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B. N. Mandal

Bio: B. N. Mandal is an academic researcher from University of Calcutta. The author has contributed to research in topics: Scattering & Surface wave. The author has an hindex of 1, co-authored 1 publications receiving 8 citations.

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Journal ArticleDOI

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TL;DR: In this paper, an appropriate one-term Galerkin approximation is used to evaluate very accurate upper and lower bounds for the reflection and transmission coefficients in the problems of oblique water wave diffraction by a thin vertical barrier present in water of uniform finite depth.
Abstract: An appropriate one-term Galerkin approximation is used to evaluate very accurate upper and lower bounds for the reflection and transmission coefficients in the problems of oblique water wave diffraction by a thin vertical barrier present in water of uniform finite depth. Four different configurations of the barrier are considered. The barrier may be partially immersed, or it may be submerged from a finite depth and extending down to the seabed, or it may be in the form of a submerged plate which does not extend down to the bottom, or it may be in the form of a thin vertical wall with a submerged gap. Very accurate upper and lower bounds for the reflection and transmission coefficients for different values of the various parameters are obtained numerically. The results for the reflection coefficient are displayed in tables. Comparison with known results obtained by another method is also made.

40 citations

Journal ArticleDOI

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TL;DR: In this paper, a train of small-amplitude surface waves is obliquely incident on a fixed, thin, vertical plate submerged in deep water, and an appropriate one-term Galerkin approximation is employed to calculate very accurate upper and lower bounds for the reflection and transmission coefficients for any angle of incidence and any wave number.
Abstract: A train of small-amplitude surface waves is obliquely incident on a fixed, thin, vertical plate submerged in deep water. The plate is infinitely long in the horizontal direction. An appropriate one-term Galerkin approximation is employed to calculate very accurate upper and lower bounds for the reflection and transmission coefficients for any angle of incidence and any wave number thereby producing very accurate numerical results.

20 citations

Journal ArticleDOI

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TL;DR: In this paper, velocity potentials describing the irrotational infinitesimal motion of two superposed inviscid and incompressible fluids under gravity with a horizontal plane of mean surface of separation, are derived due to a vertical line source present in either of the fluids, whose strength, besides being harmonic in time, varies sinusiodal along its length.
Abstract: Velocity potentials describing the irrotational infinitesimal motion of two superposed inviscid and incompressible fluids under gravity with a horizontal plane of mean surface of separation, are derived due to a vertical line source present in either of the fluids, whose strength, besides being harmonic in time, varies sinusiodal(y along its length. The technique of deriving the potentials here is an extension of the technique used for the case of only time harmonic vertical line source. The present case is concerned with the two-dimensional modified Helmholtz's equation while the previous is concerned with the two-dimenslonal Laplace's equation.

6 citations

Book ChapterDOI

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09 Jan 2018
TL;DR: In this paper, the problem of oblique scattering by fixed thin vertical plate submerged in deep water is studied by employing single-term Galerkin approximation involving constant as basis multiplied by appropriate weight function after reducing it to solving a pair of first kind integral equations.
Abstract: The problem of oblique scattering by fixed thin vertical plate submerged in deep water is studied here, assuming linear theory, by employing single-term Galerkin approximation involving constant as basis multiplied by appropriate weight function after reducing it to solving a pair of first kind integral equations. Upper and lower bounds of reflection and transmission coefficients when evaluated numerically are seen to be very close so that their averages produce fairly accurate numerical estimates for these coefficients. Numerical estimates for the reflection coefficient are depicted graphically against the wave number for different values of various parameters. The numerical results obtained by the present method are found to be in an excellent agreement with the known results.

2 citations

Journal ArticleDOI

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TL;DR: In this paper, the problem of the transmission of a train of surface water waves obliquely incident on a thin plane vertical barrier with a narrow gap is reduced to the solution of an integral equation and the transmission and reflection coefficients are also obtained approximately and represented graphically against the different angles of incidence for fixed wave numbers.
Abstract: This note is concerned with the transmission of a train of surface water waves obliquely incident on a thin plane vertical barrier with a narrow gap. Within the framework of the linearized theory of water waves, the problem is reduced to the solution of an integral equation which is solved approximately. The transmission and reflection co-efficients are also obtained approximately and represented graphically against the different angles of incidence for fixed wave numbers.

1 citations