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Journal ArticleDOI

Nonlinear wave interaction with a vertical circular cylinder. Part I: Diffraction theory

01 Jan 1990-Ocean Engineering (Pergamon)-Vol. 17, Iss: 4, pp 345-377
TL;DR: In this article, a closed-form solution for the velocity potential resulting from the interaction of second-order Stokes waves with a large vertical circular cylinder was developed, which was then used to determine the theoretical free surface elevations around the cylinder consistent to second order.
About: This article is published in Ocean Engineering.The article was published on 1990-01-01. It has received 76 citations till now. The article focuses on the topics: Potential flow around a circular cylinder & Stokes wave.
Citations
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Journal ArticleDOI
TL;DR: In this paper, the second-order theory explains a significant portion of the nonlinear wave run-up distribution measured at all angles around a large diameter vertical circular cylinder, and the design curves are presented for estimating the maximum secondorder wave runup for a wide range of conditions in terms of the relative depth, relative cylinder size, and wave steepness.

115 citations

Journal ArticleDOI
TL;DR: In this article, the Open Field Operation and Manipulation (OpenFoam®) package is used to simulate wave-structure interactions and a new wave boundary condition is developed for extreme waves.

106 citations


Cites background or methods from "Nonlinear wave interaction with a v..."

  • ...The main purpose of this case is to provide a comparison between the OF prediction and theoretical models which are based on linear and second-order diffraction theory (see Kriebel, 1998), as well as reported experimental work (see Kriebel, 1998)....

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  • ...7%, as described by Kriebel (1998). Fig. 15 also illustrates the OF prediction with second order Stokes wave boundary condition, the OF prediction agrees with the experiment at the maximum force is predicted within 0.5% and the mean force is predicted within 15%. In comparison with second-order theory, OF agrees well; the maximum force is predicted within 0.4% and the mean force is predicted within 0.5%. The nonlinearities are the result of dominance of the second order plane wave components and are common features of nonlinear inertial forces experienced at small kr < 0.4, as discussed by Kriebel (1998). A small difference in the result is expected because the physical data is averaged over 10 wave periods, whereas the numerical result represents one wave cycle only once a steady state has been reached....

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  • ...More recently, second-order theories (Kriebel, 1998, Rahman and Heaps, 1983 and Taylor and Hung 1987), which consider the nonlinearity and can give more accurate wave force predictions, were proposed....

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  • ...The nonlinearities are the result of dominance of the second order plane wave components and are common features of nonlinear inertial forces experienced at small kr 0.4, as discussed by Kriebel (1998)....

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  • ...…simulated an oscillating water column device in waves by solving the Navier Stokes equations with the level set method for the free surface, and Boccotti et al. (2012), Boo (2002, 2006), Dixon et al. (1979), Chaplin et al. (1997) and Kriebel (1998) have also investigated wave forces on structures....

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Journal ArticleDOI
TL;DR: In this paper, a two-dimensional, fully nonlinear Computational Fluid Dynamics (CFD) model was developed to analyse the efficiency of fixed Oscillating Water Column (OWC) Wave Energy Conversion (WEC) devices with linear power take off systems.

101 citations

Journal ArticleDOI
TL;DR: In this paper, the second-order water wave diffraction of an incident monochromatic wave field by an array of bottom-mounted circular cylinders is solved by a semi-analytical approach.
Abstract: The problem of second-order water wave diffraction of an incident monochromatic wave field by an array of bottom-mounted circular cylinders is solved by a semi-analytical approach. The solution for the second-order potential is obtained by combining eigenfunction expansions with an integral representation. Unlike the indirect approach for second-order forces (Lighthill 1979; Molin 1979), this approach gives complete information about local flow characteristics (pressure, velocities, wave elevation, etc.) thus providing a basis for solving the third-order problem. The results obtained are compared with other published data, and new detailed results, useful for benchmarking purposes, are given. Finally the influences of wave incidence, cylinder radius and cylinder configuration are considered. This leads to the suggestion that there exists a near-trapping phenomenon for the second-order wave in an array of cylinders, at half the wave frequency at which the corresponding linear near-trapped mode occurs.

100 citations


Cites methods from "Nonlinear wave interaction with a v..."

  • ...Another method of obtaining the second-order forces is the direct integration of the pressure over the body surface up to second order (e.g. Chau 1989; Kim & Yue 1989; Scolan & Molin 1989; Kriebel 1990)....

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Journal ArticleDOI
TL;DR: In this article, a physical model study of the run-up heights and runup distribution on two shapes of foundations for offshore wind turbines, including both regular and irregular waves, is presented.

78 citations


Cites methods from "Nonlinear wave interaction with a v..."

  • ...They found that linear diffraction theory is inadequate and used the superposition method of Kriebel (1992), which was still found inadequate for their regime of interest (Table 1), although it did give an improvement of linear diffraction theory....

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  • ...Extension of diffraction theory to the second order has been carried out by several other authors (Kriebel, 1990; Martin et al., 2001), using different approaches....

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  • ...…first kind and bm ¼ 1; m ¼ 0 bm ¼ 2ð−1Þmim; mN0 k ¼ 2k=L; wave number The run-up Ru(θ) around the cylinder is the maximum value of η. Extension of diffraction theory to the second order has been carried out by several other authors (Kriebel, 1990; Martin et al., 2001), using different approaches....

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References
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Journal ArticleDOI
TL;DR: In this paper, the authors present an algebraic extension of LINEAR TRANSFORMATIONS and QUADRATIC FORMS, and apply it to EIGEN-VARIATIONS.
Abstract: Partial table of contents: THE ALGEBRA OF LINEAR TRANSFORMATIONS AND QUADRATIC FORMS. Transformation to Principal Axes of Quadratic and Hermitian Forms. Minimum-Maximum Property of Eigenvalues. SERIES EXPANSION OF ARBITRARY FUNCTIONS. Orthogonal Systems of Functions. Measure of Independence and Dimension Number. Fourier Series. Legendre Polynomials. LINEAR INTEGRAL EQUATIONS. The Expansion Theorem and Its Applications. Neumann Series and the Reciprocal Kernel. The Fredholm Formulas. THE CALCULUS OF VARIATIONS. Direct Solutions. The Euler Equations. VIBRATION AND EIGENVALUE PROBLEMS. Systems of a Finite Number of Degrees of Freedom. The Vibrating String. The Vibrating Membrane. Green's Function (Influence Function) and Reduction of Differential Equations to Integral Equations. APPLICATION OF THE CALCULUS OF VARIATIONS TO EIGENVALUE PROBLEMS. Completeness and Expansion Theorems. Nodes of Eigenfunctions. SPECIAL FUNCTIONS DEFINED BY EIGENVALUE PROBLEMS. Bessel Functions. Asymptotic Expansions. Additional Bibliography. Index.

4,525 citations

Book
01 Sep 1983
TL;DR: In this paper, the authors present an introduction to classical water wave theory for the college senior or first year graduate student, with a set of homework problems exercising and sometimes extending the material presented in the chapter.
Abstract: This book is intended as an introduction to classical water wave theory for the college senior or first year graduate student. The material is self-contained; almost all mathematical and engineering concepts are presented or derived in the text, thus making the book accessible to practicing engineers as well.The book commences with a review of fluid mechanics and basic vector concepts. The formulation and solution of the governing boundary value problem for small amplitude waves are developed and the kinematic and pressure fields for short and long waves are explored. The transformation of waves due to variations in depth and their interactions with structures are derived. Wavemaker theories and the statistics of ocean waves are reviewed. The application of the water particle motions and pressure fields are applied to the calculation of wave forces on small and large objects. Extension of the linear theory results to several nonlinear wave properties is presented. Each chapter concludes with a set of homework problems exercising and sometimes extending the material presented in the chapter. An appendix provides a description of nine experiments which can be performed, with little additional equipment, in most wave tank facilities.

2,339 citations

Book
01 Jan 1983
TL;DR: In this article, the authors present selected theoretical topics on ocean wave dynamics, including basic principles and applications in coastal and offshore engineering, all from a deterministic point of view, and the bulk of the material deals with the linearized theory.
Abstract: The aim of this book is to present selected theoretical topics on ocean wave dynamics, including basic principles and applications in coastal and offshore engineering, all from the deterministic point of view. The bulk of the material deals with the linearized theory.

2,003 citations

Book
01 Jan 1949

1,445 citations

01 Jul 1958
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.

1,244 citations