Towards a mathematical theory of fluid turbulence via singular vortex dynamics
| Project/Area Number |
21340017
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Hokkaido University |
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Principal Investigator |
SAKAJO Takashi 北海道大学, 大学院・理学研究院, 教授 (10303603)
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| Co-Investigator(Renkei-kenkyūsha) |
NAWA Hayato 大阪大学, 大学院・基礎工学研究科, 教授 (90218066)
MATSUMOTO Takeshi 京都大学, 大学院・理学研究科, 助教 (20346076)
AKAHORI Takahumi 静岡大学, 大学院・数理システム工学科, 准教授 (90437187)
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| Project Period (FY) |
2009 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥9,750,000 (Direct Cost: ¥7,500,000、Indirect Cost: ¥2,250,000)
Fiscal Year 2012: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2011: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2009: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
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| Keywords | 乱流 / 点渦 / 渦層 / 散逸的弱解 / オイラー方程式 / オイラーα方程式 / 点渦系 / 衝突解 / 一様等方乱流 / 点渦力学 / α点渦系 / 自己相似衝突解 / エンストロフィー / 乱流モデル / 衝突多様体 / 点渦統計力学 / 位相正則化 / クゥエット流 / Euler-α方程式 |
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| Research Abstract |
It has been pointed out that dissipative weak solutions of the hydrodynamic equations plays an important role in understand the statistical theory of turbulence. But the existence of such a singular solution has not yet proven and its dynamical property is uncertain. In the present project, we successfully obtain a self-similar collapsing solution of α point vortex system. This is a dissipative weak solution of 2D Euler equation, which acquires one of the important properties observed in 2D turbulence.
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Report
(5 results)
Research Products
(24 results)
