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Journal ArticleDOI

Three-dimensional wave scattering by elliptical breakwaters

01 Jan 1988-Ocean Engineering (Pergamon)-Vol. 15, Iss: 2, pp 103-118
TL;DR: In this paper, the diffraction of small-amplitude surface waves by floating and submerged stationary elliptical breakwaters in water of arbitrary uniform depth is investigated analytically, and the theoretical formulation leads to solutions for the fluid velocity potential in terms of series of Mathieu and modified Mathieu functions of real argument.
About: This article is published in Ocean Engineering.The article was published on 1988-01-01. It has received 22 citations till now. The article focuses on the topics: Mathieu function & Surface wave.
Citations
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Journal ArticleDOI
TL;DR: In this paper, the behavior of a flexible, floating breakwater consisting of a moored, compliant, beam-like structure anchored to the seabed and possessing a small buoyancy chamber at the tip was investigated.
Abstract: This study investigated the behavior of a flexible, floating breakwater consisting of a moored, compliant, beam-like structure anchored to the seabed and possessing a small buoyancy chamber at the tip. The fluid domain is treated utilizing the boundary integral equation method, modifications have been made to the basic formulation to account for the zero thickness of the idealized structure. The dynamic behavior of the breakwater is described through an appropriate Green's function and the coupled fluid-structure system is then solved numerically. Example results have been presented which illlustrate the effects of the various waves and structural parameters on the efficiency of the breakwater as a barrier to wave action. It was found that for typical wave conditions relatively stiff structures are required in order to obtain high wave reflection coefficients.

50 citations

Journal ArticleDOI
TL;DR: In this paper, a semi-analytical solution methodology for the linear hydrodynamic diffraction induced by arrays of elliptical cylinders subjected to incident waves is presented, where the solution of the Laplace equation in elliptic coordinates for both the incident and the diffracted waves is formulated analytically in terms of the even and odd periodic and radial Mathieu functions.

43 citations


Cites background from "Three-dimensional wave scattering b..."

  • ...The works reported in the literature that treat the hydrodynamic interaction problem of incident wave fields with elliptical bodies using semi-analytical formulations, limit the investigation to single bodies [16–18]....

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Journal ArticleDOI
TL;DR: In this paper, an analytic solution for the total velocity potential for an arbitrary body of the array and accordingly, to express the hydrodynamic pressure, the exciting forces and the wave elevation in compact analytic closed-form.

29 citations

Journal ArticleDOI
TL;DR: The diffraction of small-amplitude surface waves by a horizontally submerged disk of elliptic cross section located at a finite depth beneath the free surface is investigated analytically in this article.
Abstract: The diffraction of small-amplitude surface waves by a horizontally submerged disk of elliptic cross section located at a finite depth beneath the free surface is investigated analytically. The fluid domain is divided into three regions, two internal regions, one above and one beneath the disk, and an external region extending to infinity in the horizontal plane. The theoretical formulation leads to solutions for the fluid velocity potentials in each region in terms of series of Mathieu and modified Mathieu functions of real argument. Numerical results are presented for the wave-induced forces and moments, and the variation of water surface elevation in the vicinity of the disk for a range of wave and structural parameters. In particular, the results for the hydrodynamic loads show significant differences from the corresponding estimates for a circular disk, while the results for the water surface elevation clearly show the effect of wave focusing around the rear of the disk.

25 citations

Journal ArticleDOI
TL;DR: A second-order nonlinear theory for an array of curved flap-type wave energy converters (WECs) in open sea, excited by oblique incident waves is presented in this paper.

22 citations

References
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Book
01 Jan 1964

2,100 citations

Journal ArticleDOI
TL;DR: In this article, the scattering of surface gravity waves by a circular dock is considered in order to determine the horizontal and vertical forces and torque on the dock, and the solution is shown to have phase independent of depth and so may be obtained from an infinite set of real equations.
Abstract: The scattering of surface gravity waves by a circular dock is considered in order to determine the horizontal and vertical forces and torque on the dock. An incident plane wave is expanded in Bessel functions, and for each mode the problem is formulated in terms of the potential on the cylindrical surface containing the dock and extending to the bottom. The solution is shown to have phase independent of depth and so may be obtained from an infinite set of real equations, which are solved numerically by Galerkin's method. The convergence of the solution is discussed, and some numerical results are presented.This problem has been investigated previously by Miles & Gilbert (1968) by a different method, but their work contained errors.

261 citations

Journal ArticleDOI
TL;DR: In this paper, two approximate methods are presented for the calculation of the wave induced forces and moments on a vertical, surface-piercing cylinder of elliptic cross section, which provide a substantial reduction in computational effort when Compared with the exact solution which involves the numerical evaluation of Mathieu functions.
Abstract: Two approximate methods are presented for the calculation of the wave induced forces and moments on a vertical, surface‐piercing cylinder of elliptic cross section. Both methods provide a substantial reduction in computational effort when Compared with the exact solution which involves the numerical evaluation of Mathieu functions. One method involves the expansion of the exact expressions for the forces and moments for small values of the elliptic eccentricity parameter. The second method is based on Green's theorem and gives rise to an integral equation for the fluid velocity potential on the cylinder surface. Numerical results are presented for a range of relevant parameters and show excellent agreement with the computed values of the exact solution.

45 citations

Journal ArticleDOI
TL;DR: In this article, the mathematical solution to the diffraction problem is obtained on the basis of the linearized long-wave approximation for a shiplike body with beam-to-length ratio approximately equal to 0.2.
Abstract: Exciting forces and moments due to plane incident waves on a stationary platform are studied in the report. The platform is a vertical cylinder with a finite draft and elliptical cross section. The mathematical solution to the diffraction problem is obtained on the basis of the linearized long-wave approximation. Numerical results via Mathieu functions are presented for a shiplike body with beam-to-length ratio approximately equal to 0.2. Various draft-to-depth ratios and angles of incidence are considered. Results have been checked with the limiting case of a circular cylinder for the long-wavelength range. Aside from its own practical interest, the present theory provides a basis for comparison with other approximate theories of slender-body type and serves as a prelude to the corresponding calculations for arbitrary wavelengths. (Author)

38 citations

Journal ArticleDOI
TL;DR: Algor i thm 352 is a package of double-precision FORTRAN rout ines which consists of the following p r imary Rout ines : MFCVAL, M A T H, and BESSEL.

37 citations