| Project/Area Number |
18K03429
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 12040:Applied mathematics and statistics-related
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| Research Institution | Japan Women's University |
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Principal Investigator |
SHOJI Mayumi 日本女子大学, 理学部, 研究員 (10216161)
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| Project Period (FY) |
2018-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2020: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2019: ¥130,000 (Direct Cost: ¥100,000、Indirect Cost: ¥30,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 重力表面張力波 / ２層流 / 渦あり流れ / 分岐問題 / 数値シミュレーション / よどみ点 |
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| Outline of Final Research Achievements |
Stationary waves of constant shape and constant propagation speed on rotational flows of two layers are computed numerically. Two layers are assumed to be of distinct constant vorticity distributions. Vorticity is created near the bottom by the friction, or near the free boundary by the wind. Accordingly, two-layer vorticity is a step closer to the real water wave. Three different kinds of waves of finite depth are considered: pure capillary, capillary-gravity, and gravity waves.
The problem is formulated as a bifurcation problem, which involves many parameters and produces a complicated structure of solutions. We adopted a numerical method by which waves with stagnation points can be computed, and obtained variety of new solutions. It is also reported that the locations of the stagnation points vary curiously with the prescribed parameters and that they offer an interesting problem.
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| Academic Significance and Societal Importance of the Research Achievements |
深さ有限な流体では、底の方には摩擦によって、自由表面の近くには風によって渦が発生する。よって多層流を考えることでより実際に近い問題設定を扱うことができる。しかし最もシンプルな２層流ですら関わるパラメータが多い。理論だけで解析することは非常に難しく数値シミュレーションに頼らざるを得ない。そして数値計算結果ですら未だほとんどわかっていないのが現状である。
そこで数値シミュレーションで様々な解を具体的に求め、よどみ点の発生状況や分岐構造を明らかにできたことは非常に意義深い。本研究用に開発した計算プログラムも、多層流の計算など今後更に研究を展開する際の手がかりを与えるものと考える。
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