2018 Fiscal Year Final Research Report
Three-dimensional stability of rotating flows of stratified and electrically conducting fluid on the ground of deepening the concept of the helicity
| Project/Area Number |
16K05476
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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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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Kyushu University |
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Principal Investigator |
Fukumoto Yasuhide 九州大学, マス・フォア・インダストリ研究所, 教授 (30192727)
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| Research Collaborator |
Okulov V. I.
Tribrelsky M. I.
Abarzhi S. I.
Zou R.
Franco-Medrano F
Habibah U.
Hazarika H.
Miyachi Yuki
Wada Keigo
Zhao X.
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Keywords | 回転成層流 / レイリー・テイラー不安定性 / 眠りごま / 磁気回転不安定性 / 予混合火炎 / ダリウス・ ランダウ不安定性 / 圧縮性 / トポロジカル流体力学 |
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| Outline of Final Research Achievements |
Stability of the rotating flow whose density varies in the vertical direction has a link with the global environmental problems, the stability of the rotating flow of the magnetic fluid with formation of stars, and the stability of the combustion flame with the development of clean energy sources. The rotational flow in the spheroid is equivalent to the motion of the symmetrical top, but the rotational stratified flow confined in the inclined ellipsoid is equivalent to the motion of the symmetrical top with the top axis misaligned from the symmetry axis. We discovered a new long wave mode of the magneto-rotational instability.
We have also investigated the effect of weak compressibility on stability of a flame front. The compressibility acts, in the very thin reaction zone, to reduce the traveling speed of a flame front, which brings in possibility for suppressing the Darrieus-Landau instability.
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| Free Research Field |
流体力学
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| Academic Significance and Societal Importance of the Research Achievements |
密度が変化する流体の回転流や電磁流体の回転流、そして、燃焼は極めて複雑な流体現象で、スーパーコンピュータでも、直接計算することは困難極まる。速度や密度の急激な変化によって特徴づけられる層状領域の形状の安定性を解析するための、特異摂動法やハミルトン力学系などの数理的な手法を編み出して、これまで見落とされてきた新しい不安定性、あるいはレイリー・テイラー不安定性やダリウス・ ランダウ不安性が抑制される可能性を見出した。これらのトポロジー的な側面を明らかにし、一見異なる現象を数理的な観点から統一的に捉えることを可能にした。
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