# Diffraction of non-linear surface waves by a circular cylinder

TL;DR: In this paper, a nonlinear diffraction theory of periodic gravity waves due to their interaction with a circular cylinder which extends from the ocean bottom through the free surface is presented, where the velocity potential, free surface elevation and the frequency parameter are expanded as series in powers of a parameter which is the ratio of the amplitude to wave length.

Abstract: A non-linear diffraction theory of periodic gravity waves due to their interaction with a circular cylinder which extends from the ocean bottom through the free surface is presented. In order to obtain the solution, the velocity potential, the free surface elevation and the frequency parameter are expanded as series in powers of a parameter which is the ratio of the amplitude to wave length. Knowing the velocity potential of the incident wave, the velocity potential of the scattered wave for the corresponding order is obtained satisfying the proper boundary conditions and the radiation condition. The total potential governing the motion is thus obtained as a sum of incident and scattered potential for computing the pressures and forces on the cylinder.

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TL;DR: In this paper, the evanescent field structure over the wave front, as represented by equiphase planes, is identified as one of the most important and easily recognizable forms of surface wave.

Abstract: This paper calls attention to some of the most important and easily recognizable forms of surface wave, pointing out that their essential common characteristic is the evanescent field structure over the wave front, as represented by equiphase planes. The problems of launching and supporting surface waves must, in general, be distinguished from one another and it does not necessarily follow that because a particular surface is capable of supporting a surface wave that a given aperture distribution of radiation, e.g. a vertical dipole, can excite such a wave. The paper concludes with a discussion of the behavior of surface waves and their applications.

1,187 citations

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01 Dec 1954

TL;DR: In this paper, a quantitative understanding of the forces developed by wave action against circular piling is presented, where the authors focus on the effect of wave action on circular piling and show that wave action is a powerful force against piling.

Abstract: : Although circular piling is a much-used structural element in shore protection, harbor, and other maritime structures, only recently have significant advances been made toward gaining a quantitative understanding of the forces developed by wave action against piling. The present report deals with this subject.

481 citations

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29 Jan 2011

TL;DR: In this article, the results of the fifth order theory and values of the various coefficients as a function of the parameter d/L were presented for gravity waves of greater steepness.

Abstract: In dealing with problems connected with gravity waves, scientists and engineers frequently find it necessary to make lengthy theoretical calculations involving such wave characteristics as wave height, wave length, period, and water depth. Several approximate theoretical expressions have been derived relating the above parameters. Airy, for instance, contributed a very valuable and complete theory for waves traveling over a horizontal bottom in any depth of water. Due to the simplicity of the Airy theory, it is frequently used by engineers. This theory, however, was developed for waves of very small heights and is inaccurate for waves of finite height. Stokes presented a similar solution for waves of finite height by use of trigonometric series. Using five terms in the series, this solution will extend the range covered by the Airy theory to waves of greater steepness. No attempt has been made in this paper to specify the range where the theory is applicable. The coefficients in these series are very complicated and for a numerical problem, the calculations become very tedious. Because of this difficulty, this theory would be very little used by engineers unless the value of the coefficient is presented in tabular form. The purpose of this paper is to present the results of the fifth order theory and values of the various coefficients as a function of the parameter d/L.

170 citations

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30 Nov 1971

TL;DR: In this paper, an intermediate-level text on the use of integral transforms in applied mathematics and engineering is presented, which is divided into five parts covering integral transform pairs, the Laplace transform, Fourier transforms, Hankel transform, and finite Fourier transform.

Abstract: An intermediate-level text on the use of integral transforms in applied mathematics and engineering. Existing works either cover the subject in more elementary form or are advanced treatises. In a very lucid style the author deals with the use of this important mathematical tool to solve ordinary and partial differential equations in problems in electrical circuits, mechanical vibration and wave motion, heat conduction, and fluid mechanics. The book is divided into five parts covering integral transform pairs, the Laplace transform, Fourier transforms, Hankel transforms, and finite Fourier transforms. A basic knowledge of complex variables and elementary differential equations is assumed. There are many exercises and examples drawn from the above fields, tables of the transform pairs needed in the text, and a glossary of terms with which the student may be unfamiliar. For the student who seeks further background on the subject, an annotated bibliography is provided.

42 citations

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