Analytical and numerical investigation of tsunami trapped waves over a hyperbolic-cosine squared ocean ridge

Wang Gang; Hu Jian; Wang Peitao; Zhang Zhenwei

doi:10.3969/j.issn.0253-4193.2018.05.002

Article Contents

Article Navigation > Haiyang Xuebao > 2018 > 40(5): 15-23

Wang Gang, Hu Jian, Wang Peitao, Zhang Zhenwei. Analytical and numerical investigation of tsunami trapped waves over a hyperbolic-cosine squared ocean ridge[J]. Haiyang Xuebao, 2018, 40(5): 15-23. doi: 10.3969/j.issn.0253-4193.2018.05.002

Citation:

Wang Gang, Hu Jian, Wang Peitao, Zhang Zhenwei. Analytical and numerical investigation of tsunami trapped waves over a hyperbolic-cosine squared ocean ridge[J]. Haiyang Xuebao, 2018, 40(5): 15-23. doi: 10.3969/j.issn.0253-4193.2018.05.002

Citation:

PDF( 10346 KB)

Analytical and numerical investigation of tsunami trapped waves over a hyperbolic-cosine squared ocean ridge

doi: 10.3969/j.issn.0253-4193.2018.05.002

1.
Key Laboratory of Coastal Disaster and Defence, Ministry of Education, Hohai University, Nanjing 210098, China;College of Harbour, Coastal and Offshore Engineering, Hohai University, Nanjing 210098, China
2.
College of Harbour, Coastal and Offshore Engineering, Hohai University, Nanjing 210098, China
3.
National Marine Environmental Forecasting Center, Beijing 100081, China
4.
Island Research Center, State Oceanic Administration, Pingtan 350400, China

Received Date: 2017-12-12
Rev Recd Date: 2018-02-04

Abstract

Abstract

Tsunami can be guided by oceanic ridges propagation as trapped waves transferring energy to thousands of kilometers away, which threatens the safety of harbor and coastal. Based on the linear shallow water approximation, analytical solutions of trapped waves over a hyperbolic-cosine squared ocean ridge are derived, which could be described by combining the associated Legendre functions of the first and second kinds. The corresponding dispersion relation is also obtained. For various fixed frequency ω, there are infinite wavenumber k_y satisfied the dispersion relation. MIKE21-BW was used to simulate tsunami generated on the top of the ridge and propagation along it. The results show that only small part of the energy transfers as free waves and most of it is rapped over the ridge. The trapped wave propagates as traveling wave along the ocean ridge. The envelope of trapped waves is prolonged while the maximum amplitude decreases and the number of the trapped waves increases. The energy of trapped wave is mainly composed of two parts:solitary wave characteristic component with different frequencies travelling with the same speed and dispersive wave characteristic component with fixed frequency range.
- oceanic guided waves,
- trapped waves,
- tsunami,
- oceanic ridge,
- Boussinesq model

FullText(HTML)

References(21)

References

Wilson R I, Admire A R, Borrero J C, et al. Observations and impacts from the 2010 Chilean and 2011 Japanese tsunamis in California (USA)[J]. Pure and Applied Geophysics, 2013, 170(6/8):1127-1147.

于福江, 原野, 赵联大, 等. 2010年2月27日智利8.8级地震海啸对我国影响分析[J]. 科学通报, 2011, 56(3):239-246. Yu Fujiang, Yuan Ye, Zhao Lianda, et al. Evaluation of potential hazards from teletsunami in China:tidal observations of a teletsunami generated by the Chile 8.8 Mw earthquake[J]. Chinese Science Bulletin, 2011, 56(3):239-246.

Titov V, Rabinovich A B, Mofjeld H O, et al. The global reach of the 26 December 2004 Sumatra tsunami[J]. Science, 2005, 309(5743):2045-2048.

Rabinovich A B, Candella R N, Thomson R E. Energy decay of the 2004 Sumatra tsunami in the world ocean[J]. Pure and Applied Geophysics, 2011, 168(11):1919-1950.

Rabinovich A B, Lobkovsky L I, Fine I V, et al. Near-source observations and modeling of the Kuril Islands tsunamis of 15 November 2006 and 13 January 2007[J]. Advances in Geosciences, 2008, 14:105-116.

Seo S N, Liu P L F. Edge waves generated by atmospheric pressure disturbances moving along a shoreline on a sloping beach[J]. Coastal Engineering, 2014, 85:43-59.

Seo S N, Liu P L F. Edge waves generated by the landslide on a sloping beach[J]. Coastal Engineering, 2013, 73:133-150.

Longuet-Higgins M S. On the trapping of wave energy round islands[J]. Journal of Fluid Mechanics, 1967, 29(4):781-821.

Niu Xiaojing, Yu Xiping. Analytic solution of long wave propagation over a submerged hump[J]. Coastal Engineering, 2011, 58(2):143-150.

Jones D S. The eigenvalues of ▽²u+λu=0 when the boundary conditions are given on semi-infinite domains[J]. Mathematical Proceedings of the Cambridge Philosophical Society, 1953, 49(4):668-684.

Longuet-Higgins M S. On the trapping of waves along a discontinuity of depth in a rotating ocean[J]. Journal of Fluid Mechanics, 1968, 31(3):417-434.

Buchwald V T. Long waves on oceanic ridges[J]. Proceedings of the Royal Society A:Mathematical, Physical and Engineering Sciences, 1969, 308(1494):343-354.

Shaw R P, Neu W. Long-wave trapping by oceanic ridges[J]. Journal of Physical Oceanography, 1981, 11(10):1334-1344.

Zheng Jinhai, Xiong Mengjie, Wang Gang. Trapping mechanism of submerged ridge on trans-oceanic tsunami propagation[J]. China Ocean Engineering, 2016, 30(2):271-282.

Titov V V, Synolakis C E. Modeling of breaking and nonbreaking long-wave evolution and runup using vtcs-2[J]. Journal of Waterway, Port, Coastal, and Ocean Engineering, 1995, 121(6):308-316.

Oishi Y, Imamura F, Sugawara D. Near-field tsunami inundation forecast using the parallel TUNAMI-N2 model:application to the 2011 Tohoku-Oki earthquake combined with source inversions[J]. Geophysical Research Letters, 2015, 42(4):1083-1091.

Grilli S T, Ioualalen M, Asavanant J, et al. Source constraints and model simulation of the December 26, 2004, Indian ocean tsunami[J]. Journal of Waterway, Port, Coastal, and Ocean Engineering, 2007, 133(6):414-428.

Wang G, Hu J, Zheng J H, et al. Trapped waves over the hyperbolic-cosine ocean ridge[C]//Proceedings of the 9th International Conference on Asia and Pacific Coasts (APAC 2017). Pasay City, Philippine:World Scientific Publishing Co Pte Ltd, 2017:44-54.

Madsen P A, Murray R, Sørensen O R. A new form of the Boussinesq equations with improved linear dispersion characteristics[J]. Coastal Engineering, 1991, 15(4):371-388.

Madsen P A, Sørensen O R. A new form of the Boussinesq equations with improved linear dispersion characteristics. Part 2. A slowly-varying bathymetry[J]. Coastal Engineering, 1192, 18(3/4):183-204.

Okada Y. Internal deformation due to shear and tensile faults in a half-space[J]. Bulletin of the Seismological Society of America, 1992, 82(2):1018-1040.

Relative Articles

Supplements(0)

Cited By

Proportional views