Author

# P. K. Kundu

Bio: P. K. Kundu is an academic researcher from University of Calcutta. The author has contributed to research in topics: Reflection (physics) & Scattering. The author has an hindex of 2, co-authored 4 publications receiving 24 citations.

##### Papers

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TL;DR: In this paper, the scattering of surface water waves by a nearly vertical plate, completely submerged in deep water, has been deduced employing two mathematical methods: integral equation formulation of the problem obtained by a suitable use of Green's integral theorem in the fluid region, while the second method concerns a simple and straightforward perturbational analysis along with the application of Green’s integral theorem.

Abstract: Some new results concerning the scattering of surface water waves by a nearly vertical plate, completely submerged in deep water, have been deduced employing two mathematical methods. The first method concerns an integral equation formulation of the problem obtained by a suitable use of Green’s integral theorem in the fluid region, while the second method concerns a simple and straightforward perturbational analysis along with the application of Green’s integral theorem. The two methods produce the same result for the first order corrections to the reflection and transmission coefficients. Considering some particular shapes of the curved plate, numerical calculations are also performed.

16 citations

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TL;DR: In this paper, an alternative but simple approach is employed to reinvestigate the two-dimensional problem of incoming surface water waves against a rigid vertical cliff, which is the same problem we consider in this paper.

Abstract: An alternative but simple approach is employed to reinvestigate the two-dimensional problem of incoming surface water waves against a rigid vertical cliff.

6 citations

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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

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TL;DR: In this paper , the Fourier transform with respect to space and the Laplace transform with time are used to obtain the form of the free surface in terms of multiple integrals.

Abstract: Abstract The problem of generation of two-dimensional unsteady motion in a viscous incompressible fluid of finite depth is investigated here. The motion is generated due to initial disturbances in the form of prescribed surface pressure or displacement at the free surface. The Fourier transform with respect to space and the Laplace transform with respect to time are used to obtain the form of the free surface in terms of multiple integrals. Finally, an asymptotic form of the free surface is obtained using the method of steepest descent.

##### Cited by

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TL;DR: In this article, the problem of oblique water wave diffraction by two equal thin, parallel, fixed vertical barriers with gaps present in uniform finite-depth water is investigated, and three types of barrier configurations are considered.

Abstract: The problem of oblique water wave diffraction by two equal thin, parallel, fixed vertical barriers with gaps present in uniform finite-depth water is investigated here. Three types of barrier configurations are considered. A one-term Galerkin approximation is used to evaluate upper and lower bounds for reflection and transmission coefficients for each configuration. These bounds are seen to be very close numerically for all wave numbers and as such their averages produce good numerical estimates for these coefficients. Only the bounds for the reflection coefficient are numerically computed. These are also numerically compared with the results obtained by using multiterm Galerkin approximations involving Chebyshev polynomials for a wide range of parameters. Numerical results for the reflection coefficients for the three barrier configurations are presented graphically. It is seen that total reflection occurs only for the surface-piercing barriers while total transmission occurs for all the three configurations considered here. It is also observed that the introduction of an equal second barrier to a submerged barrier increases the reflection coefficient considerably in some frequency bands and as such submerged double barrier configurations are preferable to a submerged single barrier for the purpose of reflecting more wave energy into the open sea.

50 citations

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TL;DR: In this article, the problem of oblique wave scattering by a submerged thin vertical wall with a gap in finite-depth water and its modification when another identical wall is introduced, is investigated.

Abstract: The problem of oblique wave scattering by a submerged thin vertical wall with a gap in finite-depth water and its modification when another identical wall is introduced, are investigated in this paper. The techniques of both one-term and multiterm Galerkin approximations have been utilized in the mathematical analysis. The multi-term approximations in terms of appropriate Chebyshev polynomials provide extremely accurate numerical estimates for the reflection coefficient. The reflection coefficient is depicted graphically for a number of geometries. It is found that by the introduction of another identical wall, there occurs zero reflection for certain wave numbers. This may have some bearings on the modelling of a breakwater.

24 citations

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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

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TL;DR: In this paper, a class of boundary value problems involving propagation of two-dimensional surface water waves, associated with deep water and a plane vertical rigid barrier is investigated under the assumption that the surface is covered by a thin sheet of ice.

Abstract: A class of boundary value problems involving propagation of two-dimensional surface water waves, associated with deep water and a plane vertical rigid barrier is investigated under the assumption that the surface is covered by a thin sheet of ice. Assuming that the ice-cover behaves like a thin isotropic elastic plate, the problems under consideration lead to those of solving the two-dimensional Laplace equation in a quarter-plane, under a Neumann boundary condition on the vertical boundary and a condition involving up to fifth order derivatives of the unknown function on the horizontal ice-covered boundary, along with two appropriate edge conditions, ensuring the uniqueness of the solutions. Two different methods are employed to solve the mixed boundary value problems completely, by determining the unique solution of a special type of integral equation of the first kind in the first method and by exploiting the analyticity property of the Fourier cosine transform in the second method.

19 citations

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TL;DR: In this paper, a rigid, nearly vertical, partially immersed wide plate is constrained to rotate about a horizontal axis through it, and the amplitude of small rolling oscillations of the plate is studied.

Abstract: A rigid, nearly vertical, partially immersed wide plate is constrained to rotate about a horizontal axis through it. The waves from small rolling oscillations of the plate are studied. Expressions for the first-order corrections to the amplitudes of the wave motion so set at large distances on the right and left sides of the plate are obtained by the use of Green’s integral theorem. Assuming a Fourier expansion of a function related to the shape of the plate, these corrections are calculated explicitly. Considering some particular explicit forms for the shape function, numerical calculations are performed.

9 citations