Development of Lagrangian hydrodynamics for three-dimensional nonlinear instability of vortices
| Project/Area Number |
21540390
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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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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| Co-Investigator(Renkei-kenkyūsha) |
HATTORI Yuji 東北大学, 流体科学研究所, 教授 (70261469)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 流体物理 / ケルヴィン波 / ラグランジュ的記述 / 波のエネルギー / 波-平均流相互作用 / 擬運動量 / ハミルトン的ホップ分岐 / 三波相互作用 / ホールMHD渦輪 / 波・平均流相互作用 / 弱非線形安定性 / 振幅方程式 / ハミルトン的標準形 / ハミルトン的ピッチフォーク分岐 / 渦輪 / 楕円形渦核 / 楕円型不安定性 / WKB法 / 速い歳差回転 |
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| Research Abstract |
A circular-cylindrical vortex embedded in an inviscid incompressible fluid is neutrally stable, but can be destabilized by symmetry-breaking perturbations. The Eulerian treatment has difficulty in calculating the mean flow nonlinearly induced by waves. We have developed a method of exploiting the Lagrangian variables for calculating unambiguously the mean flow, whereby all the coefficients of the amplitude equations were determined to third order in amplitude. These equations were converted into canonical Hamltonian equations by normalizing dependent variables. Besides, we investigated the short-wavelength stability by use of the WKB method, to complement the normal-mode analyses.
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Report
(4 results)
Research Products
(84 results)
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[Presentation] Y. Fukumoto, M. Hirota, Y. Mie2009
Author(s)
Y. Fukumoto, M. Hirota, Y. Mie
Organizer
Turbulent Mixing and Beyond
Place of Presentation
The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy
Year and Date
2009-07-28
Related Report
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