PROPAGATION AND RUNUP OF TSUNAMI WAVES WITH BOUSSINESQ MODEL
No. 32 (2010), Swash, Nearshore Currents, and Long Waves
No. 32 (2010)

PROPAGATION AND RUNUP OF TSUNAMI WAVES WITH BOUSSINESQ MODEL

Swash, Nearshore Currents, and Long Waves
https://doi.org/10.9753/icce.v32.currents.9
Published 2011-01-30
Xi Zhao
Benlong Wang
Hua Liu
Proceedings of the 32nd International Conference
PDF

Keywords

tsunami waves
N-wave
runup
Boussinesq equations

How to Cite

Zhao, X., Wang, B., & Liu, H. (2011). PROPAGATION AND RUNUP OF TSUNAMI WAVES WITH BOUSSINESQ MODEL. Coastal Engineering Proceedings, 1(32), currents.9. https://doi.org/10.9753/icce.v32.currents.9
ACM ACS APA ABNT Chicago Harvard IEEE MLA Turabian Vancouver

Download Citation

Endnote/Zotero/Mendeley (RIS) BibTeX

Abstract

With certain profiles of bottom movements, orders of wave height of submarine earthquake-induced tsunami both in deep ocean and nearshore area have been studied using the Boussinesq equations. An earthquake of large magnitude generates a typical N-wave which can propagate long distance in open ocean without deformation. Since the magnitude and length of tsunami waves related to vertical and horizontal scale of geological movements, solitary wave and N-wave are extended to waves not tied to solitary property which represent tsunami waves better. In a horizontal one dimensional numerical wave flume, runup of solitary wave, N-wave, single crest and N-wave composed by a single crest and a single trough on a slope beach have been simulated. The results fit analytical solutions of nonlinear shallow water equations well. The Indian Ocean tsunami has been simulated with the horizontal two dimensional high order Boussinesq model. Comparison between numerical results and measured data from field survey validates the numerical model.
https://doi.org/10.9753/icce.v32.currents.9
PDF

References

Hammack, J. 1973. A note on tsunamis: their generation and propagation in an ocean of uniform depth. J. Fluid Mech., 60, 769-799. http://dx.doi.org/10.1017/S0022112073000479

Kânoglu, U. and Synolakis, C.E. 1998. Long wave runup on piecewise linear topographies. J. Fluid Mech., 374, 1-28.http://dx.doi.org/10.1017/S0022112098002468

Kawata, Y., Tsuji. Y., Sugimoto, Y., Hayashi, H., Matsutomi, H., Okamura, Y., Hayashi, I., Kayane, H., Tanioka, Y., Fujima, K., Imamura, F., Matsuyama, M., Takahashi, T., Maki, N., Koshimura, S., Yasuda, T., Shigihara, Y., Nishimura, Y., Horie, K., Nishi, Y., Yamamoto, H., Fukao, J., Seiko, S., Takakuwa, F. Comprehensive analysis of the damage and its impact on coastal zones by the 2004 Indian Ocean tsunami disaster. http://www.tsunami.civil.tohoku.ac.jp/sumatra2004/report.html.

Lay, T., Kanamori, H., Ammon, C., Nettles, M., Ward, S., Aster, R., Beck, S., Bilek, S., Brudzinski, M., Bulter, R., DeShon, H., Ekstrom, G., Satake, K., Sipkin, S. 2005. The great Sumatra-Andaman earthquake of 26 December 2004. Science, 308, 1127-1133. PMid:15905392http://dx.doi.org/10.1126/science.1112250

Liu, P.L.-F., Cho, Y.S., Briggs, M.J., Kânoglu, U., Synolakis, C.E. 1995. Runup of solitary waves on a circular island. J. Fluid Mech., 302, 259-285. http://dx.doi.org/10.1017/S0022112095004095

Madsen, P.A., Bingham, H. and Liu, H. 2002. A new Boussinesq method for fully nonlinear waves from shallow to deep water. J. Fluid Mech., 462, 1-30. http://dx.doi.org/10.1017/S0022112002008467

Madsen, P.A. and Schäffer, H.A. 2010. Analytical solution for tsunami runup on a plane beach: single waves, N-waves and transient waves. J. Fluid Mech., 645, 27-57.http://dx.doi.org/10.1017/S0022112009992485

Synolakis, C.E. 1987. The runup of solitary waves. J. Fluid Mech., 185, 523-545. http://dx.doi.org/10.1017/S002211208700329X

Synolakis, C.E., Bernard, E.N., Titov, V.V., Kânoglu, U., González, F.I. 2008. Validation and verification of tsunami numerical models. Pure appl. Geophys., 165, 2197-2228.http://dx.doi.org/10.1007/s00024-004-0427-y

Tadepalli, S. and Synolakis C.E. 1994. The run-up of N-waves on sloping beaches. Proc. R. Soc. Lond. A., 445, 99-112. http://dx.doi.org/10.1098/rspa.1994.0050

Tadepalli, S. and Synolakis C.E. 1996. Model for the leading waves of tsunami. Phys. Rev. Letts., 77, 2141-2144. PMid:10061867 http://dx.doi.org/10.1103/PhysRevLett.77.2141

Todorovska, M.I., Trifunac, M.D. 2001. Generation of tsunamis by a slowly spreading uplift of the sea floor. Soil Dynamics and Earthquake Engineering, 21, 151-167.http://dx.doi.org/10.1016/S0267-7261(00)00096-8

Wang, B.L. and Liu, H. 2006. Solving a fully nonlinear highly dispersive Boussinesq model with mesh-less least square-based finite difference method. Int. J. Numer. Meth. Fluids., 52, 213-235. http://dx.doi.org/10.1002/fld.1175

Wang, B.L., Zhu, Y.Q., Song, Z.P., Liu, H. 2006. Boussinesq-type modeling in surf zone using meshless least-square-based finite difference method. Conference of Global Chinese Scholars on Hydrodynamics, shanghai, China.

Ward, S.N. 2002. Tsunamis. Encyclopedia of Physical Science and Technology, Academic Press.

Witting, J.M. 1984. A united model for the evolution of nonlinear water waves. J Comput Phys., 56, 203-236.http://dx.doi.org/10.1016/0021-9991(84)90092-5

Wu, T.Y. 2001. A unified theory for modeling water waves. Advances in Applied Mechanics, 37, 1-88. http://dx.doi.org/10.1016/S0065-2156(00)80004-6

Zakharov, V.E. 1968. Stability of periodic waves of finite amplitude on the surface of a deep fluid. J Appl Mech Tech Phys., 9, 190-194. http://dx.doi.org/10.1007/BF00913182

Zhao, X., Wang, B.L. and Liu, H. 2009. Modelling the submarine mass failure induced Tsunamis by Boussinesq equations. Journal of Asian Earth Sciences, 36, 47-55. http://dx.doi.org/10.1016/j.jseaes.2008.12.005

Authors retain copyright and grant the Proceedings right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this Proceedings.