Mach Reflection in Tsunamis

This chapter is partly motivated by the tsunami event occurred in Japan on 12th July 1993. The event devastated parts of the Okushiri island, where observed maximum run-up water elevations were of the order of 30 m. The number of fatalities reported was 239. Over several decades oceanographers have observed the occurrence of Mach reflection of tsunami bores, which may help explain the devastating power of tsunamis. Based on the two-dimensional shallow water equations and the numerical methods studied in this book, this chapter presents an analytical and numerical study of bore reflection phenomena, confirming that both regular and Mach reflection patternsOkushiri island tsunami (1993) are possible in shallow water flows.