Stability for flows in a generalized two-dimensional fluid
| Project/Area Number |
20540424
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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 |
Meteorology/Physical oceanography/Hydrology
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| Research Institution | Kobe University |
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Principal Investigator |
IWAYAMA Takahiro Kobe University, 理学研究科, 准教授 (10284598)
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| Co-Investigator(Renkei-kenkyūsha) |
WATANABE Takeshi 名古屋工業大学, 大学院・工学研究科, 准教授 (30345946)
YAMASAKI Kazuhito 神戸大学, 大学院・理学研究科, 助教 (20335417)
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| Research Collaborator |
SUEYOSHI Masakazu 気象庁, 気象研究所気候研究部, 研究員
YAJIMA Takahiro 東京理科大学, 理学部, 博士研究員
MURAKAMI Shinya 神戸大学, 大学院・自然科学研究科, 大学院生
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| Project Period (FY) |
2008 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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| Keywords | 一般化された2次元流体 / α乱流系 / 流れの安定性 / Green関数 / Hamilton構造 / グリーン関数 / 平行流の安定性 / 波動活動度保存則 / Okubo-Weissの基準 / リースポテンシャル / 非整数冪ラプラシアン / 安定性 / 波の共鳴 |
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| Research Abstract |
Stability of parallel shear flows for a generalized two-dimensional (2D) fluid system, which is a unified form of some geophysical 2D fluid systems, is investigated. First, the conservation of the wave activity is derived. Second, it is shown that the governing equation for the generalized 2D fluid system can be written in the form of non canonical Hamiltonian form. Using them, a necessary condition for a linear stability of parallel shear flows is derived as: "if the transverse derivative of the generalized vorticity for the basic state is positive or negative definite, the flow is stable". Moreover, the Green's function for the generalized 2D fluid system is derived. Using the Green's function, physically realizable systems for the generalized 2D fluid system exist only for \alpha less than or equal 3. Here, \alpha is a real parameter describing the scale separation between the generalized vorticity and the velocity. In addition, the transition of the small scale behavior of the generalized vorticity at alpha=2, a well known property of forced and dissipated turbulence for the generalized 2D fluid, is explained in terms of the Green's function.
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Report
(4 results)
Research Products
(34 results)
