flow of a stratified rotating medium resulting from the...     

Computational Analysis of the Oscillatory Mixed Convection Flow along a Horizontal Circular Cylinder in Thermally Stratified Medium

The present work emphasizes the significance of oscillatory mixed convection stratified fluid and heat transfer characteristics at different stations of non-conducting horizontally circular cylinder in the presence of thermally stratified medium. To remove the difficulties in illustrating the coupled PDE’s, the finite-difference scheme with efficient primitive-variable formulation is proposed to transform dimensionless equations. The numerical simulations of coupled non-dimensional equations are computed in terms velocity of fluid, temperature and magnetic field which are computed to examine the fluctuating components of skin friction, heat transfer and current density for various emerging parameters. The governing parameters namely, thermally stratification parameter     

Intraocular light scatter as modeled through a stratified medium

Intraocular light scatter is modeled through a stratified medium. It is shown that the eye lens possesses properties of an interference filter. In conditions that may mimic opacification, as found with cataract formation, such a filter may have stop zones with reflectance up to 1 in the band of visible light.     

The uniform asymptotic form of the internal gravity-wave field generated by a source moving above a smoothly varying bottom

The uniform asymptotic form of the internal gravity-wave field generated by a source moving above a smoothly varying bottom is constructed. The problem of reconstructing non-harmonic internal gravity-wave packets generated by a source moving in a stratified ocean is considered. The solution is proposed in terms of wave modes, propagating independently at the adiabatic approximation, and described as a non-integral-degree series of a small parameter characterizing the stratified medium. A specific form of the wave packets, which can be parameterized in terms of model functions (Airy functions), depends on the local behavior of the dispersion curves of the individual wave mode. A modified space?Ctime ray method was proposed, which belongs to the class of geometrical-optics methods. The key point of the proposed technique is the possibility to derive the asymptotic representation of the solution in terms of a non-integral-degree series of the some small parameter.     

Vector diffraction problem of focusing a category 1 aberrated wavefront through a multilayered lossless medium

Abstract

In optical storage and other imaging applications, a laser beam is focused through a transparent lossless medium of different refractive index. Applications include optical and magneto-optical recording. It is highly likely that, in the near future, conventional magnetic recording will transition to optically/thermally assisted magnetic recording technology. In all these applications, it is necessary to ascertain the quality of the image formed by the focusing apparatus on an imaging surface when in the neighbourhood of the focus, the focused beam of light passes through a stratified lossless medium. This paper examines the vector diffraction problem of focusing radiation through a multilayered medium. The solution is accomplished by first deriving a general solution of the focusing problem in any homogenous medium. This solution is then used to obtain the solution in the multilayered medium by applying continuity of the electric and magnetic fields at the interfaces. The technique used here allows one to calculate the field quantities in the entire image space. Furthermore, the focusing lens may have Seidel aberrations of the fourth order. The salient feature of this method is that the vector diffraction problem is solved only once - for the zeroth layer, immediately next to the exit pupil. In the remaining layers, the results are obtained by solving linear algebraic equations. The solution of the algebraic equations is obtained in closed form.     

Elastic wave propagation in a 3‐D unbounded random heterogeneous medium coupled with a bounded medium. Application to seismic soil–structure interaction (SSSI)

We present a sub‐structuring method for the coupling between a large elastic structure, and a stratified soil half‐space exhibiting random heterogeneities over a bounded domain and impinged by incident waves. Both media are also weakly dissipative. The concept of interfaces classically used in sub‐structuring methods is extended to ‘volume interfaces’ in the proposed approach. The random dimension of the stochastic fields modelling the heterogeneities in the soil is reduced by introducing a Karhunen–Loéve expansion of these stochastic fields. The coupled overall problem is solved by Monte‐Carlo simulation techniques. A realistic example of a large industrial structure interacting with an uncertain stratified soil medium under earthquake is finally presented. This case study and others validate the presented methodology and its ability to handle complex mechanical systems. Copyright © 2002 John Wiley & Sons, Ltd.     

Can a Travelling Electromagnetic Wave be Present in a Layered Medium?

Abstract

The problem of the presence of a travelling electromagnetic wave in an inhomogeneous medium is addressed. An argument is presented in favour of the option that the Poynting vector determines whether the wave is travelling or not. A strict harmonic solution to the Maxwell equations in a plane stratified medium is shown not to be a travelling wave. This solution can be decomposed into two travelling fields which separately do not satisfy the Maxwell equations and which are identified as the transmitted and return fields. The direction of the Poynting vector for the transmitted field satisfies the generalized Snell's law. The reflectance of a layer of such a medium is calculated and shown to be zero for some incidence angles. Phases of the two travelling fields are considered and shown to be different from those of geometric optics.     

Radiance-irradiance inversion algorithm for estimating the absorption and backscattering coefficients of natural waters: vertically stratified water bodies

A full multiple-scattering algorithm for inverting profiles of the upwelling and downwelling irradiances to yield profiles of the absorption and backscattering coefficients in a vertically stratified water body is described and tested with simulated data. The algorithm does not require knowledge of the scattering phase function of the medium. The results are better the closer the phase function assumed in the retrievals is to the true phase function, although excellent retrievals of the absorption coefficient can still be obtained with an inaccurate phase function. Simulations show that the algorithm is capable of determining the vertical structure of a stratified water body and usually provides the absorption coefficient profile with an error ?2% and the backscattering coefficient profile with an error ?10%, as long as the spacing between pseudodata samples is sufficiently small that the necessary derivatives of the irradiances can be accurately computed. The performance is only slightly degraded when the upwelling radiance (nadir viewing) is substituted for the upwelling irradiance.     

Electromagnetic diffraction of light focused through a stratified medium

We consider the focusing of light by a high-aperture lens into a stratified medium. The solution is based on our previously obtained results [J. Opt. Soc. Am. A 12, 325 (1995)], where we represented the illumination incident upon a plane interface between media with mismatched refractive indices as a sum of plane waves. The present solution is obtained in terms of plane waves, and it satisfies Maxwell's equations. The diffraction integrals are obtained in a form that is readily computable. We present numerical examples for some practical cases.     

Application of the Darboux transform to spectral problems in ocean acoustics

We propose a generalization of the n-order Darboux transform, which can be applied to solving spectral problems in ocean acoustics in cases when the medium can be considered stratified with respect to density. For a second-order Darboux transform with the boundary conditions characteristic of a single-layer shallow sea model, conditions are determined under which the spectra of the initial and transformed spectral problems coincide. It is demonstrated that, within the framework of this model, it is possible to use the n-order Darboux transform for constructing sound velocity profiles admitting exact solutions.