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. © 1984 American Institute of Physics.

B MANDAL

S K GOSWAMI

Fulltext

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The scattering of an obliquely incident surface wave by a submerged fixed vertical plate

Journal of Mathematical Physics

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. © 2020, Springer Nature Switzerland AG.

Studies in Systems, Decision and Control

Use of Galerkin Technique in Some Water Wave Scattering Problems Involving Plane Vertical Barriers

The paper involves oblique scattering of water waves by three non-identical thin vertical barriers arranged asymmetrically in deep water. The asymmetry in the configuration of the barriers is in the sense that the outer barriers are situated at two different distances from the inner (middle) barrier. Two geometries of the barriers have been considered. In the first one, the two outer barriers are partially immersed and the inner barrier is completely submerged and extends infinitely downwards while the second one is its complementary. Each problem is reduced to a system of three simultaneous first kind integral equations involving differences of potential functions across the barriers. These integral equations are solved approximately by employing single-term Galerkin's approximations where the single term is the exact solution of the corresponding integral equation arising in the problem of scattering of normally incident water waves by a single thin vertical barrier in deep water. Fairly accurate numerical estimates for the reflection and transmission coefficients are obtained which satisfy the energy identity. For both the configurations of the barriers, the behavior of reflection coefficient is observed by depicting it graphically against wavenumber for different values of various parameters. It is observed that the reflection coefficient vanishes for a sequence of discrete wavenumbers only when the outer two barriers are identical and equidistant from the inner barrier. However, this phenomenon may differ sometimes for the second configuration of the barriers. Numerical results available in the literature are recovered as special cases thereby validating the accuracy of the numerical estimates obtained here. © 2019 The Japan Society of Fluid Mechanics and IOP Publishing Ltd.

Fluid Dynamics Research

Water wave scattering by three thin vertical barriers arranged asymmetrically in deep water

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. © 1989, Hindawi Publishing Corporation. All rights reserved.

International Journal of Mathematics and Mathematical Sciences

Transmission of Obliquely Incident Surface Waves Through a Narrow Gap

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 sinusiodally 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-dimensional Laplace’s equation. © 1986, Hindawi Publishing Corporation. All rights reserved.

Two-Dimensional Source Potentials in a Two-Fluid Medium for the Modified Helmholtzâ€™S Equation

The problem of scattering of surface water waves obliquely incident on a fixed half immersed circular cylinder is solved approximately by reducing it to the solution of an integral equation and also by the method of multipoles. For different values of the angle of incidence and the wave number the reflection and transmission coefficients obtained by both methods are evaluated numerically and represented graphically to compare the results obtained by the respective methods. © 1984, Cambridge Philosophical Society. All rights reserved.

Mathematical Proceedings of the Cambridge Philosophical Society

Scattering of surface waves obliquely incident on a fixed half immersed circular cylinder

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. © 1983 Martinus Nijhoff Publishers.

Journal	Journal of Mathematical Physics
Publisher	-
ISSN	0022-2488