| Project/Area Number |
26400410
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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 | Aichi Institute of Technology |
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Principal Investigator |
KANEDA Yukio 愛知工業大学, 工学部, 教授 (10107691)
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| Co-Investigator(Kenkyū-buntansha) |
石原 卓 岡山大学, 環境生命科学研究科, 教授 (10262495)
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| Project Period (FY) |
2014-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 乱流境界層 / 統計理論 / 直接数値シミュレーション / 線形応答理論 / ラグランジュ的繰り込み理論 / 統計的普遍則 / 壁乱流 / 対数則 |
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| Outline of Final Research Achievements |
Turbulent boundary layer (TBL) near solid boundary is common in science and technology. In TBL, the flow field changes rapidly in space, and the TBL strongly affects the whole flow field. In this study, we clarified quantitatively the position- and direction- dependence of representative length-scales characterizing the TBL, on the basis of the data of large-scale direct numerical simulation (DNS) of turbulent flow between two parallel planes (turbulent channel flow: TCF).
By generalizing the idea of linear response theory well known in the statistical mechanics of systems at or near thermal equilibrium state to TBL, we derived a theory for one-point statistics in the TBL, and confirmed that the theory is in good agreement with the data of high resolution DNS of TCF.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究では熱平衡系の統計力学で知られた線形応答理論の考えを一般化して乱流境界層の統計理論を導き、その理論が乱流の大規模DNSデータとよく合うことを示した。このことは、熱平衡系と乱流境界層の間にそのお互いの見かけの違いにも関わらず何らかの共通性があることを示唆しており、乱流に限らない超多自由度の非線形力学系の理解に貢献すると期待される。
また、その理論の与える有限のレイノルズ数による影響の評価および本研究で得られた乱流境界層中の代表的長さについての知見は、乱流の予測や制御を必要とする科学技術の諸分野への貢献が期待される。
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