Event Type:

Applied Mathematics and Computation Seminar

Date/Time:

Friday, November 30, 2012 - 04:00

Location:

GLK 113

Event Link:

Guest Speaker:

Institution:

OSU Civil and Construction Engrg

Abstract:

Tsunami is a translational long wave created by seafloor displacement. Here we focus on the tsunamis generated by co-seismic fault rupture and discuss the characteristics of tsunami generation, propagation, and runup of the 2011 Tohoku/Japan Tsunami. Then we ask if genesis of the tsunami could evolve into a series of solitons as predicted by the theory, and identify what the important factors would be to determine the tsunami waveform. Two examples of the close interplay between theory and application are presented. First, a mathematical recipe for the initial-valued problem of cylindrical wave equation is used to yield a practical and surprisingly accurate estimate for the directivity of tsunami energy emission for the 2004 Indian Ocean Tsunami. This recipe is also applied to solve the nonlinear shallow water equation for tsunami runup problem. The outcomes resulted in the basis for FEMA’s design guidelines for tsunami evacuation buildings. Second, performing the laboratory experiments revealed the difference between the KP soliton and the KdV soliton. Recognizing the difference necessarily makes us to modify the KP soliton solution, which in turn leads to significant expansion of applicability of the KP theory. We then introduce a few more tsunami-related problems that mathematical analyses can contribute. Those are the topics of undular bores and the extreme wave splash-up that were observed in the 2011 Tohoku/Japan Tsunami.