SIMULATION OF ANALYTICAL TRANSIENT WAVE DUE TO DOWNWARD BOTTOM THRUST

Sugih Sudharma Tjandra, Sri Redjeki Pudjaprasetya, Leo Hari Wiryanto


Abstract


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.

DOI : http://dx.doi.org/10.22342/jims.21.2.189.93-104


Keywords


analytical solution; dispersive waves; bottom motion

References


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.


Full Text: PDF

Refbacks

  • There are currently no refbacks.


Journal of the Indonesian Mathematical Society ( p-ISSN:2086-8952 | e-ISSN:2460-0245) published by the Indonesian Mathematical Society (IndoMS).

Indexed by:

logo DOAJLogo SintaThe Indonesian Publication Index-Portal Garuda Google Scholar logo zbMath Logo AMSLogo CrossrefLogo Thomson Reuters

Visitor Number : web statistics View My Stats


Creative Commons License
Journal of the Indonesian Mathematical Society by http://jims-a.org/index.php/jimsa is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

p-ISSN:2086-8952e-ISSN:2460-0245