Clustering and negative temperatute state of vortices in geophysical flow: Statistical mechanics of quasi-geostrophic point vortices
| Project/Area Number |
25400462
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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 |
Meteorology/Physical oceanography/Hydrology
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| Research Institution | The University of Electro-Communications |
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Principal Investigator |
Miyazaki Takeshi 電気通信大学, 情報理工学(系)研究科, 教授 (50142097)
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| Co-Investigator(Kenkyū-buntansha) |
TAKAHASHI Naoya 東京電機大学, 工学部, 教授 (40313423)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
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| Keywords | 地球流体運動 / 秩序渦構造 / 統計力学 / 準地衡風近似 / 最大エントロピー理論 / 負温度状態 / 地球流体渦 / 点渦系 / 大規模数値計算 |
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| Outline of Final Research Achievements |
The statistical mechanics of quasi-geostrophic vortices is investigated numerically and theoretically. Direct numerical simulations of a point vortex system of mixed sign under periodic boundary conditions are performed using a fast special-purpose computer for molecular dynamics. Clustering of point vortices of like sign is observed and a columnar dipole structure appears
as an equilibrium state.
These numerical results are explained from the viewpoint of the classical statistical mechanics. A three-dimensional mean field equation is derived based on the maximum entropy theory. The numerically obtained end states are shown to be the 2D sn-sn dipole solutions of the mean field equation. We present other branches of 2D and 3D solution of the mean field equation, whose entropy is smaller than that of the two-dimensional sn-sn dipole branch. These findings explain the reason why only the two-dimensional sn-sn dipole states are found in the numerical simulations of point vortices.
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Report
(4 results)
Research Products
(14 results)
