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- Giving to Math

Event Type:

Applied Mathematics and Computation Seminar

Date/Time:

Friday, May 27, 2011 - 05:00

Location:

GLK 113

Event Link:

Guest Speaker:

Harry Yeh

Institution:

OSU Structural and Ocean Engineering

Abstract:

When a solitary wave (a model of tsunami in the nearshore shallow water) impinges on a reflective vertical wall, it can take the formation of Mach reflection (a geometrically similar reflection from acoustics). The mathematical theory predicts that the amplification at the reflection is not twice, but four times the incident wave amplitude. Evidently, this has an important implication to engineering design practice. Our laboratory experiments verify detailed features of the Mach reflection phenomenon, whereas contradict the theory in terms of the maximum four-fold amplification: the maximum amplification observed in the laboratory was 2.92, instead. The reason for the discrepancy is discussed. In addition, we show that a tsunami along the reflective wall can reach higher than the maximum solitary wave height. Once the wave breaking happens along the wall, the substantial increase in water-surface slope results along the wave crest away from the wall.