Analysis of free boundary problems in shallow water systems

2023 Fiscal Year Final Research Report

• Project/Area Number: 17K05313
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Tokyo University of Marine Science and Technology
• Principal Investigator: Ohnawa Masashi 東京海洋大学, 学術研究院, 准教授 (10443243)
• Co-Investigator(Kenkyū-buntansha): 鈴木 政尋 名古屋工業大学, 工学(系)研究科(研究院), 准教授 (30587895)
• Project Period (FY): 2017-04-01 – 2024-03-31
• Keywords: 不連続流 / 流体の遷移 / 漸近安定性

Outline of Final Research Achievements

In this study, we investigate how flows of water and air, which include discontinuous changes, are maintained. Examples in practice can be observed when river flows descend downstream of weirs or when downhill winds cross over mountains and disturb airflow as they approach flat terrain. In these flows, orographic changes of the fluid bed accelerate flows faster than the propagation speed of wave patterns, causing energy release when they abruptly decelerate upon encountering gentle terrain, causing external damage. Previous studies were constrained to flows in limited terrains. However, this study overcome those limitations and elucidated the mechanism for sustaining the structure of such flows.

Free Research Field

流体力学　微分方程式

Academic Significance and Societal Importance of the Research Achievements

流れが不連続に変化するときにはエネルギーを解放します．河川の堰では人工的に急勾配の後に平らな地形を続けてそのような流れを作り出し，流れの勢いを弱めるものですが，洪水や津波が堤防を乗り越えた際には，周囲の建築物や堤防自体を損傷させるため，このような流れの形成や維持の仕組みを理解することは防災上重要なことです．本研究では実際に現れるあらゆる地形での流れを解析できる手法を開発できました．将来的には流れを制御し，防災に役立てられることが期待されます．