Based on angular spectrum expansion and 4 × 4 matrix theory, the reflection and transmission characteristics of a Laguerre Gaussian(LG) beam from uniaxial anisotropic multilayered media are studied. The reflected...Based on angular spectrum expansion and 4 × 4 matrix theory, the reflection and transmission characteristics of a Laguerre Gaussian(LG) beam from uniaxial anisotropic multilayered media are studied. The reflected and transmitted beam fields of an LG beam are derived. In the case where the principal coordinates of the uniaxial anisotropic media coincide with the global coordinates, the reflected and transmitted beam intensities from a uniaxial anisotropic slab and three-layered media are numerically simulated. It is shown that the reflected intensity components of the incident beam, especially the TM polarized incident beam, are smaller than the transmitted intensity components. The distortion of the reflected intensity component is more evident than that of the transmitted intensity component. The distortion of intensity distribution is greatly affected by the dielectric tensor and the thickness of anisotropic media. We finally extend the application of the method to general anisotropic multilayered media.展开更多
The reflection and transmission of a finite-power Airy beam incident on a dielectric slab are investigated by an analytical method.Based on the plane-wave angular spectrum expansion and Fresnel approximation,the analy...The reflection and transmission of a finite-power Airy beam incident on a dielectric slab are investigated by an analytical method.Based on the plane-wave angular spectrum expansion and Fresnel approximation,the analytical expressions of the reflected field,internal field as well as transmitted field in each region are obtained.Through numerical simulations,the intensity distributions of the incident beam,reflected beam,internal beam as well as transmitted beam are presented at oblique incidence.Besides,we also compare the intensity distributions of the geometrical-optics beam field,the first order beam mode field and the actual beam field,which indicates that the contribution of each order beam mode field to the actual beam field is related to the refractive index of the dielectric slab.Meanwhile,the reflection characteristics of the Airy beams in the special cases of Brewster incidence and total reflection are investigated.Finally,the effects of the optical thickness and refractive index of the dielectric slab on the peak intensity distributions and beam shifts of the reflected and transmitted beams are also discussed in detail.The analytical and numerical results will be useful to analyze the propagation dynamics of Airy beam in the dielectric slab and provide some theoretical supports to the design of optical film.展开更多
Wave propagation in horizontally layered media is a classical problem in seismic-wave theory.In semi-infinite space,a nondispersive Rayleigh wave mode exists,and the eigendisplacement decays exponentially with depth.I...Wave propagation in horizontally layered media is a classical problem in seismic-wave theory.In semi-infinite space,a nondispersive Rayleigh wave mode exists,and the eigendisplacement decays exponentially with depth.In a layered model with increasing layer velocity,the phase velocity of the Rayleigh wave varies between the S-wave velocity of the bottom half-space and that of the classical Rayleigh wave propagated in a supposed half-space formed by the parameters of the top layer.If the phase velocity is the same as the P-or S-wave velocity of the layer,which is called the critical mode or critical phase velocity of surface waves,the general solution of the wave equation is not a homogeneous(expressed by trigonometric functions)or inhomogeneous(expressed by exponential functions)plane wave,but one whose amplitude changes linearly with depth(expressed by a linear function).Theories based on a general solution containing only trigonometric or exponential functions do not apply to the critical mode,owing to the singularity at the critical phase velocity.In this study,based on the classical framework of generalized reflection and transmission coefficients,the propagation of surface waves in horizontally layered media was studied by introducing a solution for the linear function at the critical phase velocity.Therefore,the eigenvalues and eigenfunctions of the critical mode can be calculated by solving a singular problem.The eigendisplacement characteristics associated with the critical phase velocity were investigated for different layered models.In contrast to the normal mode,the eigendisplacement associated with the critical phase velocity exhibits different characteristics.If the phase velocity is equal to the S-wave velocity in the bottom half-space,the eigendisplacement remains constant with increasing depth.展开更多
In the present paper,we consider a problem of reflection and transmission of plane waves at an interface between two different transversely isotropic micropolar piezoelectric half-spaces.The plane wave solution of gov...In the present paper,we consider a problem of reflection and transmission of plane waves at an interface between two different transversely isotropic micropolar piezoelectric half-spaces.The plane wave solution of governing equations for micropolar piezoelectric medium indicates the propagation of three coupled plane waves.An incident plane wave at an interface between two dissimilar half-spaces generates three reflected and three transmitted waves.The relations between amplitude ratios of reflected and transmitted waves are derived which,in general,depend on material parameters and angle of incidence.The explicit expressions for energy ratios of reflected and transmitted waves are also obtained.For relevant material parameters,the results are illustrated graphically to show the micropolar piezoelectric effects on variations of amplitude ratios and the square root of energy ratios against the angle of incidence.展开更多
Pump-probe differential reflection and transmission spectroscopy is a very effective tool to study the nonequilibrium carrier dynamics of graphene. The reported sign of differential reflection from graphene is not exp...Pump-probe differential reflection and transmission spectroscopy is a very effective tool to study the nonequilibrium carrier dynamics of graphene. The reported sign of differential reflection from graphene is not explicitly explained and not consistent. Here, we study the differential reflection and transmission signals of graphene on a dielectric substrate. The results reveal the sign of differential reflection changes with the incident direction of the probe beam with respect to the substrate. The obtained theory can be applied to predict the differential signals of other two-dimensional materials placed on various dielectric substrates.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
Chen's technique of computing synthetic seismograms,which decomposes every vector with a set of basis of orthogonality and completeness before applying the Luco-Apsel-Chen(LAC)generalized reflection and transmissi...Chen's technique of computing synthetic seismograms,which decomposes every vector with a set of basis of orthogonality and completeness before applying the Luco-Apsel-Chen(LAC)generalized reflection and transmission coefficients method,is confirmed to be efficient in dealing with elastic waves in multi-layered media and accurate in any frequency range.In this article,we extend Chen's technique to the computation of coupled seismic and electromagnetic(EM)waves in layered porous media.Expanding the involved mechanical and electromagnetic fields by a set of scalar and vector wave-function basis,we obtain the fundamental equations which are subsequently solved by using a recently developed version of the LAC generalized reflection and transmission coefficients method.Our approach and corresponding program is validated by reciprocity tests.We also show a numerical example of a two-layer model with an explosion source.The P-to-EM conversion waves radiated from the interface may have potential application.展开更多
The plasma sheath covering hypersonic vehicles has a significant effect on the propagation of electromagnetic waves.Based on the calculation of the flow field of a conical cylindrical,this work studies the propagation...The plasma sheath covering hypersonic vehicles has a significant effect on the propagation of electromagnetic waves.Based on the calculation of the flow field of a conical cylindrical,this work studies the propagation of electromagnetic waves in plasma sheath at L-band and Ku-band,and discusses the propagation characteristics in the head,side and tail of the sheath.The dielectric properties of plasma sheath are related to flight speed and altitude.A flight condition corresponds to a unique distribution of dielectric properties.For the conical cylindrical,the results show that flight speed is generally negatively correlated with the transmissivity of the plasma sheath.The reflection characteristics of electromagnetic waves at the L-band and Kuband when obliquely incident to the plasma sheath show a downward trend.When the frequency is increased to Ku-band,the propagation characteristics of electromagnetic waves in the plasma sheath are related to the position of the sheath.展开更多
The present study analyzes the reflection and transmission phenomenon of water-waves in a two-layer ice-covered system. The upper layer is covered by an ice-sheet, whereas the bottom of the lower layer is undulated an...The present study analyzes the reflection and transmission phenomenon of water-waves in a two-layer ice-covered system. The upper layer is covered by an ice-sheet, whereas the bottom of the lower layer is undulated and permeable. By using regular perturbation analysis and Fourier transform technique, the problem is solved and the first order reflection and transmission coefficients are determined. It is found that these coefficients depend on the shape as well as the permeability of the undulating bottom. Therefore, from the practical viewpoint, an undulating bottom topography is considered to determine all the aforesaid coefficients. The role of various system parameters, such as porosity, angle of incidence and ice parameters, are discussed to analyze the transformation of incident water wave energy from one layer to another layer. The outcomes are demonstrated in graphical forms.展开更多
The diffraction of obliquely incident wave by two unequal barriers with different porosity in infinitely deep water is investigated by using two-dimensional linearized potential theory.Reflection and transmission coef...The diffraction of obliquely incident wave by two unequal barriers with different porosity in infinitely deep water is investigated by using two-dimensional linearized potential theory.Reflection and transmission coefficients are computed numerically using appropriate Galerkin approximations for two partially immersed and two submerged barriers.The amount of energy dissipation due to the permeable barriers is derived using Green’s integral theorem.The coefficient of wave force is determined using the linear Bernoulli equation of dynamic pressure jump on the porous barriers.The numerical results of hydrodynamics quantities are illustrated graphically.展开更多
In this work,an enriched model describing the longitudinal wave propagation is established based on Mindlin’s Second Strain Gradient(SSG)theory,which can describe the heterogeneity caused by the micro-structure inter...In this work,an enriched model describing the longitudinal wave propagation is established based on Mindlin’s Second Strain Gradient(SSG)theory,which can describe the heterogeneity caused by the micro-structure interactions in the frame of continuum mechanics.The governing equation and associated boundary conditions are derived based on Hamilton’s principle,then the dispersion relation of non-classical longitudinal wave together with the extra-waves appearing exclusively in SSG theory model are investigated.The investigations are based on the modal density,energy flow,and forced response of the rod.Wave transmission and reflection through planar interfaces based on the proposed model have been calculated.Finally,the results of the enriched model are well interpreted by comparing with the classical theory results,and some useful conclusions are derived on the SSG theory based model in the wave propagation characterization.展开更多
Using linear water-wave theory,wave scattering by a horizontal circular cylinder submerged in a three-layer ocean consisting of a layer of finite depth bounded above by finite depth water with free surface and below b...Using linear water-wave theory,wave scattering by a horizontal circular cylinder submerged in a three-layer ocean consisting of a layer of finite depth bounded above by finite depth water with free surface and below by an infinite layer of fluid of greater density is considered.The cylinder is submerged in either of the three layers.In such a situation time-harmonic waves with given frequency can propagate with three different wave numbers.Employing the method of multipoles the problem is reduced to an infinite system of linear equations which are solved numerically by standard technique after truncation.The transmission and reflection coefficients are obtained and depicted graphically against the wave number for all cases.In a two-layer fluid there are energy identities that exist connecting the transmission and reflection coefficients that arise.These energy identities are systematically extended to the three-fluid cases which are obtained.展开更多
An analysis is presented for the propagation of oblique water waves passing through an asymmetric submarine trench in presence of surface tension at the free surface.Reflection and transmission coefficients are evalua...An analysis is presented for the propagation of oblique water waves passing through an asymmetric submarine trench in presence of surface tension at the free surface.Reflection and transmission coefficients are evaluated applying appropriate multi-term Galerkin approximation technique in which the basis functions are chosen in terms of Gegenbauer polynomial of order 1/6 with suitable weights.The energy identity relation is derived by employing Green’s integral theorem in the fluid region of the problem.Reflection and transmission coefficients are represented graphically against wave numbers in many figures by varying several parameters.The correctness of the present method is confirmed by comparing the results available in the literature.The effect of surface tension on water wave scattering is studied by analyzing the reflection and transmission coefficients for a set of parameters.It can be observed that surface tension plays a qualitatively relevant role in the present study.展开更多
Assuming linear theory,the two dimensional problem of water wave scattering past thick rectangular barrier in presence of thin ice cover,is investigated here.Mainly four types of thick barriers are considered here and...Assuming linear theory,the two dimensional problem of water wave scattering past thick rectangular barrier in presence of thin ice cover,is investigated here.Mainly four types of thick barriers are considered here and also the ice cover is taken as a thin elastic plate.May be the barrier is partially immersed or bottom standing or fully submerged in water or in the form of thick rectangular wall with a submerged gap presence in water.The problem is formulated in terms of a first kind integral equation by considering the symmetric and antisymmetric parts of velocity potential function.The integral equation is solved by using multi term Galerkin approximation method involving ultraspherical Gegenbauer polynomials as its basis function.The numerical solutions of reflection and transmission coefficients are obtained for different parametric values and these are seen to satisfy the energy identity.These coefficients are depicted graphically against the wave number in a number of figures.Some figures available in the literature drawn by using different mathematical methods as well as laboratory experiments are also recovered following the present analysis without the presence of ice cover,thereby confirming the correctness of the results presented here.It is also observed that the reflection and transmission coefficients depend significantly on the width of the barriers.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61475123,61571355,and 61308025)the Natural Science Basic Research Plan in Shaanxi Province,China(Grant No.2016JQ4015)the Overseas Training Program for Young Backbones Teachers Sponsored by China Scholarship Council and Xidian University
文摘Based on angular spectrum expansion and 4 × 4 matrix theory, the reflection and transmission characteristics of a Laguerre Gaussian(LG) beam from uniaxial anisotropic multilayered media are studied. The reflected and transmitted beam fields of an LG beam are derived. In the case where the principal coordinates of the uniaxial anisotropic media coincide with the global coordinates, the reflected and transmitted beam intensities from a uniaxial anisotropic slab and three-layered media are numerically simulated. It is shown that the reflected intensity components of the incident beam, especially the TM polarized incident beam, are smaller than the transmitted intensity components. The distortion of the reflected intensity component is more evident than that of the transmitted intensity component. The distortion of intensity distribution is greatly affected by the dielectric tensor and the thickness of anisotropic media. We finally extend the application of the method to general anisotropic multilayered media.
基金the National Natural Science Foundation of China(Grant Nos.62071359,61975158,62001377,and 61801349)China Postdoctoral Science Foundation(Grant No.2016M602770)+3 种基金Natural Science Basic Research Plan in Shaanxi Province of China(Grant Nos.2019JQ405,2019JM-238,2020JM-192,and 2021JM-135)Natural Science Basic Research Program of Shaanxi,China(Grant No.2020JQ-331)Postdoctoral Science Foundation in Shaanxi Province and the Fundamental Research Funds for the Central Universities,Scientific Research Program Funded by Shaanxi Provincial Education Department(Grant No.20JS059)the Open Foundation of Laboratory of Pinghu,Pinghu,China。
文摘The reflection and transmission of a finite-power Airy beam incident on a dielectric slab are investigated by an analytical method.Based on the plane-wave angular spectrum expansion and Fresnel approximation,the analytical expressions of the reflected field,internal field as well as transmitted field in each region are obtained.Through numerical simulations,the intensity distributions of the incident beam,reflected beam,internal beam as well as transmitted beam are presented at oblique incidence.Besides,we also compare the intensity distributions of the geometrical-optics beam field,the first order beam mode field and the actual beam field,which indicates that the contribution of each order beam mode field to the actual beam field is related to the refractive index of the dielectric slab.Meanwhile,the reflection characteristics of the Airy beams in the special cases of Brewster incidence and total reflection are investigated.Finally,the effects of the optical thickness and refractive index of the dielectric slab on the peak intensity distributions and beam shifts of the reflected and transmitted beams are also discussed in detail.The analytical and numerical results will be useful to analyze the propagation dynamics of Airy beam in the dielectric slab and provide some theoretical supports to the design of optical film.
基金supported by the National Natural Science Foundation of China(No.U1839209).
文摘Wave propagation in horizontally layered media is a classical problem in seismic-wave theory.In semi-infinite space,a nondispersive Rayleigh wave mode exists,and the eigendisplacement decays exponentially with depth.In a layered model with increasing layer velocity,the phase velocity of the Rayleigh wave varies between the S-wave velocity of the bottom half-space and that of the classical Rayleigh wave propagated in a supposed half-space formed by the parameters of the top layer.If the phase velocity is the same as the P-or S-wave velocity of the layer,which is called the critical mode or critical phase velocity of surface waves,the general solution of the wave equation is not a homogeneous(expressed by trigonometric functions)or inhomogeneous(expressed by exponential functions)plane wave,but one whose amplitude changes linearly with depth(expressed by a linear function).Theories based on a general solution containing only trigonometric or exponential functions do not apply to the critical mode,owing to the singularity at the critical phase velocity.In this study,based on the classical framework of generalized reflection and transmission coefficients,the propagation of surface waves in horizontally layered media was studied by introducing a solution for the linear function at the critical phase velocity.Therefore,the eigenvalues and eigenfunctions of the critical mode can be calculated by solving a singular problem.The eigendisplacement characteristics associated with the critical phase velocity were investigated for different layered models.In contrast to the normal mode,the eigendisplacement associated with the critical phase velocity exhibits different characteristics.If the phase velocity is equal to the S-wave velocity in the bottom half-space,the eigendisplacement remains constant with increasing depth.
文摘In the present paper,we consider a problem of reflection and transmission of plane waves at an interface between two different transversely isotropic micropolar piezoelectric half-spaces.The plane wave solution of governing equations for micropolar piezoelectric medium indicates the propagation of three coupled plane waves.An incident plane wave at an interface between two dissimilar half-spaces generates three reflected and three transmitted waves.The relations between amplitude ratios of reflected and transmitted waves are derived which,in general,depend on material parameters and angle of incidence.The explicit expressions for energy ratios of reflected and transmitted waves are also obtained.For relevant material parameters,the results are illustrated graphically to show the micropolar piezoelectric effects on variations of amplitude ratios and the square root of energy ratios against the angle of incidence.
基金supported by the Chinese National Key Basic Research Special Fund (2011CB922003)International Science and Technology Cooperation Program of China (2013DFA51430)+1 种基金NSFC—National Natural Science Foundation of China (11174159, 11374164, 11304166)the Fundamental Research Funds for the Central Universities (65145005)
文摘Pump-probe differential reflection and transmission spectroscopy is a very effective tool to study the nonequilibrium carrier dynamics of graphene. The reported sign of differential reflection from graphene is not explicitly explained and not consistent. Here, we study the differential reflection and transmission signals of graphene on a dielectric substrate. The results reveal the sign of differential reflection changes with the incident direction of the probe beam with respect to the substrate. The obtained theory can be applied to predict the differential signals of other two-dimensional materials placed on various dielectric substrates.
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 the Natural R&D Special Fund for Public Welfare Industry(No.200808069)National Natural Science Foundation of China(Nos.40974038,40774028 and 40821062)
文摘Chen's technique of computing synthetic seismograms,which decomposes every vector with a set of basis of orthogonality and completeness before applying the Luco-Apsel-Chen(LAC)generalized reflection and transmission coefficients method,is confirmed to be efficient in dealing with elastic waves in multi-layered media and accurate in any frequency range.In this article,we extend Chen's technique to the computation of coupled seismic and electromagnetic(EM)waves in layered porous media.Expanding the involved mechanical and electromagnetic fields by a set of scalar and vector wave-function basis,we obtain the fundamental equations which are subsequently solved by using a recently developed version of the LAC generalized reflection and transmission coefficients method.Our approach and corresponding program is validated by reciprocity tests.We also show a numerical example of a two-layer model with an explosion source.The P-to-EM conversion waves radiated from the interface may have potential application.
文摘The plasma sheath covering hypersonic vehicles has a significant effect on the propagation of electromagnetic waves.Based on the calculation of the flow field of a conical cylindrical,this work studies the propagation of electromagnetic waves in plasma sheath at L-band and Ku-band,and discusses the propagation characteristics in the head,side and tail of the sheath.The dielectric properties of plasma sheath are related to flight speed and altitude.A flight condition corresponds to a unique distribution of dielectric properties.For the conical cylindrical,the results show that flight speed is generally negatively correlated with the transmissivity of the plasma sheath.The reflection characteristics of electromagnetic waves at the L-band and Kuband when obliquely incident to the plasma sheath show a downward trend.When the frequency is increased to Ku-band,the propagation characteristics of electromagnetic waves in the plasma sheath are related to the position of the sheath.
基金financially supported by the Council of Scientific and Industrial Research(CSIR),Govt.of India
文摘The present study analyzes the reflection and transmission phenomenon of water-waves in a two-layer ice-covered system. The upper layer is covered by an ice-sheet, whereas the bottom of the lower layer is undulated and permeable. By using regular perturbation analysis and Fourier transform technique, the problem is solved and the first order reflection and transmission coefficients are determined. It is found that these coefficients depend on the shape as well as the permeability of the undulating bottom. Therefore, from the practical viewpoint, an undulating bottom topography is considered to determine all the aforesaid coefficients. The role of various system parameters, such as porosity, angle of incidence and ice parameters, are discussed to analyze the transformation of incident water wave energy from one layer to another layer. The outcomes are demonstrated in graphical forms.
基金partially supported by a SERB,DST(EMR/2016/005315)
文摘The diffraction of obliquely incident wave by two unequal barriers with different porosity in infinitely deep water is investigated by using two-dimensional linearized potential theory.Reflection and transmission coefficients are computed numerically using appropriate Galerkin approximations for two partially immersed and two submerged barriers.The amount of energy dissipation due to the permeable barriers is derived using Green’s integral theorem.The coefficient of wave force is determined using the linear Bernoulli equation of dynamic pressure jump on the porous barriers.The numerical results of hydrodynamics quantities are illustrated graphically.
基金supported by the LabEx CeLyA (Centre Lyonnais d’Acoustique, ANR-10-LABX-0060) of Universitéde Lyon。
文摘In this work,an enriched model describing the longitudinal wave propagation is established based on Mindlin’s Second Strain Gradient(SSG)theory,which can describe the heterogeneity caused by the micro-structure interactions in the frame of continuum mechanics.The governing equation and associated boundary conditions are derived based on Hamilton’s principle,then the dispersion relation of non-classical longitudinal wave together with the extra-waves appearing exclusively in SSG theory model are investigated.The investigations are based on the modal density,energy flow,and forced response of the rod.Wave transmission and reflection through planar interfaces based on the proposed model have been calculated.Finally,the results of the enriched model are well interpreted by comparing with the classical theory results,and some useful conclusions are derived on the SSG theory based model in the wave propagation characterization.
文摘Using linear water-wave theory,wave scattering by a horizontal circular cylinder submerged in a three-layer ocean consisting of a layer of finite depth bounded above by finite depth water with free surface and below by an infinite layer of fluid of greater density is considered.The cylinder is submerged in either of the three layers.In such a situation time-harmonic waves with given frequency can propagate with three different wave numbers.Employing the method of multipoles the problem is reduced to an infinite system of linear equations which are solved numerically by standard technique after truncation.The transmission and reflection coefficients are obtained and depicted graphically against the wave number for all cases.In a two-layer fluid there are energy identities that exist connecting the transmission and reflection coefficients that arise.These energy identities are systematically extended to the three-fluid cases which are obtained.
基金Higher Education,Science and Tech-nology and Bio-Technology,Government of West Bengal Memo no:14(Sanc.)/ST/P/S&T/16G-38/2017.
文摘An analysis is presented for the propagation of oblique water waves passing through an asymmetric submarine trench in presence of surface tension at the free surface.Reflection and transmission coefficients are evaluated applying appropriate multi-term Galerkin approximation technique in which the basis functions are chosen in terms of Gegenbauer polynomial of order 1/6 with suitable weights.The energy identity relation is derived by employing Green’s integral theorem in the fluid region of the problem.Reflection and transmission coefficients are represented graphically against wave numbers in many figures by varying several parameters.The correctness of the present method is confirmed by comparing the results available in the literature.The effect of surface tension on water wave scattering is studied by analyzing the reflection and transmission coefficients for a set of parameters.It can be observed that surface tension plays a qualitatively relevant role in the present study.
基金This work is supported by DST through the INSPIRE fellowship to AS.(IF170841).
文摘Assuming linear theory,the two dimensional problem of water wave scattering past thick rectangular barrier in presence of thin ice cover,is investigated here.Mainly four types of thick barriers are considered here and also the ice cover is taken as a thin elastic plate.May be the barrier is partially immersed or bottom standing or fully submerged in water or in the form of thick rectangular wall with a submerged gap presence in water.The problem is formulated in terms of a first kind integral equation by considering the symmetric and antisymmetric parts of velocity potential function.The integral equation is solved by using multi term Galerkin approximation method involving ultraspherical Gegenbauer polynomials as its basis function.The numerical solutions of reflection and transmission coefficients are obtained for different parametric values and these are seen to satisfy the energy identity.These coefficients are depicted graphically against the wave number in a number of figures.Some figures available in the literature drawn by using different mathematical methods as well as laboratory experiments are also recovered following the present analysis without the presence of ice cover,thereby confirming the correctness of the results presented here.It is also observed that the reflection and transmission coefficients depend significantly on the width of the barriers.
