Acta Geotechnica

, Volume 4, Issue 2, pp 129–137 | Cite as

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

  • Yingchun Liu
  • Yaolin Shi
  • David A. Yuen
  • Erik O. D. Sevre
  • Xiaoru Yuan
  • Hui Lin Xing
Review Article


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.


China Sea Nonlinear shallow-water equations Numerical computation Tsunami waves 



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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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Yingchun Liu
    • 1
    • 4
  • Yaolin Shi
    • 2
  • David A. Yuen
    • 3
    • 4
  • Erik O. D. Sevre
    • 4
  • Xiaoru Yuan
    • 6
  • Hui Lin Xing
    • 5
  1. 1.South China Sea Institute of OceanologyChinese Academy of SciencesGuangzhouChina
  2. 2.Graduate University of Chinese Academy of SciencesBeijingChina
  3. 3.Department of Geology and GeophysicsUniversity of MinnesotaMinneapolisUSA
  4. 4.Minnesota Supercomputing InstituteUniversity of MinnesotaMinneapolisUSA
  5. 5.ESSCC, University of QueenslandBrisbaneAustralia
  6. 6.Key Lab of Machine Perception and School of EECSPeking UniversityBeijingChina

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