# Three-dimensional wave scattering by elliptical breakwaters

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.

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TL;DR: In this paper, the effect of incident wave's deviation angle on the force on the unit length of one elliptical vertical cylinder located within deep waters examined with finite element method was investigated.

Abstract: Today, a vast range of offshore structures is used in different parts of the world. Computing the force on an offshore structure is one of the first measures for designing the structure and also one of the most difficult steps in the design process. Most of offshore structures are considered as large structures. In these cases, it is used from diffraction theory for computing the imposed force. Using cylindrical elements is common in construction these structures. In this study, the effect of incident wave’s deviation angle on the force on the unit length of one elliptical vertical cylinder located within deep waters examined with finite element method. The obtained results show that the used numerical method had acceptable accuracy and the surge force on the vertical cylinder decreases with deviation angle increasing and consequently the sway force increases.

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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

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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

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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

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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