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.
45 citations
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.
22 citations
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 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