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Abstract <p>Mathematical modeling is one of the most powerful and flexible tools for studying complex natural phenomena, but setting up a direct full-scale experiment is, as a rule, impossible. Tsunami waves generated in oceans and seas after submarine earthquakes, volcanic explosions, underwater slumping, and coastal landslides, as well as high-energy atmospheric disturbances, are dangerous natural phenomenon characterized by low frequency and severe consequences. This 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 tsunamis (operational warning and coastal tsunami zoning) is discussed. This work was written for a special issue of <i>Atmospheric and Oceanic Physics</i> dedicated to the 100th anniversary of Academician G.I. Marchuk, so it is limited mainly to the results obtained by the authors during their work at the Computing Center (CC) at the Siberian Branch of the USSR Academy of Sciences (SB AS) in the 1970s–1980s.</p>

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Mathematical Modeling in the Tsunami Problem: Methodology and Practical Applications

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • V. K. Gusiakov,
  • L. B. Chubarov

摘要

Abstract

Mathematical modeling is one of the most powerful and flexible tools for studying complex natural phenomena, but setting up a direct full-scale experiment is, as a rule, impossible. Tsunami waves generated in oceans and seas after submarine earthquakes, volcanic explosions, underwater slumping, and coastal landslides, as well as high-energy atmospheric disturbances, are dangerous natural phenomenon characterized by low frequency and severe consequences. This 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 tsunamis (operational warning and coastal tsunami zoning) is discussed. This work was written for a special issue of Atmospheric and Oceanic Physics dedicated to the 100th anniversary of Academician G.I. Marchuk, so it is limited mainly to the results obtained by the authors during their work at the Computing Center (CC) at the Siberian Branch of the USSR Academy of Sciences (SB AS) in the 1970s–1980s.