Clustering and negative temperatute state of vortices in geophysical flow: Statistical mechanics of quasi-geostrophic point vortices

• Project/Area Number: 25400462
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Meteorology/Physical oceanography/Hydrology
• Research Institution: The University of Electro-Communications
• Principal Investigator: Miyazaki Takeshi 電気通信大学, 情報理工学(系)研究科, 教授 (50142097)
• Co-Investigator(Kenkyū-buntansha): TAKAHASHI Naoya 東京電機大学, 工学部, 教授 (40313423)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥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)
• 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

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.

Research Products

• [Journal Article] Statistical Mechanics of Quasi-geostrophic Vortices (2016)
  • Author(s): T. Miyazaki, Y. Shimoda, K. Saga
  • Journal Title: Proceedings of International Conference on Mathematical Fluid Dynamics, Present and Future Volume: 印刷中
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Maximum and extremum entropy states of quasi-geostrophic point vortices (2015)
  • Author(s): Takeshi Miyazaki, Hironori Miyamoto, Satoshi Funakoshi, Satoshi Taguchi
  • Journal Title: J. Physics Volume: 印刷中
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] 軌道の特徴量を用いたボールの空力係数の推定 (2014)
  • Author(s): 安田海人、坪井一洋、田中晃平、宮嵜武
  • Journal Title: 日本機械学会論文集 Volume: 80/ 814 Pages: 1-10
  • NAID: 130005004863
  • Peer Reviewed
• [Journal Article] Temperature Cancellation Method of Motion-Capturing PSP System (2014)
  • Author(s): Y.Yamada, T.Okabe, T.Miyazaki, H.Sakaue
  • Journal Title: Proc. 30th AIAA Aerodynamic Measurement Technology and Ground Testing Conference Volume: 2942 Pages: 1-11
  • Peer Reviewed
• [Journal Article] Pressure/Temperature Measurement of a Free-Flight Object by PSP/TSP (2014)
  • Author(s): M.Ishii, Y.Yamada, T.Miyazaki, H.Sakaue
  • Journal Title: Proc. AIAA Atmospheric Flight Mechanics Conference Volume: 2542 Pages: 1-8
  • Peer Reviewed
• [Journal Article] 卓球ボールの空力特性 (2014)
  • Author(s): 田中晃平、福重貴之、宮嵜武、姫野龍太郎
  • Journal Title: ながれ Volume: 33 Pages: 37-45
  • NAID: 110009809566
  • Peer Reviewed
• [Presentation] Clustering and Entropy Growth of Quasi-geostrophic Point Vortices (2016)
  • Author(s): T. Miyazaki, M. Ishihara, Y. Konno, N. Takahashi
  • Organizer: 24th International Congress of Theoretical and Applied Mechanics (ICTAM2016)
  • Place of Presentation: Palais des congres, Montreal, Canada
  • Year and Date: 2016-08-21
• [Presentation] Vortex dynamics of the high energy (negative temperature) state in quasi-geostrophic turbulence (2015)
  • Author(s): M. Ishihara, N. Takahashi, T. Miyazaki, N. Hatakeyama, Y. Hattori
  • Organizer: Fifteenth International Symposium on Advanced Fluid Information
  • Place of Presentation: Sendai International Center (Sendai-shi, Miyagi)
  • Year and Date: 2015-10-27
  • Int'l Joint Research
• [Presentation] 準地衡風渦系の統計力学 -直接数値計算と渦領域モデルの比較- (2015)
  • Author(s): 石原雅也、嵯峨圭晟、今野優哉、宮嵜武
  • Organizer: 日本流体力学会年会2015
  • Place of Presentation: 東京工業大学（東京都目黒区）
  • Year and Date: 2015-09-26
• [Presentation] Clustering and entropy growth of quasi-geostrophic point vortices under periodic boundary conditions (2015)
  • Author(s): T. Miyazaki, Y. Shimoda, Y. Konno
  • Organizer: Japan-Russia Workshop on Supercomputer Modeling, Instability and Turbulence in Fluid Dynamics
  • Place of Presentation: Keldysh Institute of Applied Mathematics, Moscow
  • Year and Date: 2015-03-04 – 2015-03-06
  • Invited
• [Presentation] Statistical Mechanics of Quasi-geostrophic Voryices (2014)
  • Author(s): Takeshi Miyazaki
  • Organizer: CREST-SBN International Conference
  • Place of Presentation: Waseda Univ., Tokyo
  • Year and Date: 2014-11-11 – 2014-11-14
  • Invited
• [Presentation] Vortex dynamics of the high energy (negative temperature) state in quasi-geostrophic turbulence (2014)
  • Author(s): M.Ishihara, N. Takahashi, T.Miyazaki, N. Hatakeyama, Y.Hattori
  • Organizer: Proc. 11th International Cobference on Flow Dynamics
  • Place of Presentation: Tohoku Univ., Sendai
  • Year and Date: 2014-10-09
• [Presentation] 準地衡風渦系の統計力学 (2013)
  • Author(s): 嵯峨圭晟、宮本大士、宮嵜武
  • Organizer: 日本流体力学会年会2013
  • Place of Presentation: 東京農工大学小金井キャンパス
• [Presentation] Maximum entropy states of quasi-geostrophic point vortices under periodic boundary conditions (2013)
  • Author(s): Takeshi Miyazaki, Hironori Miyamoto, Satoshi Funakoshi
  • Organizer: International conference "Turbulence and wave processes"
  • Place of Presentation: Lomonosov Moscow State University, Moscow, Russia
  • Invited