### 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.

#### Keywords

analytical solution; dispersive waves; bottom motion

#### References

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

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