# The Problem of Oblique Scattering by a Thin Vertical Submerged Plate in Deep Water Revisited

09 Jan 2018-Iss: 9789811320941, pp 225-236

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.

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TL;DR: In this article, the mixed boundary value problem associated with scattering of obliquely incident water waves by a flexible porous barrier of different barrier configurations is considered and a novel connection is established between the solution potential of the converted problem and a resolvable potential in the quarter-plane.

2Â citations

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01 Jan 2020

TL;DR: In this article, the Galerkin method with simple polynomials multiplied by appropriate weights was used to solve the problem of water wave scattering in a single thin plane vertical barrier partially immersed or completely submerged in water.

Abstract: The explicit solutions exist for normal incidence of the surface wave train or a single thin plane vertical barrier partially immersed or completely submerged in deep water. However, for oblique incidence of the wave train and/or for finite depth water, no such explicit solution is possible to obtain. Some approximate mathematical techniques are generally employed to solve them approximately in the sense that quantities of physical interest associated with each problem, namely the reflection and transmission coefficients, can be obtained approximately either analytically or numerically. The method of Galerkin approximations has been widely used to investigate such water wave scattering problems involving thin vertical barriers. Use of Galerkin method with basis functions involving somewhat complicated functions in solving these problems has been carried out in the literature. Choice of basis functions as simple polynomials multiplied by appropriate weights dictated by the edge conditions at the submerged end points of the barrier providing fairly good numerical estimates for the reflection and transmission coefficients have been demonstrated in this article.

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283Â citations

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TL;DR: In this article, a thin vertical plate makes small, simple harmonic rolling oscillations beneath the surface of an incompressible, irrotational liquid, and a train of plane waves of frequency equal to the frequency of oscillation of the plate, is normally incident on the plate.

Abstract: A thin vertical plate makes small, simple harmonic rolling oscillations beneath the surface of an incompressible, irrotational liquid. The plate is assumed to be so wide that the resulting equations may be regarded as two-dimensional. In addition, a train of plane waves of frequency equal to the frequency of oscillation of the plate, is normally incident on the plate. The resulting linearized boundary-value problem is solved in closed form for the velocity potential everywhere in the fluid and on the plate. Expressions are derived for the first- and second-order forces and moments on the plate, and for the wave amplitudes at a large distance either side of the plate. Numerical results are obtained for the case of the plate held fixed in an incident wave-train. It is shown how these results, in the special case when the plate intersects the free surface, agree, with one exception, with results obtained by Ursell (1947) and Haskind (1959) for this problem.

118Â citations

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01 Sep 1969

TL;DR: In this paper, the authors used a method due to Williams to discuss the scattering of surface waves of small amplitude on water of infinite depth by a fixed vertical plane barrier extending indefinitely downwards from a finite depth.

Abstract: In this paper we use a method due to Williams(1) to discuss the scattering of surface waves of small amplitude on water of infinite depth by a fixed vertical plane barrier extending indefinitely downwards from a finite depth.

53Â citations