Linear Wave Interaction with a Vertical Cylinder of Arbitrary Cross Section: An Asymptotic Approach
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 143, Issue 5
Abstract
An asymptotic approach to the linear problem of regular water waves interacting with a vertical cylinder of an arbitrary cross section is presented. The incident regular wave was one-dimensional, water was of finite depth, and the rigid cylinder extended from the bottom to the water surface. The nondimensional maximum deviation of the cylinder cross section from a circular one plays the role of a small parameter of the problem. A fifth-order asymptotic solution of the problem was obtained. The problems at each order were solved by the Fourier method. It is shown that the first-order velocity potential is a linear function of the Fourier coefficients of the shape function of the cylinder, the second-order velocity potential is a quadratic function of these coefficients, and so on. The hydrodynamic forces acting on the cylinder and the water surface elevations on the cylinder are presented. The present asymptotic results show good agreement with numerical and experimental results of previous investigations. Long-wave approximation of the hydrodynamic forces was derived and used for validation of the asymptotic solutions. The obtained values of the forces are exact in the limit of zero wave numbers within the linear wave theory. An advantage of the present approach compared with the numerical solution of the problem by an integral equation method is that it provides the forces and the diffracted wave field in terms of the coefficients of the Fourier series of the deviation of the cylinder shape from the circular one. The resulting asymptotic formula can be used for optimization of the cylinder shape in terms of the wave loads and diffracted wave fields.
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Acknowledgments
Preliminary results of this paper were reported at the International Workshop on Water Waves and Floating Bodies 2015 (Disibuyuk and Korobkin 2015). This research was started while the first author was visiting the School of Mathematics, University of East Anglia, as a visiting research scientist during the period from October 2014 to February 2015. This visit was supported by YÖK (Council of Higher Education of Turkey). The first author was also supported by a grant (BİDEB-2211) from TÜBİTAK (Scientific and Technological Research Council of Turkey). These supports are greatly acknowledged. The authors thank the reviewers for their suggestions.
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Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 143 • Issue 5 • September 2017
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© 2017 American Society of Civil Engineers.
History
Received: Jul 8, 2016
Accepted: Feb 21, 2017
Published online: Jun 16, 2017
Published in print: Sep 1, 2017
Discussion open until: Nov 16, 2017
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