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.
References
Au, M. C., and Brebbia, C. A. (1983). “Diffraction of water waves for vertical cylinders using boundary elements.” Appl. Math. Modell., 7(2), 106–114.
Black, J. L., Mei, C. C., and Bray, M. C. G. (1971). “Radiation and scattering of water waves by rigid bodies.” J. Fluid Mech., 46(1), 151–164.
Chen, H. S., and Mei, C. C. (1971). “Scattering and radiation of gravity waves by an elliptical cylinder.” Rep. No. 140, Parsons Laboratory, Dept. of Civil Engineering, Massachusetts Institute of Technology, Cambridge, MA.
Chen, H. S., and Mei, C. C. (1973). “Wave forces on a stationary platform of elliptical shape.” J. Ship Res., 17(2), 61–71.
De Vos, L., Frigaard, P., and De Rouck, J. (2007). “Wave run-up on cylindrical and cone shaped foundations for offshore wind turbines.” Coastal Eng., 54(1), 17–29.
Disibuyuk, N. B., and Korobkin, A. A. (2015). “Wave forces on a vertical cylinder with non-circular cross section.” Proc., 30th Int. Workshop On Water Waves And Floating Bodies, International Workshop on Water Waves and Floating Bodies, Oslo, Norway, 53–56.
Eatock Taylor, R., and Hu, C. S. (1991). “Multipole expansions for wave diffraction and radiation in deep water.” Ocean Eng., 18(3), 191–224.
Eatock Taylor, R., and Hung, S. M. (1987). “Second order diffraction forces on a vertical cylinder in regular waves.” Appl. Ocean Res., 9(1), 19–30.
Fichtenholtz, G. M. (2001). Course of differential and integral calculus, Vol. 3, Fizmatlit, Moscow (in Russian).
Garrett, C. J. R. (1971). “Wave forces on a circular dock.” J. Fluid Mech., 46(1), 129–139.
Haskind, M. D. (1973). Hydrodynamic theory of ship rolling, Fizmatlit, Moscow (in Russian).
Havelock, T. H. (1940). “The pressure of water waves upon a fixed obstacle.” Proc. R. Soc. A, 175(963), 409–421.
Hwang, L.-S., and Tuck, E. O. (1970). “On the oscillations of harbours of arbitrary shape.” J. Fluid Mech., 42(3), 447–464.
Iafrati, A., and Korobkin, A. A. (2006). “Breaking wave impact onto elastic wall.” Proc., 4th Int. Conf. on Hydroelasticity in Marine Technology, National Defence Industry Press, Beijing, 139–148.
Isaacson, M. (1978). “Vertical cylinders of arbitrary section in waves.” J. Waterway, Port, Coastal, Ocean Div., 104(3), 309–324.
Korobkin, A. A. (2008). “Wagner theory of steep wave impact.” Proc., 23rd Int. Workshop on Water Waves and Floating Bodies, Jeju, Korea., 112–115.
Korobkin, A. A., and Malenica, S. (2007). “Steep wave impact onto elastic wall.” Proc., 22nd Int. Workshop on Water Waves and Floating Bodies, International Workshop on Water Waves and Floating Bodies, Oslo, Norway.
Liu, J., Guo, A., and Li, H. (2016). “Analytical solution for the linear wave diffraction by a uniform vertical cylinder with an arbitrary smooth cross-section.” Ocean Eng., 126, 163–175.
Lykke Andersen, T., Frigaard, P., Damsgaard, M. L., and De Vos, L. (2011). “Wave run-up on slender piles in design conditions—Model tests and design rules for offshore wind.” Coastal Eng., 58(4), 281–289.
MacCamy, R. C., and Fuchs, R. A. (1954). “Wave forces on piles: A diffraction theory.” Rep. No. 69, U.S. Army Corps of Engineers, Beach Erosion Board, Washington, DC.
Mansour, A. M., Williams, A. N., and Wang, K. H. (2002). “The diffraction of linear waves by a uniform vertical cylinder with cosine-type radial perturbations.” Ocean Eng., 29(3), 239–259.
Mei, C. C., Stiassnie, M., and Yue, D. K.-P. (2005). Theory and applications of ocean surface waves. Part 1: Linear aspects, vol. 23 of advanced series on ocean engineering, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ.
Mogridge, G. R., and Jamieson, W. W. (1976). “Wave forces on square caissons.” Proc., 15th Int. Conf. on Coastal Engineering, 133, ASCE, Reston, VA, 2271–2289.
Thorne, R. C. (1953). “Multipole expansions in the theory of surface waves.” Math. Proc. Cambridge Philos. Soc., 49(4), 707–716.
Ursell, F. (1950). “Surface waves on deep water in the presence of a submerged circular cylinder I.” Math. Proc. Cambridge Philos. Soc., 46(1), 141–152.
Wang, Y., Ren, X., Dong, P., and Wang, G. (2011). “Three-dimensional numerical simulation of wave interaction with perforated quasi-ellipse caisson.” Water Sci. Eng., 4(1) 46–60.
Williams, A. N. (1985). “Wave forces on an elliptic cylinder.” J. Waterway, Port, Coastal, Ocean Eng., 433–449.
Wrobel, L. C., Sphaier, S. H., and Esperança, P. T. T. (1985). “Propagation of surface waves.” Topics in boundary element research, Vol. 2, Springer, Berlin, 156–190.
Wu, X.-J., and Price, W. G. (1991). “Evaluation of wave drift forces on vertical cylinders of arbitrary geometry, with application to tension leg platforms (TLPs).” Ocean Eng., 18(1), 1–15.
Yeung, R. W. (1981). “Added mass and damping of a vertical cylinder in finite-depth waters.” Appl. Ocean Res., 3(3), 119–133.
Zhu, S., and Moule, G. (1994). “Numerical calculation of forces induced by short-crested waves on a vertical cylinder of arbitrary cross-section.” Ocean Eng., 21(7), 645–662.
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© 2017 American Society of Civil Engineers.
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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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