# The scattering of an obliquely incident surface wave by a submerged fixed vertical plate

01 Jun 1984-Journal of Mathematical Physics (American Institute of Physics)-Vol. 25, Iss: 6, pp 1780-1783

TL;DR: In this article, the problem of scattering of surface waves obliquely incident on a submerged fixed vertical plate is solved approximately for a small angle of incidence by reducing it to the solution of an integral equation.

Abstract: The problem of scattering of surface waves obliquely incident on a submerged fixed vertical plate is solved approximately for a small angle of incidence by reducing it to the solution of an integral equation The correction to the reflection and transmission coefficients over their normal incidence values for a small angle of incidence are obtained For different values of the incident angle these coefficients are evaluated numerically, taking particular values of the wave number and the depth of the plate, and represented graphically

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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

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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, 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.

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##### References

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01 Jul 1966

TL;DR: In this article, an alternative approach is presented to the problem of the scattering of small amplitude two-dimensional water waves by a fixed barrier, one edge of the barrier lying in the free surface of the water.

Abstract: Introduction. In this note an alternative approach is presented to the problem of the scattering of small amplitude two-dimensional water waves by a fixed barrier, one edge of the barrier lying in the free surface of the water. This problem was first solved by Ursell ((1)) and generalizations of the problem have been considered by John ((2)) and Lewin ((3)).

45 citations

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TL;DR: In this paper, the effect of a rigid circular cylinder, wholly immersed within and lying parallel to the free surface of an incompressible and inviscid fluid, on straight-crested surface waves passing overhead is investigated.

Abstract: The effect of a rigid circular cylinder, wholly immersed within and lying parallel to the free surface of an incompressible and inviscid fluid, on straight‐crested surface waves passing overhead is investigated. A mode of analysis is developed, on the hypotheses of small amplitude and time‐periodic fluid motions, that encompasses all directions of incidence of the primary wave; and is used to extend results previously obtained in the case of normal incidence. It is shown, in particular, that the absence of surface‐wave reflection at normal incidence gives way to a partial reflection for other primary directions, which in turn verges on completeness as the direction of the incoming wave becomes more closely aligned with that of the cylinder axis.

34 citations

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TL;DR: In this article, the diffraction of surface waves, obliquely incident on a partially immersed fixed vertical barrier in deep water, is solved approximately by reducing it to the solution of an integral equation, for small angle of incidence of the incident wave.

Abstract: The problem of the diffraction of surface waves, obliquely incident on a partially immersed fixed vertical barrier in deep water, is solved approximately by reducing it to the solution of an integral equation, for small angle of incidence of the incident wave. The corrections to the reflection and transmission coefficients over their normal incidence values for small angle of incidence are obtained and presented graphically for some intermediate values of wave numbers.

13 citations

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