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water wave scattering by a Nearly Circular Cylinder Submerged Beneath an Ice-cover

Journal of Marine Science and Application 2015年第1期14卷 69-75页

作者： Rumpa Chakraborty Birendra Nath Mandal Physics and Applied Mathematics Unit Indian Statistical Institute Kolkata 700108 India

Assuming linear theory, the two-dimensional problem of water wave scattering by a horizontal nearly circular cylinder submerged in infinitely deep water with an ice cover modeled as a thin-elastic plate floating on water, is investigated here. The cross-section of the nearly circular cylinder is taken as r=a（1＋δC（θ））, where a is the radius of the corresponding circular cross-section of the cylinder, δ is a measure of small departure of the cross-section of the cylinder from its circularity and C（θ） is the shape function. Using a simplified perturbation technique the problem is reduced to two independent boundary value problems up to first order in δ. The first one corresponds to water wave scattering by a circular cylinder submerged in water with an ice-cover, while the second problem describes wave radiation by a submerged circular cylinder and involves first order correction to the reflection and transmission coefficients. The corrections are obtained in terms of integrals involving the shape function. Assuming a general Fourier expansion of the shape function, these corrections are evaluated approximately. It is well known that normally incident wave trains experience no reflection by a circular cylinder submerged in infinitely deep water with an ice cover. It is shown here that the reflection coefficient also vanishes up to first order for some particular choice of the shape function representing a nearly circular cylinder. For these cases, full transmission occurs, only change is in its phase which is depicted graphically against the wave number in a number of figures and appropriate conclusions are drawn.

关键词： water wave scattering ice-cover nearly circular cylinder shape function reflection coefficient transmission coefficient

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孔隙率对矩形沟槽上垂直多孔屏障的波浪散射效应影响

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哈尔滨工程大学学报（英文版） 2024年第1期23卷 85-100页

作者： Gour Das Rumpa Chakraborty Department of Mathematics Jadavpur UniversityKolkata-700032India Department of Mathematics Diamond Harbour Women’s UniversitySouth 24 Parganas-743368India

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 *** fluid region is divided into four subregions depending on the position of the barrier and the *** 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 *** 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 *** the solutions of the integral equations,the reflection coefficient,transmission coefficient,energy dissipation coefficient and horizontal wave force are determined and depicted *** 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 *** 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 *** present results are likely to play a crucial role in the analysis of surface wave propagation in oceans involving porous barrier over submarine trench.

关键词： water wave scattering Rectangular trench Vertical porous barriers Havelock’s inversion formula Multi-term galerkin approximation Reflection and transmission coefficients Energy dissipation Hydrodynamic force

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scattering of water waves by thick rectangular barriers in presence of ice cover

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Journal of Ocean Engineering and Science 2020年第3期5卷 279-293页

作者： Anushree Samanta Rumpa Chakraborty Department of Mathematics Jadavpur UniversityKolkata-700032India Department of Mathematics Diamond Harbour Women’s UniversitySouth 24 Parganas-743368India

Assuming linear theory,the two dimensional problem of water wave scattering past thick rectangular barrier in presence of thin ice cover,is investigated *** four types of thick barriers are considered here and also the ice cover is taken as a thin elastic *** 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 *** problem is formulated in terms of a first kind integral equation by considering the symmetric and antisymmetric parts of velocity potential *** integral equation is solved by using multi term Galerkin approximation method involving ultraspherical Gegenbauer polynomials as its basis *** numerical solutions of reflection and transmission coefficients are obtained for different parametric values and these are seen to satisfy the energy *** coefficients are depicted graphically against the wave number in a number of *** 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 *** is also observed that the reflection and transmission coefficients depend significantly on the width of the barriers.

关键词： Rectangular thick barrier Ice cover water wave scattering Multi term Galerkin approximation technique Reflection and transmission coefficients

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Propagation of oblique water waves by an asymmetric trench in the presence of surface tension

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Journal of Ocean Engineering and Science 2021年第2期6卷 206-214页

作者： Anjan Sasmal Soumen De Department of Applied Mathematics University of Calcutta92A.P.C.RoadKolkata 700009India

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 *** 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 *** energy identity relation is derived by employing Green’s integral theorem in the fluid region of the *** and transmission coefficients are represented graphically against wave numbers in many figures by varying several *** correctness of the present method is confirmed by comparing the results available in the *** effect of surface tension on water wave scattering is studied by analyzing the reflection and transmission coefficients for a set of *** can be observed that surface tension plays a qualitatively relevant role in the present study.

关键词： water wave scattering Surface tension Asymmetric trench Gegenbauer polynomial of order 1/6 Galerkin approximation Reflection and transmission coefficients

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wave Interaction with Dual Circular Porous Plates

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Journal of Marine Science and Application 2015年第4期14卷 366-375页

作者： Arpita Mondal R. Gayen Department of Mathematics Indian Institute of Technology Kharagpur 721302 India

In this paper we have investigated the reflection and the transmission of a system of two symmetric circular-arc-shaped thin porous plates submerged in deep water within the context of linear theory. The hypersingular integral equation technique has been used to analyze the problem mathematically. The integral equations are formulated by applying Green＇s integral theorem to the fundamental potential function and the scattered potential function into a suitable fluid region, and then using the boundary condition on the porous plate surface. These are solved approximately using an expansion-cure-collocation method where the behaviour of the potential functions at the tips of the plates have been used. This method ultimately produces a very good numerical approximation for the reflection and the transmission coefficients and hydrodynamic force components. The numerical results are depicted graphically against the wave number for a variety of layouts of the arc. Some results are compared with known results for similar configurations of dual rigid plate systems available in the literature with good agreement.

关键词： water wave scattering circular-arc-shaped plates hypersingular integral equation Green's integral theorem reflection coefficient energy identity hydrodynamic force

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Effect of Porosity on Oblique wave Diffraction by Two Unequal Vertical Porous Barriers

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Journal of Marine Science and Application 2019年第4期18卷 417-432页

作者： Anjan Sasmal Sandip Paul Soumen De Department of Applied Mathematics University of Calcutta700009KolkataIndia Department of Mathematics Dr.B.C.Roy Engineering College713206DurgapurIndia

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 *** and transmission coefficients are computed numerically using appropriate Galerkin approximations for two partially immersed and two submerged *** amount of energy dissipation due to the permeable barriers is derived using Green’s integral *** coefficient of wave force is determined using the linear Bernoulli equation of dynamic pressure jump on the porous *** numerical results of hydrodynamics quantities are illustrated graphically.

关键词： water wave scattering Galerkin approximation Porosity Two unequal barriers Reflection and transmission coefficients

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