# 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.

##### Citations

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TL;DR: In this article, the authors investigated the hydrodynamic interactions induced by arrays of elliptical cylinders subjected to regular waves using the Mathieu functions addition theorem, which converts elliptical harmonics from one elliptic coordinate system to a remote elliptic coordinates system.

17 citations

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TL;DR: In this paper, a semi-analytical model for solving wave radiation from a truncated cylinder of arbitrary cross section is presented based on linear potential flow theory, where the water domain is divided into the interior domain beneath the cylinder and the exterior domain outside the vertical cylinder column.

16 citations

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12 Jul 2018TL;DR: In this article, the most important geometries for hydrodynamic boundary value problems are unified, which allow for the development of analytical solutions for hydroynamics boundary value problem.

Abstract: The value of analytical solutions relies on the rigorous formulation, and a strong mathematical background. This comprehensive volume unifies the most important geometries, which allow for the development of analytical solutions for hydrodynamic boundary value problems. It offers detailed explanations of the Laplance domain and numerical results associated with such problems, providing deep insight into the theory of hydrodynamics. Extended numerical calculations are provided and discussed, allowing the reader to use them as benchmarks for their own computations and making this an invaluable resource for specialists in in various disciplines, including hydrodynamics, acoustics, optics, electrostatics, and brain imaging.

16 citations

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TL;DR: In this article, a finite array of floating flap gates oscillating wave surge converter (OWSC) in water of constant depth was considered and the diffraction and radiation potentials were solved in terms of elliptical coordinates and Mathieu functions.

Abstract: We consider a finite array of floating flap gates oscillating wave surge converter (OWSC) in water of constant depth. The diffraction and radiation potentials are solved in terms of elliptical coordinates and Mathieu functions. Generated power and capture width ratio of a single gate excited by incoming waves are given in terms of the radiated wave amplitude in the far field. Similar to the case of axially symmetric absorbers, the maximum power extracted is shown to be directly proportional to the incident wave characteristics: energy flux, angle of incidence and wavelength. Accordingly, the capture width ratio is directly proportional to the wavelength, thus giving a design estimate of the maximum efficiency of the system. We then compare the array and the single gate in terms of energy production. For regular waves, we show that excitation of the out-of-phase natural modes of the array increases the power output, while in the case of random seas we show that the array and the single gate achieve the same efficiency.

16 citations

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TL;DR: In this paper, an analytic method based on linear potential flow theory was developed to solve the diffraction problem and evaluate the excitation forces and moments acting on each cylinder, where the water domain is divided into the interior regions below each cylinder and an exterior region extending to infinity in the horizontal plane.

12 citations

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

...Later, 12 these problems were re-investigated without the shallow-water restriction [21]; therefore, in 13 addition to the angular coordinates, the vertical coordinate was retained in the analysis....

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##### References

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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