A study has been made on the reflected and transmitted powers generated when an arbitrarily polarized plane wave impinges at a planar interface separating an isotropic achiral medium(IAM) and an isotropic chiral mediu...A study has been made on the reflected and transmitted powers generated when an arbitrarily polarized plane wave impinges at a planar interface separating an isotropic achiral medium(IAM) and an isotropic chiral medium(ICM). It follows that the theoretical formulas are derived for the normalized reflection and transmission powers from an IAM–ICM interface for an arbitrary polarized incident wave, and those at an ICM–IAM interface for right-hand circularly polarized(RCP) or left-hand circularly polarized(LCP) incident wave are also obtained. The behavior of the reflected and transmitted waves in different cases is studied, and the dependence of the reflection/transmission of the incident wave on the incident angle and the parameters of the media is investigated in detail. Our numerical results show that high transmission is exhibited under the impedance matching condition and the incident wave can be split into two waves of the same circular polarization state in the case of the ICM–IAM interface, which indicates that circular polarizing beam splitter is achieved.展开更多
The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water waves.The fluid region is divided into four s...The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water waves.The fluid region is divided into four subregions depending on the position of the barrier and the trench.Using the Havelock’s expansion of water wave potential in different regions along with suitable matching conditions at the interface of different regions,the problem is formulated in terms of three integral equations.Considering the edge conditions at the submerged end of the barrier and at the edges of the trench,these integral equations are solved using multi-term Galerkin approximation technique taking orthogonal Chebyshev’s polynomials and ultra-spherical Gegenbauer polynomial as its basis function and also simple polynomial as basis function.Using the solutions of the integral equations,the reflection coefficient,transmission coefficient,energy dissipation coefficient and horizontal wave force are determined and depicted graphically.It was observed that the rate of convergence of the Galerkin method in computing the reflection coefficient,considering special functions as basis function is more than the simple polynomial as basis function.The change of porous parameter of the barrier and variation of trench width and height significantly contribute to the change in the scattering coefficients and the hydrodynamic force.The present results are likely to play a crucial role in the analysis of surface wave propagation in oceans involving porous barrier over submarine trench.展开更多
The present study deals with the scattering of oblique surface water waves by small undulation on the bottom in the presence of a thin vertical barrier. Here, three different configurations of vertical barriers are in...The present study deals with the scattering of oblique surface water waves by small undulation on the bottom in the presence of a thin vertical barrier. Here, three different configurations of vertical barriers are investigated. Perturbation analysis is employed to determine the physical quantities, namely, the reflection and transmission coefficients. In this analysis, many different Boundary Value Problems (BVPs) are obtained out of which the first two bvps are considered. The zeroth order bvp is solved with the aid of eigenfunction expansion method. The first order reflection and transmission coefficients are derived in terms of the integrals by the method of the Green's integral theorem. The variation of these coefficients is plotted and analyzed for different physical parameters. Furthermore, the energy balance relation, an important relation in the study of water wave scattering, is derived and checked for assuring the correctness of the numerical results for the present problem.展开更多
The present paper is concerned with scattering of water waves from a vertical plate, modeled as an elastic plate, submerged in deep water covered with a thin uniform sheet of ice. The problem is formulated in terms of...The present paper is concerned with scattering of water waves from a vertical plate, modeled as an elastic plate, submerged in deep water covered with a thin uniform sheet of ice. The problem is formulated in terms of a hypersingular integral equation by a suitable application of Green＇s integral theorem in terms of difference of potential functicns across the barrier. This integral equation is solved by a collocation method using a finite series involving Chebyshev polynomials. Reflection and transmission coefficients are obtained numerically and presented graphically for various values of the wave number and ice-cover parameter.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61431010 and 61501350)the National Key Basic Research Program of China(Grant No.2014CB340203)
文摘A study has been made on the reflected and transmitted powers generated when an arbitrarily polarized plane wave impinges at a planar interface separating an isotropic achiral medium(IAM) and an isotropic chiral medium(ICM). It follows that the theoretical formulas are derived for the normalized reflection and transmission powers from an IAM–ICM interface for an arbitrary polarized incident wave, and those at an ICM–IAM interface for right-hand circularly polarized(RCP) or left-hand circularly polarized(LCP) incident wave are also obtained. The behavior of the reflected and transmitted waves in different cases is studied, and the dependence of the reflection/transmission of the incident wave on the incident angle and the parameters of the media is investigated in detail. Our numerical results show that high transmission is exhibited under the impedance matching condition and the incident wave can be split into two waves of the same circular polarization state in the case of the ICM–IAM interface, which indicates that circular polarizing beam splitter is achieved.
文摘The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water waves.The fluid region is divided into four subregions depending on the position of the barrier and the trench.Using the Havelock’s expansion of water wave potential in different regions along with suitable matching conditions at the interface of different regions,the problem is formulated in terms of three integral equations.Considering the edge conditions at the submerged end of the barrier and at the edges of the trench,these integral equations are solved using multi-term Galerkin approximation technique taking orthogonal Chebyshev’s polynomials and ultra-spherical Gegenbauer polynomial as its basis function and also simple polynomial as basis function.Using the solutions of the integral equations,the reflection coefficient,transmission coefficient,energy dissipation coefficient and horizontal wave force are determined and depicted graphically.It was observed that the rate of convergence of the Galerkin method in computing the reflection coefficient,considering special functions as basis function is more than the simple polynomial as basis function.The change of porous parameter of the barrier and variation of trench width and height significantly contribute to the change in the scattering coefficients and the hydrodynamic force.The present results are likely to play a crucial role in the analysis of surface wave propagation in oceans involving porous barrier over submarine trench.
基金Supported by SERB-DST Grant(No.SB/FTP/MS-034/2013)
文摘The present study deals with the scattering of oblique surface water waves by small undulation on the bottom in the presence of a thin vertical barrier. Here, three different configurations of vertical barriers are investigated. Perturbation analysis is employed to determine the physical quantities, namely, the reflection and transmission coefficients. In this analysis, many different Boundary Value Problems (BVPs) are obtained out of which the first two bvps are considered. The zeroth order bvp is solved with the aid of eigenfunction expansion method. The first order reflection and transmission coefficients are derived in terms of the integrals by the method of the Green's integral theorem. The variation of these coefficients is plotted and analyzed for different physical parameters. Furthermore, the energy balance relation, an important relation in the study of water wave scattering, is derived and checked for assuring the correctness of the numerical results for the present problem.
基金supported by the Department of Science and Technology of New Delhi (No.SR/SY/MS:521/08)
文摘The present paper is concerned with scattering of water waves from a vertical plate, modeled as an elastic plate, submerged in deep water covered with a thin uniform sheet of ice. The problem is formulated in terms of a hypersingular integral equation by a suitable application of Green＇s integral theorem in terms of difference of potential functicns across the barrier. This integral equation is solved by a collocation method using a finite series involving Chebyshev polynomials. Reflection and transmission coefficients are obtained numerically and presented graphically for various values of the wave number and ice-cover parameter.
