- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Journal of Applied Mathematics
Volume 2012 (2012), Article ID 742705, 13 pages
An Extended Analytic Solution of Combined Refraction and Diffraction of Long Waves Propagating over Circular Island
1Department of Hydraulic and Ocean Engineering, National Cheng Kung University, Tainan 701, Taiwan
2Research Center of Ocean Energy and Strategy, National Taiwan Ocean University, Keelung 202, Taiwan
3Department of Marine Environmental Engineering, National Kaohsiung Marine University, Kaohsiung 811, Taiwan
Received 18 June 2012; Revised 5 September 2012; Accepted 24 September 2012
Academic Editor: Michael Meylan
Copyright © 2012 Yu-Shu Kuo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- J. C. W. Berkhoff, “Computation of combined refraction-diffraction,” in Proceedings of the 13th International Conference on Coastal Engineering, pp. 471–490, ASCE, 1972.
- D. Porter and D. J. Staziker, “Extensions of the mild-slope equation,” Journal of Fluid Mechanics, vol. 300, pp. 367–382, 1995.
- T. W. Hsu and C. C. Wen, “On radiation boundary conditions and wave transformation across the surfzone,” China Ocean Engineering, vol. 15, no. 3, pp. 395–406, 2001.
- S. Homma, “On the behavior of seismic sea waves around circular island,” Geophysical Magazine, vol. 21, pp. 199–209, 1950.
- A. C. Vastano and R. O. Reid, “Tsunami response for islands: verification of a numerical procedure,” Journal of Marine Research, vol. 25, pp. 129–139, 1967.
- I. G. Jonsson, O. Skovgaard, and O. Brink-Kjaer, “Diffraction and refraction calculations for waves incident on an island,” Journal of Marine Research, vol. 34, no. 3, pp. 469–496, 1976.
- K. Fujima and C. Goto, “Characteristics of long waves trapped by conical islands,” Proceedings of the Japan Society of Civil Engineers, no. 497, pp. 101–110, 1994 (Japanese).
- K. Fujima, D. Yuliadi, C. Goto, K. Hayashi, and T. Shigemura, “Characteristics of long waves trapped by conical island,” Coastal Engineering Journal, vol. 38, no. 2, pp. 111–132, 1995.
- Y. Zhang and S. Zhu, “New solutions for the propagation of long water waves over variable depth,” Journal of Fluid Mechanics, vol. 278, pp. 391–406, 1994.
- S. Zhu and Y. Zhang, “Scattering of long waves around a circular island mounted on a conical shoal,” Wave Motion, vol. 23, no. 4, pp. 353–362, 1996.
- T. H. Jung, C. Lee, and Y. S. Cho, “Analytical solutions for long waves over a circular island,” Coastal Engineering, vol. 57, no. 4, pp. 440–446, 2010.
- X. Niu and X. Yu, “Long wave scattering by a vertical cylinder with idealized scour pit,” Journal of Waterway, Port, Coastal and Ocean Engineering-ASCE, vol. 137, pp. 279–285, 2011.
- H. W. Liu, J. J. Xie, and Z. H. Luo, “An analytical solution for long-wave scattering by a circular island mounted on a general shoal,” Journal of Waterway, Port, Coastal and Ocean Engineering-ASCE, vol. 139, no. 6, pp. 425–434, 2012.
- T. H. Jung and C. Lee, “Analytical solutions for long waves on a circular island with combined topographies,” Wave Motion, vol. 49, pp. 152–164, 2012.
- H. W. Liu, P. Lin, and N. J. Shankar, “An analytical solution of the mild-slope equation for waves around a circular island on a paraboloidal shoal,” Coastal Engineering, vol. 51, no. 5-6, pp. 421–437, 2004.
- X. Niu and X. Yu, “An analytic solution for combined wave diffraction and refraction around a vertical cylinder with idealized scour pit,” Coastal Engineering, vol. 67, pp. 80–87, 2012.
- J. N. Hunt, “Direct solution of wave dispersion equation,” Journal of Waterway, Port, Coastal and Ocean Engineering-ASCE, vol. 105, no. 1979, pp. 457–459, 1979.
- X. Yu and B. Zhang, “An extended analytic solution for combined refraction and diffraction of long waves over circular shoals,” Ocean Engineering, vol. 30, no. 10, pp. 1253–1267, 2003.
- S. Rojanakamthorn, M. Isobe, and A. Watanabe, “A mathematical model of wave transformation over a submerged breakwater,” in Proceedings of the Coastal Engineering in Japan, vol. 32, pp. 209–234, 1989.