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Comparison of linear and nonlinear shallow wave water equations applied to tsunami waves over the China Sea

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Abstract

This paper discusses the applications of linear and nonlinear shallow water wave equations in practical tsunami simulations. We verify which hydrodynamic theory would be most appropriate for different ocean depths. The linear and nonlinear shallow water wave equations in describing tsunami wave propagation are compared for the China Sea. There is a critical zone between 400 and 500 m depth for employing linear and nonlinear models. Furthermore, the bottom frictional term exerts a noticeable influence on the propagation of the nonlinear waves in shallow water. We also apply different models based on these characteristics for forecasting potential seismogenic tsunamis along the Chinese coast. Our results indicate that tsunami waves can be modeled with linear theory with enough accuracy in South China Sea, but the nonlinear terms should not be neglected in the eastern China Sea region.

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References

  1. Cho Y-S, Sohna D-H, Lee S (2007) Practical modified scheme of linear shallow-water equations for distant propagation of tsunamis. Ocean Eng V34:1769–1777

    Google Scholar 

  2. Comer RP (1984) Tsunami generation: a comparison of traditional and normal mode approaches. Geophys J Int 77(1):29–41

    Google Scholar 

  3. Geist EL (1998) Local tsunamis and earthquake source parameters. Adv Geophys 39:116–209

    Google Scholar 

  4. George DL, LeVeque RJ (2006) Finite volume methods and adaptive refinement for global tsunami propagation and indundation, Science of Tsunami Hazards, No. 5, V25, pp 319–328

  5. Goto C, Ogawa Y, Shuto N, Imamura N (1997) Numerical method of tsunami simulation with the leap-frog scheme (IUGG/IOC Time Project), IOC manual, UNESCO, No. 35

  6. Grilli S, Svendsen I, Subramanya R (1997) Breaking criterion and characteristics for solitary waves on slopes. J Waterway Port Coastal Ocean Eng 123(3):102–112

    Article  Google Scholar 

  7. Gutenberg B, Richter CF (1949) Seismicity of the Earth and associated phenomena, Princeton University Press, Princeton

    Google Scholar 

  8. Kajiura K (1970) Tsunami source, energy and the directivity of wave radiation. Bull Earthquake Res Inst Tokyo Univ 48:835–869

    Google Scholar 

  9. Jensen A, Pedersem GK, Wood DJ (2003) An experimental study of wave run-up at a steep beach ATLE. J Fluid Mech 486:61–188

    Article  Google Scholar 

  10. Novikova T, Wen K-L, Huang B-S (2000) Amplification of gravity and Rayleigh waves in a layered water–soil model. Earth Planets Space 52:579–586

    Google Scholar 

  11. Liu Y, Santos A, Wang SM, Shi Y, Liu H, Yuen DA (2007) Tsunami hazards from potential earthquakes along South China Coast. Phys Earth Planet Inter 163:233–245

    Google Scholar 

  12. Liu Y, Shi Y, Sevre EOD, Yuen DA, Xing H (2007) Probabilistic forecast of tsunami hazards along Chinese Coast. Visual Geosciences (Book), Springer, Heidelberg (submitted)

  13. Liu Z et al (1988) South China Sea geology tectonic and continental margin extension (in Chinese), Science Press, Beijing

  14. Okada Y (1985) Surface deformation due to shear and tensile faults in a half-space. Bull Seism Soc Am 75:1135–1154

    Google Scholar 

  15. Reiter L (1990) Earthquake hazard analysis: issues and insights. Columbia University Press, New York

    Google Scholar 

  16. Wang F, Zhang Z (2005) Earthquake tsunami record in Chinese ancient books. Chinese Earthquakes 21, V03:437–443

    Google Scholar 

  17. Wang J (1996) Global linear stability of the two-dimensional shallow-water equations: an application of the distributive theorem of roots for polynomials on the unit circle. Mon Wea Rev 124:1301–1310

    Article  Google Scholar 

  18. Ward S (1982) On tsunami nucleation: an instantaneous modulated line source. Phys Earth Planet Int 27:273–285

    Article  Google Scholar 

  19. Wells D, Coppersmith K (1994) New empirical relationships among magnitude, rupture length, rupture area, and surface displacement. Bull Seismol Soc Am 84:974–1002

    Google Scholar 

  20. Yamashita T, Sato R (1976) Correlation of tsunami and sub-oceanic Rayleigh wave amplitudes. J Phys Earth 24:397–416

    Google Scholar 

  21. Zang S, Ning J (2002) Interaction between Philippine Sea Place (PH) and Eurasia (EU) Plate and its influence on the movment eastern Asia. Chinese Journal of Geophysics, 45, V01:188–197

    Google Scholar 

Download references

Acknowledgments

We would like to thank Professor Fumihiko Imamura for providing computational codes TUNAMI_N1 and TUNAMI_N2, and his kind guidance on tsunami numerical modeling. This research is supported by National Science Foundation of China (NSFC-40574021, 40728004) and the EAR program of the US National Science Foundation.

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Authors and Affiliations

  1. South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou, China

    Yingchun Liu

  2. Graduate University of Chinese Academy of Sciences, Beijing, China

    Yaolin Shi

  3. Department of Geology and Geophysics, University of Minnesota, Minneapolis, USA

    David A. Yuen

  4. Minnesota Supercomputing Institute, University of Minnesota, Minneapolis, USA

    Yingchun Liu, David A. Yuen & Erik O. D. Sevre

  5. ESSCC, University of Queensland, Brisbane, Australia

    Hui Lin Xing

  6. Key Lab of Machine Perception and School of EECS, Peking University, Beijing, China

    Xiaoru Yuan

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  1. Yingchun Liu
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  2. Yaolin Shi
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  3. David A. Yuen
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  4. Erik O. D. Sevre
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  5. Xiaoru Yuan
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  6. Hui Lin Xing
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Correspondence to Yingchun Liu.

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Liu, Y., Shi, Y., Yuen, D.A. et al. Comparison of linear and nonlinear shallow wave water equations applied to tsunami waves over the China Sea. Acta Geotech. 4, 129–137 (2009). https://doi.org/10.1007/s11440-008-0073-0

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  • DOI: https://doi.org/10.1007/s11440-008-0073-0

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