Sugih Sudharma Tjandra, Sri Redjeki Pudjaprasetya, Leo Hari Wiryanto


Generation process is an important part of understanding waves, especially tsunami. Large earthquake under the sea is one major cause of tsunamis. The sea surface deforms as a response from the sea bottom motion caused by the earthquake. Analytical description of surface wave generated by bottom motion can be obtained from the linearized dispersive model. For a bottom motion in the form of a downward motion, the result is expressed in terms of improper integral. Here, we focus on analyzing the convergence of this integral, and then the improper integral is approximated into a finite integral so that the integral can be evaluated numerically. Further, we simulate free surface elevation for three different type of bottom motions, classified as impulsive, intermediate, and slow  movements. We demonstrate that the wave propagating to the right, with a depression as the leading wave, followed with subsequent wave crests. This phenomena is often observed in most tsunami events.



analytical solution; dispersive waves; bottom motion

Full Text:



Hammack, J.L., Tsunamis-a model of their generation and propagation,W. M. Keck Lab. Hydraul. and Water Res., Calif. Inst. Tech. Rep. KH-R-28, 1972.

Hammack, J.L., A note on tsunami: their generation and propagation in an ocean of uniform depth, J. Fluid Mech., 4 (1973), 769-799.

Mei, C.C. and Yue, D.P., Advanced series on Ocean Engineering, World Scientific, 2005.

Dutykh, D., Dias, F. Tsunami and non linear waves, Springer, 2007.

Kervella, Y., Dutykh, D., Dias, F., Comparison between three dimensional linear and non linear tsunami generation models, Theor. Fluid Dyn., 21 (2007), pp. 245-269.

Fuhrman, D.R., Madsen, P.A., Tsunami generation, propagation, and run-up with a highorder Boussinesq model, Coastal Engineering, 56 (2009), pp. 747-758.

Lynett, P., Liu, P.L.F, A numerical study of submarine-landslide-generated waves and run-up, Proc. R. Soc. Lond. A, 458 (2002), pp. 2885-2910.

Kreyszig, E., Advanced Engineering Mathematics, John Wiley and Sons, 1999.



  • There are currently no refbacks.

Journal of the Indonesian Mathematical Society
Mathematics Department, Universitas Gadjah Mada
Senolowo, Sinduadi, Mlati, Sleman Regency, Special Region of Yogyakarta 55281, Telp. (0274) 552243

p-ISSN: 2086-8952 | e-ISSN: 2460-0245

Journal of the Indonesian Mathematical Society is licensed under a Creative Commons Attribution 4.0 International License

web statistics
View My Stats