Mathematical models of large-amplitude and nonlinear ocean waves

2022 Fiscal Year Final Research Report

• Project/Area Number: 17H02856
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Ibaraki University
• Principal Investigator: Murashige Sunao 茨城大学, 理工学研究科(理学野), 教授 (40302749)
• Co-Investigator(Kenkyū-buntansha): 片岡 武 神戸大学, 工学研究科, 准教授 (20273758) ; 井口 達雄 慶應義塾大学, 理工学部(矢上), 教授 (20294879) ; 柿沼 太郎 鹿児島大学, 理工学域工学系, 准教授 (70371755) ; 丸野 健一 早稲田大学, 理工学術院, 教授 (80380674)
• Project Period (FY): 2017-04-01 – 2022-03-31
• Keywords: 非線形波動 / 数理モデル / 応用数学 / 流体力学 / 数値解析

Outline of Final Research Achievements

Large-amplitude ocean waves may cause serious damage such as tsunami disaster and ship capsizing. Also it has been observed that the density stratification may generate internal waves propagating in the sea with large-amplitude more than 100m. On the other hand, ocean wave motion can be formulated as a mathematical problem with fluid dynamics and some approximate theories for small-amplitude waves theory have been developed, while it is highly challenging to solve this problem for large-amplitude waves due to the strong nonlinearity of boundary conditions at the sea surface. Therefore this work has not only academic but also practical significance. This work models this nonlinear phenomenon using some mathematical techniques such as asymptotic theory, complex analysis and integrable system theory. Theoretical analyses and numerical examples demonstrate that the proposed mathematical models elucidate some essential characteristics of large-amplitude motion of ocean waves very well.

Free Research Field

流体力学

Academic Significance and Societal Importance of the Research Achievements

流体力学に基づいた海洋波の運動の数理的研究は比較的古くから行われているが，そのほとんどは波の振幅が微小であることを仮定する弱非線形水波理論に基づいている．それに対して，実際に重要な海洋波の多くは，津波や転覆のような海難事故のように振幅の大きな波動である．また，海中では水深方向の密度成層により振幅が100mを超える波（内部波）が発生し，環境に影響を与えることが知られている．したがって，振幅の大きな海洋波の非線形運動に対する数学的理論の構築と数値計算法の開発は，学術的だけではなく社会的にも意義がある．