Mathematical Modeling in the Tsunami Problem: Methodology and Practical Applications

Mathematical modeling is one of the most powerful and flexible tools for studying complex natural phenomena, in which the setting up of a direct full-scale experiment is, as a rule, impossible. A typical example of a dangerous natural phenomenon characterized by low frequency and severe consequences are tsunami waves that are generated in the oceans and the seas after submarine earthquakes, volcanic explosions, underwater slumping and coastal landslides as well as by high-energy atmospheric disturbances. The paper examines mathematical models used to study the three main stages of tsunami wave evolution: generation by underwater or surface sources, propagation in the deep ocean and on the shelf, and run-up to the coast. Their application to solving two main scientific and applied problems related to the tsunami problem (operational warning and coastal tsunami zoning) is discussed. The work was written for this issue of the journal dedicated to the 100th anniversary of Academician G.I. Marchuk, therefore the review is limited mainly to the results obtained by the authors during their work at the Computing Center of the Siberian Branch of the USSR Academy of Sciences in the 1970-80s.