Three-dimensional motion of a vortex tube and quest for its optimality based on topological variational principle

2008 Fiscal Year Final Research Report

• Project/Area Number: 19540406
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Kyushu University
• Principal Investigator: FUKUMOTO Yasuhide Kyushu University, 大学院・数理学研究院, 教授 (30192727)
• Co-Investigator(Renkei-kenkyūsha): HATTORI Yuji 九州工業大学, 大学院・工学研究院, 教授 (70261469)
• Project Period (FY): 2007 – 2008
• Keywords: 流体物理

Research Abstract

非圧縮流体中を運動する定常渦流は「インパルス一定の拘束条件下での等循環面上のエネルギー極大/極小状態である」を証明した. これより導かれる変分原理を高レイノルズ数での渦輪の運動に適用して, 速度公式を大幅に改善した. また, 低レイノルズ数極限で, すべての時刻にわたって渦輪の運動速度を書き下した. この解より決定した最適渦輪のパラメータは実験データと符合する. さらに, トポロジー的変分原理に立脚して, 渦管に立つ波のエネルギーと非線形的に誘導される平均流を計算した.

Research Products

• [Journal Article] A generalised vortex ring model (2009)
  • Author(s): F. Kaplanski, S. Sazhin, Y. Fukumoto, B. Steven, H. Morgan
  • Journal Title: Journal of Fluid Mechanics Vol.622 Pages: 233-258
  • Peer Reviewed
• [Journal Article] Short-wavelength stability analysis of a helical vortex tube (2009)
  • Author(s): Y. Hattori, Y. Fukumoto
  • Journal Title: Physics of Fluids Vol.21 Pages: 014104(7)
  • Peer Reviewed
• [Journal Article] Elliptical instability of a vortex tube and driftcurrent induced by it (2009)
  • Author(s): Y. Fukumoto, M. Hirota
  • Journal Title: Physica Scripta Vol.T132 Pages: 014041(9)
  • Peer Reviewed
• [Journal Article] A unified view of topological invariants of fluid flows (2008)
  • Author(s): Y. Fukumoto
  • Journal Title: Topologica Vol.1 Pages: 003(12)
  • Peer Reviewed
• [Journal Article] Action-angle variables for the continuous spectrum of ideal magnetohydrodynamics (2008)
  • Author(s): M. Hirota, Y. Fukumoto
  • Journal Title: Physics of Plasmas Vol.15 Pages: 122101(11)
  • Peer Reviewed
• [Journal Article] Energy of hydrodynamic and magneto-hydrodynamic waves with point and continuous spectra (2008)
  • Author(s): M. Hirota, Y. Fukumoto
  • Journal Title: Journal of Mathematical Physics Vol.49 Pages: 083101(28)
  • Peer Reviewed
• [Journal Article] Kinematic variational principle for motion of vortex rings (2008)
  • Author(s): Y.Fukumoto, H.K.Moffatt
  • Journal Title: Physica D Vol.237 Pages: 2210-2217
  • Peer Reviewed
• [Journal Article] Global time evolution of an axisymmetric vortex ring at low Reynolds numbers (2008)
  • Author(s): Y. Fukumoto, F. Kaplanski
  • Journal Title: Physics of Fluids Vol.20 Pages: 053103(13)
  • Peer Reviewed
• [Journal Article] Analogy of a vortex-jet filament with the Kirchhoff elastic rod (2008)
  • Author(s): Y. Fukumoto
  • Journal Title: Proc. of IUTAM Symposium on Hamiltonian dynamics(vortex structure and turbulence (ed.A.V.Borisov, V.V.Kozlov, I.S.Manaev and M.A. Sokolovskiy, Springer, 2008)) Pages: 77-87
  • Peer Reviewed
• [Journal Article] Super-complex wave-vortex multiscale phenomena induced in laser-matter interactions (2007)
  • Author(s): S. Lugomer, Y. Fukumoto, B. Farkas, T. Sorenyi, A. Toth
  • Journal Title: Physical Reviews E Vol.76 Pages: 016305 (15)
  • Peer Reviewed
• [Journal Article] Analogy between a vortex-jet filament and the Kirchhoff elastic rod (2007)
  • Author(s): Y. Fukumoto
  • Journal Title: Fluid Dynamics Research Vol.39 Pages: 511-520
  • Peer Reviewed
• [Journal Article] Evolution of an elliptical flow in weakly nonlinear regime (2007)
  • Author(s): Y. Hattori, Y. Fukumoto, K. Fujimura
  • Journal Title: Proc. of IUTAM Symposium on Computational Physics and New Perspectives in Turbulence (ed.Y.Kaneda, Springer) Pages: 433-438
  • Peer Reviewed
• [Journal Article] Instability of an elliptical flow : Weakly nonlinear analysis (2007)
  • Author(s): Y. Hattori, Y. Fukumoto, K. Fujimura
  • Journal Title: Proc. of the Sixth International Conference on Advances in Fluid Mechanics(Fluid Structure Interaction and Moving Boundary Problems IV (eds.S.K.Chakrabarti and C.A.Brebbia, WIT press) Pages: 193-201
  • Peer Reviewed
• [Presentation] 太い渦輪の線形安定性 (2009)
  • Author(s): 服部裕司, 泥谷圭亮
  • Organizer: 日本物理学会64回年次大会
  • Place of Presentation: 立教学院池袋キャンパス, 東京
  • Year and Date: 2009-03-27
• [Presentation] Linear and weakly nonlinear stability of an elliptic flow from the viewpoint of Hamiltonian spectra (2009)
  • Author(s): Y. Fukumoto, M. Hirota
  • Organizer: International workshop on verified computations and related topics
  • Place of Presentation: University of Karlsruhe (TH), Karlsruhe, Germany
  • Year and Date: 2009-03-07
• [Presentation] 渦流の3次元不安定性とそれよるドリフト流の誘導 : ラグランジュ的アプローチ (2008)
  • Author(s): 福本康秀, 廣田真
  • Organizer: 研究集会「乱流現象及び多自由度系の動力学, 構造と統計法則」
  • Place of Presentation: 九州大学応用力学研究所, 春日
  • Year and Date: 2008-11-14
• [Presentation] Short-wave stability of a helical vortex tube (2008)
  • Author(s): Y. Hattori, Y. Fukumoto
  • Organizer: IUTAM symposium 150 Years of Vortex Dynamics
  • Place of Presentation: Technical University of Denmark, Lyngby, Denmark
  • Year and Date: 2008-10-16
• [Presentation] Global time evolution of viscous vortex rings [*Keynote lecture] (2008)
  • Author(s): Y. Fukumoto
  • Organizer: IUTAM symposium 150 Years of Vortex Dynamics
  • Place of Presentation: Technical University of Denmark, Lyngby, Denmark
  • Year and Date: 2008-10-16
• [Presentation] 短波長極限におけるらせん渦の不安定性 (2008)
  • Author(s): 服部裕司, 福本康秀
  • Organizer: 日本流体力学会年会2008
  • Place of Presentation: 神戸大学六甲台キャンパス, 神戸
  • Year and Date: 2008-09-06
• [Presentation] Curvature Instability of a vortex ring and a helical vortex tube (2008)
  • Author(s): Y. Hattori, Y. Fukumoto
  • Organizer: XXII International Congress of Theoretical and Applied Mechanics(ICTAM)
  • Place of Presentation: Adelaide Convention Center, Adelaide, Australia
  • Year and Date: 2008-08-26
• [Presentation] Motion of vortex rings with and without magnetic field (2008)
  • Author(s): Y. Fukumoto, H. K. Moffatt, S. Ooshiro
  • Organizer: XXII International Congress of Theoretical and Applied Mechanics(ICTAM)
  • Place of Presentation: Adelaide Convention Center, Adelaide, Australia
  • Year and Date: 2008-08-26
• [Presentation] 渦構造の曲率不安定性 (2008)
  • Author(s): 服部裕司, 福本康秀
  • Organizer: 研究集会「オイラー方程式の数理 : 渦運動150年」
  • Place of Presentation: 京都大学数理解析研究所, 京都
  • Year and Date: 2008-07-18
• [Presentation] らせん渦の短波長線形不安定性 (2008)
  • Author(s): 服部裕司, 三宅俊甫, 福本康秀
  • Organizer: 日本物理学会第63回年次大会
  • Place of Presentation: 近畿大学大学本部キャンパス, 東大阪
  • Year and Date: 2008-03-23
• [Presentation] 渦流の3次元不安定性とそれよって誘導されるドリフト流 : ラグランジュ的アプローチ (2008)
  • Author(s): 福本康秀
  • Organizer: 第三回九州大学産業技術数理研究センターワークショップ「自然現象における階層構造と数理的アプローチ」
  • Place of Presentation: 九州大学情報基盤研究開発センター, 福岡
  • Year and Date: 2008-03-08
• [Presentation] Global stability analysis of a rotating fluid columns subjected to a weak external Coriolis force (2008)
  • Author(s): Y. Fukumoto, M. Hirota, M. Adachi
  • Organizer: US-Japan workshop on shocks, hydro-instabilities, turbulence and hot(warm) dense matter and related phenomena
  • Place of Presentation: 大阪大学レーザーエネルギー科学研究所, 豊中
  • Year and Date: 2008-01-16
• [Presentation] 低レイノルズ数領域での渦輪の全時間領域にわたる挙動 (2007)
  • Author(s): 福本康秀, F. Kaplanski
  • Organizer: 日本物理学会第62回年次大会
  • Place of Presentation: 北海道大札幌キャンパス, 札幌
  • Year and Date: 2007-09-22
• [Presentation] Nonlinear evolution of a vortex ring (2007)
  • Author(s): Y. Hattori, Y. Fukumoto
  • Organizer: EUROMECH Colloquium 491 : Vortex dynamics from quantum to geophysical scales
  • Place of Presentation: University of Exeter, Exeter, UK
  • Year and Date: 2007-09-12
• [Presentation] Elliptical instability of a vortex tube and driftcurrent induced by it (2007)
  • Author(s): Y. Fukumoto, M. Hirota
  • Organizer: International Conference Turbulent Mixing and Beyond
  • Place of Presentation: The Abdus Salam International Centre for Theoretical Physics(ICTP), Trieste, Italy
  • Year and Date: 2007-08-24
• [Presentation] 直接数値シミュレーションによる渦輪の曲率不安定性の検証 (2007)
  • Author(s): 服部裕司, 福本康秀
  • Organizer: 日本流体力学会年会2007
  • Place of Presentation: 東大教養学部, 東京
  • Year and Date: 2007-08-08
• [Presentation] Numerical detection of a new instability mode of a vortex ring (2007)
  • Author(s): Y. Hattori, Y. Fukumoto
  • Organizer: 5th Joint ASME/JSME Fluids Engineering Conference(3rd Symposium on Fundamental Issues and Perspectives in Fluid Mechanics)
  • Place of Presentation: Sheraton San Diego Hotel & Marina, San Diego, CA, USA
  • Year and Date: 2007-08-01
• [Presentation] 渦のキネマティックスとダイナミックス (2007)
  • Author(s): 福本康秀
  • Organizer: プラズマ科学のフロンティア2007研究会
  • Place of Presentation: 核融合科学研究所, 土岐(招待講演)
  • Year and Date: 2007-08-01
• [Presentation] Nonlinear evolution of disturbed vortex ring (2007)
  • Author(s): Y. Hattori, Y. Fukumoto
  • Organizer: US-Japan workshop on shocks, hydro-instabilities(turbulence and hot(warm)dense matter and related phenomena)
  • Place of Presentation: Universidade do Porto, Porto, Portugal
  • Year and Date: 2007-06-26
• [Presentation] Kinematic variational principle for motion of vortex rings (2007)
  • Author(s): Y. Fukumoto
  • Organizer: Euler Equations : 250 Years On
  • Place of Presentation: Centre Paul Langevin, Aussois, France
  • Year and Date: 2007-06-20
• [Book] 第5章「渦を破壊せよ」,「技術に生きる現代数学」(若山正人編) (2008)
  • Author(s): 福本康秀[分担執筆]
  • Total Pages: 206
  • Publisher: 岩波書店
• [Remarks] 福本康秀
  • URL: http://hyoka.ofc.kyushu-u.ac.jp/search/details/K000449/index.html
• [Remarks] 服部裕司
  • URL: http://www.ifs.tohoku.ac.jp/divisions/jp/cfd_acfdl.html