Development of Lagrangian hydrodynamics for three-dimensional nonlinear instability of vortices

2011 Fiscal Year Final Research Report

• Project/Area Number: 21540390
• 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 九州大学, マス・フォア・インダストリ研究所, 教授 (30192727)
• Co-Investigator(Renkei-kenkyūsha): HATTORI Yuji 東北大学, 流体科学研究所, 教授 (70261469)
• Project Period (FY): 2009 – 2011
• Keywords: 流体物理

Research Abstract

A circular-cylindrical vortex embedded in an inviscid incompressible fluid is neutrally stable, but can be destabilized by symmetry-breaking perturbations. The Eulerian treatment has difficulty in calculating the mean flow nonlinearly induced by waves. We have developed a method of exploiting the Lagrangian variables for calculating unambiguously the mean flow, whereby all the coefficients of the amplitude equations were determined to third order in amplitude. These equations were converted into canonical Hamltonian equations by normalizing dependent variables. Besides, we investigated the short-wavelength stability by use of the WKB method, to complement the normal-mode analyses.

Research Products

• [Journal Article] Effects of axial flow on the stability of a helical vortex tube (2012)
  • Author(s): Y. Hattori, Y. Fukumoto
  • Journal Title: Physics of Fluids Volume: Vol.24 Pages: 054102(15)
  • Peer Reviewed
• [Journal Article] Reynolds-number effect on vortex ring evolution in a viscous fluid (2012)
  • Author(s): F. Kaplanski, Y. Fukumoto, Y. Rudi
  • Journal Title: Physics of Fluids Volume: Vol.24 Pages: 033101(13)
  • Peer Reviewed
• [Journal Article] Energy and mean flow of Kelvin waves, and their application to weakly nonlinear stability of an elliptical flow (2011)
  • Author(s): Y. Fukumoto, M. Hirota, Y. Mie
  • Journal Title: In Proc. of the International Conference'Mathematical Analysis on the Navier-Stokes Equations and Related Topics, Past and Future-in memory of Professor Tetsuro Miyakawa', Mathematical Sciences and Applications Volume: Vol.43 Pages: 53-70
  • Peer Reviewed
• [Journal Article] Local instability of a rotating flow driven by precession of arbitrary frequency (2011)
  • Author(s): Me Me Naing, Y. Fukumoto
  • Journal Title: Fluid Dynamics Research Volume: Vol.43 Pages: 055502(11)
  • Peer Reviewed
• [Journal Article] Reynolds-number effect on vortex ring evolution (2011)
  • Author(s): F. Kaplanski, Y. Fukumoto, Y. Rudi
  • Journal Title: Proc. of the Sixth International Conference on Fluid Mechanics, AIP Conf. Proc Volume: Vol.1376 Pages: 58-61
  • Peer Reviewed
• [Journal Article] Lagrangian approach to weakly nonlinear stability of elliptical flow (2010)
  • Author(s): Y. Fukumoto, M. Hirota, Y. Mie
  • Journal Title: Physica Scripta Volume: Vol.142 Pages: 014049(7)
  • Peer Reviewed
• [Journal Article] Weakly nonlinear saturation of stationary resonance of a rotating flow in an elliptic cylinder (2010)
  • Author(s): Y. Mie, Y. Fukumoto
  • Journal Title: Journal of Math-for-Industry Volume: Vol.2A Pages: 27-37
  • Peer Reviewed
• [Journal Article] Dynamics of vortex rings and spray induced vortex ring-like structures (2010)
  • Author(s): F. Kaplanski, S. S. Sazhin, S. Begg, Y. Fukumoto, M. Heikal
  • Journal Title: European J. Mechanics B/Fluids Volume: Vol.29 Pages: 208-216
  • Peer Reviewed
• [Journal Article] Generation of ribbons, helicoids and complex Scherk surface in laser-matter interactions (2010)
  • Author(s): S. Lugomer, Y. Fukumoto
  • Journal Title: Phys. Rev. E Volume: Vol.81 Pages: 036311(11)
  • Peer Reviewed
• [Journal Article] Global time evolution of viscous vortex rings (2010)
  • Author(s): Y. Fukumoto
  • Journal Title: Theoretical and Computational Fluid Dynamics Volume: Vol.24 Pages: 335-347
  • Peer Reviewed
• [Journal Article] Local instability of an elliptical flow subjected to a Coriolis force (2009)
  • Author(s): Me Me Naing, Y. Fukumoto
  • Journal Title: J. Phys. Soc. Japan Volume: Vol.78 Pages: 124401(7)
  • Peer Reviewed
• [Journal Article] オイラー方程式の南部力学表現について (2009)
  • Author(s): 福本康秀
  • Journal Title: ながれ Volume: Vol.28 Pages: 499-500
• [Presentation] 3次元ケルヴィン波の輸送特性 (2012)
  • Author(s): 福本康秀
  • Organizer: 日本物理学会第67回年次大会
  • Place of Presentation: 関西学院大学・西宮上ケ原キャンパス,西宮
  • Year and Date: 2012-03-27
• [Presentation] コリオリ力を受ける円筒内の回転流体の3つのモードの相互作用による線形安定性解析 (2012)
  • Author(s): 山下晃史,福本康秀
  • Organizer: 日本物理学会第67回年次大会
  • Place of Presentation: 西学院大学・西宮上ケ原キャンパス
  • Year and Date: 2012-03-27
• [Presentation] ケルヴィン波のエネルギー,擬運動量,ストークスドリフト (2012)
  • Author(s): 福本康秀,彌榮洋一
  • Organizer: 第61回理論応用力学講演会
  • Place of Presentation: 東京大学生産技術研究所,東京
  • Year and Date: 2012-03-07
• [Presentation] 渦度のトポロジーと渦のダイナミクスへの応用 (2011)
  • Author(s): 福本康秀
  • Organizer: 日本物理学会四国支部講演会
  • Place of Presentation: 愛媛大学,松山
  • Year and Date: 2011-12-16
• [Presentation] 渦流の3次元不安定性に対するハミルトニアン分岐理論 (2011)
  • Author(s): 福本康秀,彌榮洋一
  • Organizer: 共同利用研究集会「乱流現象及び非平衡系の多様性と普遍性
  • Place of Presentation: 九州大学応用力学研究所,春日
  • Year and Date: 2011-11-12
• [Presentation] Effects of swirl on the stability of vortices (2011)
  • Author(s): Y. Fukumoto, Y. Hattori
  • Organizer: Effects of swirl on the stability of vortices
  • Place of Presentation: ホテルメトロポリタン仙台,仙台
  • Year and Date: 2011-11-10
• [Presentation] Hamiltonian bifurcation of a rotating flow confined in a cylinder with elliptically deformed cross-section (2011)
  • Author(s): Y. Fukumoto, Y. Mie
  • Organizer: International Conf." Fluxes and Structures in Fluids : Physics of Geosphere
  • Place of Presentation: V. I. Il` ichev Pacific Oceanological Insti., Vladivostok, Russia
  • Year and Date: 2011-09-27
• [Presentation] Hamiltonian bifurcation theory for a rotating flow confined in a cylinder of elliptic cross-section (2011)
  • Author(s): Y. Fukumoto, Y. Mie
  • Organizer: International Conf. on Fluid and Gas Dynamics
  • Place of Presentation: Zhejiang Normal Univ., Jinhua, China
  • Year and Date: 2011-09-24
• [Presentation] 楕円断面筒状容器内の回転流の非定常共鳴モードの弱非線形安定性 (2011)
  • Author(s): 福本康秀,彌榮洋一
  • Organizer: 日本流体力学会年会
  • Place of Presentation: 首都大学東京・南大沢キャンパス,八王子
  • Year and Date: 2011-09-08
• [Presentation] 変分原理とコンピュータ・アナトミーへの応用 (2011)
  • Author(s): 福本康秀
  • Organizer: Computer Entertainment Developers Conference(CEDEC2011)
  • Place of Presentation: パシフィコ横浜,横浜
  • Year and Date: 2011-09-06
• [Presentation] Kinematic variational principle for vortical structure of Euler flows and beyond (2011)
  • Author(s): Y. Fukumoto
  • Organizer: RIMS Camp-style Seminar Modern approach and developments to Onsager' s theory on statistical vortices
  • Place of Presentation: アピカルイン京都,京都
  • Year and Date: 2011-08-31
• [Presentation] Hamiltonian bifurcation theory for a rotating flow subject to elliptic straining field (2011)
  • Author(s): Y. Fukumoto
  • Organizer: Third International Conf. and Advanced School" Turbulent Mixing and Beyond
  • Place of Presentation: The Abdus Salam International Centre for Theoretical Physics(ICTP), Trieste, Italy
  • Year and Date: 2011-08-23
• [Presentation] 楕円断面筒状容器内の回転流のハミルトニアン分岐理論 (2011)
  • Author(s): 福本康秀,彌榮洋一
  • Organizer: 京都大学数理解析研究所研究集会「オイラー方程式の数理:カルマン渦列と非定常渦運動100年
  • Place of Presentation: 京都大学数理解析研究所,京都
  • Year and Date: 2011-07-22
• [Presentation] 歳差回転する円筒内の回転流の局所安定性 (2011)
  • Author(s): 福本康秀, Me Me Naing
  • Organizer: 日本物理学会第66回年次大会
  • Place of Presentation: 新潟大学・五十嵐キャンパス,新潟
  • Year and Date: 2011-03-25
• [Presentation] Energy and mean flowof waves on a rotating fluid flow, and their application to stability analysis (2010)
  • Author(s): Y. Fukumoto
  • Organizer: 非線形力学ワークショップ
  • Place of Presentation: 東京大学・本郷キャンパス,東京
  • Year and Date: 2010-12-09
• [Presentation] Normal-mode stability analysis of a helical vortex tube (2010)
  • Author(s): Y. Fukumoto, Y. Hattori
  • Organizer: Seven International Conf. on Flow Dynamics
  • Place of Presentation: 仙台国際センター,仙台
  • Year and Date: 2010-11-02
• [Presentation] 楕円回転流の弱非線形安定性のためのオイラー・ラグランジュ混合法 (2010)
  • Author(s): 福本康秀,廣田真,彌榮洋一
  • Organizer: 共同利用研究集会「非線形波動研究の新たな展開-現象とモデル化-
  • Place of Presentation: 九州大学・筑紫キャンパス,春日
  • Year and Date: 2010-10-30
• [Presentation] 低レイノルズ数領域でのスワールをもつ渦輪の運動 (2010)
  • Author(s): 福本康秀, F. Kaplanski
  • Organizer: 日本物理学会2010年秋季大会
  • Place of Presentation: 大阪府立大学・中百舌鳥キャンパス,堺
  • Year and Date: 2010-09-25
• [Presentation] 渦度のトポロジーと楕円流の弱非線形安定性への応用 (2010)
  • Author(s): 福本康秀
  • Organizer: 第142会エンレイソウの会
  • Place of Presentation: 北海道大学トポロジー理工学教育研究センター,札幌
  • Year and Date: 2010-09-10
• [Presentation] Energy, action and mean flow of waves on a vortex of a fluid flow, and their application to stability analysis (2010)
  • Author(s): Y. Fukumoto, M. Hirota
  • Organizer: 31st annual meeting of the Canadian Applied and Industrial Mathematics Society(CAIMS* SCMAI 2010)
  • Place of Presentation: Sheraton Hotel
  • Year and Date: 2010-07-20
• [Presentation] Hybrid method of Lagrangian and Eulerian hydrodynamics to weakly nonlinear stability of an elliptical flow (2010)
  • Author(s): Y. Fukumoto, M. Hirota, Y. Mie
  • Organizer: 2010 Chinese-German Conf. on Fluid and Gas Dynamics
  • Place of Presentation: Zhejiang Normal Univ., Jinhua, China
  • Year and Date: 2010-05-19
• [Presentation] Lagrangian approach to wave interactions on vortices and weakly nonlinear stability of an elliptical flow (2010)
  • Author(s): Y. Fukumoto
  • Organizer: Internatinal Conf. on Mathematical Fluid Dynamics
  • Place of Presentation: 早稲田大学・西早稲田キャンパス,東京
  • Year and Date: 2010-03-13
• [Presentation] Energy and mean flow of Kelvin waves, and their application to weakly nonlinear stability of an elliptical flow (2009)
  • Author(s): Y. Fukumoto
  • Organizer: International Workshop : Mathematical Analysis on the Navier-Stokes Equatins and Related Topics, Past and Future-Inmemory of Professor TetsuroMiyakawa-
  • Place of Presentation: 神戸大学・六甲台キャンパス,神戸
  • Year and Date: 2009-12-07
• [Presentation] ケルヴィン波のエネルギーと誘導される平均流,そしてその楕円流の弱非線形安定性理論への応用 (2009)
  • Author(s): 福本康秀,廣田真,彌榮洋一
  • Organizer: 未来研究ラボ「非線形ダイナミクス」研究会
  • Place of Presentation: 大阪大学基礎工学部,豊中
  • Year and Date: 2009-12-02
• [Presentation] ラグランジュ的記述による流れの短波長安定性理論 (2009)
  • Author(s): 福本康秀, Me Me Naing
  • Organizer: 日本物理学会2009年秋季大会
  • Place of Presentation: 熊本大学・黒髪キャンパス,熊本
  • Year and Date: 2009-09-26
• [Presentation] Y. Fukumoto, M. Hirota, Y. Mie (2009)
  • Author(s): Y. Fukumoto, M. Hirota, Y. Mie
  • Organizer: Turbulent Mixing and Beyond
  • Place of Presentation: The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy
  • Year and Date: 2009-07-28
• [Presentation] 渦波の非線形相互作用によって誘導される平均流 (2009)
  • Author(s): 福本康秀
  • Organizer: 京都大学数理解析研究所研究集会「オイラー方程式の数理:渦運動と音波150年
  • Place of Presentation: 京都大学大学院人間環境学研究科,京都
  • Year and Date: 2009-07-23
• [Presentation] Lagrangian approach to weakly nonlinear interactions of waves on a rotating flow (2009)
  • Author(s): Y. Fukumoto, M. Hirota, Y. Mie
  • Organizer: International Symp. on Modern Perspectives of Fluid Mechanics
  • Place of Presentation: 名古屋大学Business Laboratory,名古屋
  • Year and Date: 2009-06-27
• [Remarks] 福本康秀
  • URL: http://www.imi.kyushu-u.ac.jp/academic_staffs/view/27
• [Remarks] 服部裕司
  • URL: http://eagle.ifs.tohoku.ac.jp/hattori.html