Trapping mechanism of submerged ridge on trans-oceanic tsunami propagation

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• 作者：Jin-hai Zheng 郑金泿/a> ; Meng-jie Xiong 熊梦姿/a> ; Gang Wang 猿尿/a>
• 关键词：trapped waves ; guided waves ; shallow water equations ; analytical solutions ; tsunamis
• 刊名：China Ocean Engineering
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：30
• 期：2
• 页码：271-282
• 全文大小：618 KB
• 参考文献：Amante, C. and Eakins, B. W., 2009. ETOPO1 1 Arc-Minute Global Relief Model: Procedures, Data Sources and Analysis, NOAA Technical Memorandum NESDIS NGDC-24, National Geophysical Data Center, NOAA.
  Buchwald, V. T., 1969. Long waves on oceanic ridges, Proceedings of the Royal Society A, 308(1494): 343–354.CrossRef
  Eckart, C., 1951. Surface Waves on Water of Variable Depth, University of California, Scripps.
  Guza, R. T. and Davis, R. E., 1974. Excitation of edge waves by waves incident on a beach, J. Geophys. Res., 79(9): 1285–1291.CrossRef
  Jones, D., 1953. The eigenvalues of -2u+-u= 0 when the boundary conditions are given on semi-infinite domains, in: Mathematical Proceedings of the Cambridge Philosophical Society, Cambridge University Press, 49(04): 668–684.MathSciNet MATH
  Jung, T. H. and Lee, C., 2012. Analytical solutions for long waves on a circular island with combined topographies, Wave Motion, 49(1): 152–164.CrossRef
  Jung, T. H., Lee, C. and Cho, Y. S., 2010. Analytical solutions for long waves over a circular island, Coast. Eng., 57(4): 440–446.CrossRef
  Killworth, P. D., 1989. How much of a baroclinic coastal Kelvin wave gets over a ridge-J. Phys. Oceanogr., 19(3): 321–341.CrossRef
  Koshimura, S. I., Imamura, F. and Shuto, N., 2001. Characteristics of tsunamis propagating over oceanic ridges: Numerical simulation of the 1996 Irian Jaya earthquake tsunami, Nat. Hazards, 24(3): 213–229.CrossRef
  Kowalik, Z., Knight, W., Logan, T. and Whitmore, P., 2005. Numerical modeling of the global tsunami: Indonesian tsunami of 26 December 2004. Science of Tsunami Hazards, 23(1): 40–56.
  Kowalik, Z., Knight, W., Logan, T. and Whitmore, P., 2007. The tsunami of 26 December, 2004. Numerical modeling and energy considerations, Pure Appl. Geophys, 164, 379–393.CrossRef
  Mei, C. C., 1989. The Applied Dynamics of Ocean Surface Waves, World Scientific, Singapore.MATH
  Miller, G. R., Munk, W. H. and Snodgrass, F. E., 1962. Long-period waves over California’s continental borderland, ii, tsunamis, J. Mar. Res., 20(1): 31–41.
  Niu, X. and Yu, X., 2011. Analytic solution of long wave propagation over a submerged hump, Coast. Eng., 58(2): 143–150.CrossRef
  Olver, F., Lozier, D., Boisvert, R. and Clark, C., 2010. NIST Handbook of Mathematical Functions, Cambridge University Press, Cambridge, London and New York.MATH
  Rabinovich, A. B., Candella, R. N. and Thomson, R. E., 2011a. Energy decay of the 2004 Sumatra tsunami in the world ocean, Pure Appl. Geophys., 168(11): 1919–1950.CrossRef
  Rabinovich, A. B., Woodworth, P. L. and Titov, V. V., 2011b. Deep-sea observations and modeling of the 2004 Sumatra tsunami in Drake passage, Geophys. Res. Lett., 38(16): L16604.CrossRef
  Reid, R. O., 1958. Effect of Coriolis force on edge waves (i) investigation of the normal modes, J. Mar. Res., 16(2): 109–144.MathSciNet
  Shaw, R. P. and Neu, W., 1981. Long-wave trapping by oceanic ridges, J. Phys. Oceanogr., 11(10): 1334–1344.CrossRef
  Soloviev, S. L., and Go, C. N., 1975. A Catalogue of Tsunamis on the Western Shore of the Pacific Ocean, Academy of Sciences of the USSR, Nauka Publishing House, Moscow, 439 p.
  Stokes, G. G., 1846. Report on Recent Researches in Hydrodynamics, British Association for the Advancement of Science Report 1, 1–20.
  Titov, V., Rabinovich, A. B., Mofjeld, H. O., Thomson, R. E. and González, F. I., 2005. The global reach of the 26 December 2004 Sumatra tsunami, Science, 309(5743): 2045–2048.CrossRef
  Ursell, F., 1951. Trapping modes in the theory of surface waves, Proceedings of the Cambridge Philosophical Society, 47(3): 347–358.MathSciNet CrossRef MATH
  Ursell, F., 1952. Edge waves on a sloping beach, Proceedings of the Royal Society A, 214(1116): 79–97.MathSciNet CrossRef MATH
  Ursell, F., 1987. Mathematical aspects of trapping modes in the theory of surface waves, J. Fluid Mech., 183(1): 421–437.MathSciNet CrossRef MATH
  
• 作者单位：Jin-hai Zheng 郑金海 (1) (2)
  Meng-jie Xiong 熊梦婕 (3)
  Gang Wang 王 岗 (2) (4) (5)
  
  1. State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing, 210098, China
  2. College of Harbor, Coastal and Offshore Engineering, Hohai University, Nanjing, 210098, China
  3. Nanjing Hydraulic Research Institute, Nanjing, 210029, China
  4. State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, 116023, China
  5. The Key Laboratory of Water-Sediment Sciences and Water Disaster Prevention of Hunan Province, Changsha University of Science and Technology, Changsha, 410076, China
  
• 刊物类别：Engineering
• 刊物主题：Oceanography
  Chinese Library of Science
  Offshore Engineering
  Geoengineering, Foundations, Hydraulics
  
• 出版者：Chinese Ocean Engineering Society, co-published with Springer

文摘

Based on the linear shallow water equations, an analytic solution of trapped waves over a symmetric parabolic-profile submerged ridge is derived. The trapped waves act as propagating waves along the ridge and as standing waves across the ridge. The amplitude gets the maximum at the ridge top and decays gradually towards both sides. The decaying rate gets more gently with higher modes. Besides, an explicit first-order approximate dispersion relation is derived to simplify transcendental functions in the exact solution, which is useful to describe trapped waves over shallowly submerged ridges in reality. Furthermore, the trapping mechanism of the submerged ridge waveguides on the trans-oceanic tsunami propagation can be explained by the ray theory. A critical incident angle exists as a criterion to determine whether the wave is trapped. Besides, a trapped parameter γ is proposed to estimate the ratio of the energy trapped by the oceanic ridge if a tsunami is generated at its top.