Long-Wave Scattering by a Vertical Cylinder with Idealized Scour Pit
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 137, Issue 6
Abstract
The combined diffraction and refraction of long waves around a vertical cylinder with scour pit is studied analytically on the basis of a newly derived analytic solution of the mild-slope wave equation. The geometry of the scour pit around the cylinder is idealized to be axisymmetrical, and a simple power function is employed to represent its radial profile. The problem is solved in the polar coordinate system by separation of variables, and the resulting ordinary differential equation in the radial direction over the scour pit in this case can be transformed into the Bessel equation of real order. On the basis of the analytic solution obtained, the effect of the scour pit on wave scattering is investigated by comparing the cases with and without the presence of the scour pit. The scour pit contributes to reduce the wave run-up against the cylinder. In addition, the effects of the scour pit on wave run-up against the cylinder are more significant when the dimensions of the scour pit are larger or the incident wave is relatively shorter.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The research is supported by the Natural Science Foundation of China under Grant No. NSF10772099.
References
Abramowitz, M., and Stegun, I. A. (1972). Handbook of mathematical functions: With formulas, graphs, and mathematical tables, 10th Ed., Dover Publications, New York, 1046.
Berkhoff, J. C. W. (1972). “Computation of combined refraction-diffraction.” Proc., 13th Coastal Engineering Conf., ASCE, Reston, VA, 471–490.
Jung, T.-H., and Suh, K.-D. (2007). “An analytic solution to the mild slope equation for waves propagating over an axi-symmetric pit.” Coastal Eng., 54(12), 865–877.
Jung, T.-H., and Suh, K.-D. (2008). “An analytical solution to the extended mild-slope equation for long waves propagating over an axi-symmetric pit.” Wave Motion, 45(6), 835–845.
Lin, P., and Liu, H. (2007). “Scattering and trapping of wave energy by a submerged truncated paraboloidal shoal.” J. Waterway, Port, Coastal, Ocean Eng., 133(2), 94–103.
Liu, H., and Li, Y. (2007). “An analytical solution for long-wave scattering by a submerged circular truncated shoal.” J. Eng. Math., 57(2), 133–144.
Liu, H., Lin, P., and Shankar, N. J. (2004). “An analytical solution of the mild-slope equation for waves around a circular island on a paraboloidal shoal.” Coastal Eng., 51(5-6), 421–437.
MacCamy, R. C., and Fuchs, R. A. (1954). “Wave forces on piles: A diffraction theory.” Technical Memorandum No. 69, Beach Erosion Board, U.S. Army Corps of Engineers, Washington, DC.
Suh, K.-D., Jung, T.-H., and Haller, M. C. (2005). “Long waves propagating over a circular bowl pit.” Wave Motion, 42(2), 143–154.
Sumer, B. M., and Fredsøe, J. (1999). “Wave scour around structures.” Advances in coastal and ocean engineering, P. L.-F. Liu ed., World Scientific, Singapore, 191–249.
Sumer, B. M., Whitehouse, R. J. S., and Tørum, A. (2001). “Scour around coastal structures: A summary of recent research.” Coastal Eng., 44(2), 153–190.
Yu, X., and Zhang, B. (2003). “An extended analytic solution for combined refraction and diffraction of long waves over circular shoals.” Ocean Eng., 30(10), 1253–1267.
Zhang, Y., and Zhu, S. (1994). “New solutions for the propagation of long water waves over variable depth.” J. Fluid Mech., 278, 391–406.
Zhu, S.-P., and Harun, F. N. (2009). “An analytical solution for long wave refraction over a circular hump.” J. Appl. Math. Comput., 30(1–2), 315–333.
Zhu, S.-P., and Zhang, Y. (1996). “Scattering of long waves around a circular island mounted on a conical shoal.” Wave Motion, 23(4), 353–362.
Information & Authors
Information
Published In
Copyright
© 2011 American Society of Civil Engineers.
History
Received: Jun 20, 2010
Accepted: Mar 30, 2011
Published online: Mar 31, 2011
Published in print: Nov 1, 2011
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.