Non-modal stability of vortices and by-pass transition: towards general theory of hydrodynamic stability

• Project/Area Number: 24540391
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Tohoku University
• Principal Investigator: HATTORI Yuji 東北大学, 流体科学研究所, 教授 (70261469)
• Co-Investigator(Renkei-kenkyūsha): FUKUMOTO Yasuhide 九州大学, マス・フォア・インダストリ研究所, 教授 (30192727) ; IWAKAMI Wakana 京都大学, 基礎物理学研究所, 研究員 (50571535)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000); Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2012: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
• Keywords: 渦 / 非モード安定性 / バイパス遷移 / 遷移的成長 / WKB安定性解析 / 流れの安定性理論 / 流れのの安定性理論

Outline of Final Research Achievements

Vortices are one of the fundamental structures in various flows. The stability of vortices is the starting point in understanding the nature of the flow. Transient growth and destabilization by localized disturbances in vortices are studied theoretically and numerically in order to understand the transition to turbulence in vortical flows. In transient growth vortex stretching by straining flow is shown to be a key mechanism. Numerical results of unstable growth of localized disturbances are in good agreement with theoretical prediction. The transition to turbulence occurs after several stages of growth.

Research Products

• [Journal Article] Modal and non-modal stability of two-dimensional Taylor-Green vortices (2014)
  • Author(s): T. Gau and Y. Hattori
  • Journal Title: Fluid Dynamics Research Volume: 46 Issue: 3 Pages: 031410-031410
  • DOI: 10.1088/0169-5983/46/3/031410
  • Peer Reviewed
• [Journal Article] Evolution of localized disturbances in the elliptic instability (2014)
  • Author(s): Y. Hattori and M. S. bin Marzuki
  • Journal Title: Journal of Fluid Mechanics Volume: 755 Pages: 603-627
  • DOI: 10.1017/jfm.2014.439
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Variational Necessary and Sufficient Stability Conditions for Inviscid Shear Flow (2014)
  • Author(s): M. Hirota, P. J. Morrison and Y. Hattori
  • Journal Title: Proceedings of the Royal Society A Volume: 470 Issue: 2172 Pages: 20140322-20140322
  • DOI: 10.1098/rspa.2014.0322
  • Peer Reviewed
• [Journal Article] Dependence of Axial Flow inside Wing Tip Vortices on Wing Planforms (2014)
  • Author(s): Hiroshi Koizumi, Yuji Hattori
  • Journal Title: Proceedings of the Eleventh International Conference on Flow Dynamics Volume: - Pages: 74-75
• [Journal Article] Stability Analysis of Vortices with Axial Flow based on Energetics and its Application (2014)
  • Author(s): Yasuhide Fukumoto, Makoto Hirota, Yuji Hattori
  • Journal Title: Proceedings of the 14th International Symposium on Advanced Fluid Information Volume: - Pages: 176-177
• [Journal Article] The Continuous Spectrum in the Moore-Saffman-Tsai-Widnall Instability (2014)
  • Author(s): Yuji Hattori, Makoto Hirota, Stefan G. Llewellyn Smith
  • Journal Title: Proceedings of the 14th International Symposium on Advanced Fluid Information and Transdisciplinary Fluid Integration Volume: - Pages: 178-179
• [Journal Article] Modal stability analysis of a helical vortex tube with axial flow (2014)
  • Author(s): Yuji Hattori and Yasuhide Fukumoto
  • Journal Title: Journal of Fluid Mechanics Volume: 738 Pages: 222-249
  • DOI: 10.1017/jfm.2013.591
  • Peer Reviewed
• [Journal Article] Computational Study of Formation of Wing Tip Vortices at Low Reynolds Numbers (2013)
  • Author(s): Hiroshi Koizumi, Yuji Hattori
  • Journal Title: Proceedings of the Tenth International Conference on Flow Dynamics Volume: - Pages: 80-81
• [Journal Article] The Continuous Spectrum in the Moore-Saffman-Tsai-Windnall Instability (2013)
  • Author(s): Yuji Hattori, Makoto Hirota and Stefan G. Llewellyn Smith
  • Journal Title: Proceedings of the 13th International Symposium on Advanced Fluid Information and Transdisciplinary Fluid Integration Volume: - Pages: 152-153
• [Journal Article] A Numerical Study of the Effect of Large Deformations of a Trailing Vortex on Its Breakdown (2013)
  • Author(s): Naoya Takahashi, Takeshi Miyazaki, Nozomu Hatakeyama and Yuji Hattori
  • Journal Title: Proceedings of the 13th International Symposium on Advanced Fluid Information and Transdisciplinary Fluid Integration Volume: - Pages: 150-151
• [Journal Article] Stability Analysis of Vortices with Axial Flow based on Energetics and its Application (2013)
  • Author(s): Yasuhide Fukumoto and Yuji Hattori
  • Journal Title: Proceedings of the 13th International Symposium on Advanced Fluid Information and Transdisciplinary Fluid Integration Volume: - Pages: 168-169
• [Journal Article] Motion of axisymmetric magnetic eddies with swirl (2013)
  • Author(s): Y. Hattori and S. G. Llewellyn Smith
  • Journal Title: Procedia IUTAM Volume: 7 Pages: 243-250
  • DOI: 10.1016/j.piutam.2013.03.028
  • Peer Reviewed
• [Journal Article] A Numerical Study of the Effect of Large Deformations of a Trailing Vortex on Its Breakdown (2012)
  • Author(s): Naoya Takahashi and Yuji Hattori
  • Journal Title: Proceedings of the 12th International Symposium on Advanced Fluid Information and Transdisciplinary Fluid Integration Volume: － Pages: 154-155
• [Journal Article] Modal Stability Analysis of a Helical Vortex Tube with Axial Flow (2012)
  • Author(s): Yuji Hattori and Yasuhide Fukumoto
  • Journal Title: Proceedings of the 12th International Symposium on Advanced Fluid Information and Transdisciplinary Fluid Integration Volume: － Pages: 168-169
• [Journal Article] Error Analysis of Volume Penalization Method for Two-Dimensional Navier-Stokes Equations (2012)
  • Author(s): Yuzuru Yatagai, Wakana Iwakami Nakano, Yuji Hattori
  • Journal Title: Proceedings of the Ninth International Conference on Flow Dynamics Volume: － Pages: 92-93
• [Journal Article] Axisymmetric magnetic vortices with swirl (2012)
  • Author(s): S. G. Llewellyn Smith and Y. Hattori
  • Journal Title: Communications in Nonlinear Science and Numerical Simulation Volume: 17 Issue: 5 Pages: 2101-2107
  • DOI: 10.1016/j.cnsns.2011.06.001
  • Peer Reviewed
• [Journal Article] Effects of axial flow on the stability of a helical vortex tube (2012)
  • Author(s): Y. Hattori and Y. Fukumoto
  • Journal Title: Physics of Fluids Volume: 24 Issue: 5
  • DOI: 10.1063/1.4717769
  • Peer Reviewed
• [Presentation] Evolution of mean flow and disturbances in strained vortices (2014)
  • Author(s): Yuji Hattori
  • Organizer: 67th Annual Meeting of the APS Division of Fluid Dynamics
  • Place of Presentation: San Francisco, USA
  • Year and Date: 2014-11-24
• [Presentation] 翼端渦構造の翼平面形依存性の数値シミュレーション研究 (2014)
  • Author(s): 小泉博史, 服部裕司
  • Organizer: 日本流体力学会年会2014
  • Place of Presentation: 宮城県仙台市, 東北大学
  • Year and Date: 2014-09-16
• [Presentation] 軸流をもつ渦のパラメタ共鳴不安定性と波のエネルギー (2014)
  • Author(s): 服部裕司, 廣田真, 福本康秀
  • Organizer: 日本流体力学会年会2014
  • Place of Presentation: 宮城県仙台市, 東北大学
  • Year and Date: 2014-09-15
• [Presentation] 乱れた歪み渦の平均流 (2014)
  • Author(s): 服部裕司
  • Organizer: 日本物理学会2014年秋季大会
  • Place of Presentation: 愛知県春日井市, 中部大学
  • Year and Date: 2014-09-07
• [Presentation] 歪んだ渦と曲がった渦の不安定性
  • Author(s): 服部裕司
  • Organizer: 応用数学連携フォーラム第38回ワークショップ
  • Place of Presentation: 宮城県仙台市
  • Invited
• [Presentation] 歪んだ渦における局所擾乱の成長：線形不安定性・非線形発展・乱流
  • Author(s): 服部裕司
  • Organizer: 平成25年度NIFS共同研究研究会「MHDおよび流体力学における流れの安定性に関する理論・シミュレーション研究」
  • Place of Presentation: 岐阜県土岐市
  • Invited
• [Presentation] Computational Study of Formation of Wing Tip Vortices at Low Reynolds Numbers
  • Author(s): Hiroshi Koizumi, Yuji Hattori
  • Organizer: Tenth International Conference on Flow Dynamics
  • Place of Presentation: 宮城県仙台市
• [Presentation] The Continuous Spectrum in the Moore-Saffman-Tsai-Windnall Instability
  • Author(s): Yuji Hattori, Makoto Hirota and Stefan G. Llewellyn Smith
  • Organizer: 13th International Symposium on Advanced Fluid Information and Transdisciplinary Fluid Integration
  • Place of Presentation: 宮城県仙台市
• [Presentation] A Numerical Study of the Effect of Large Deformations of a Trailing Vortex on Its Breakdown
  • Author(s): Naoya Takahashi, Takeshi Miyazaki, Nozomu Hatakeyama and Yuji Hattori
  • Organizer: 13th International Symposium on Advanced Fluid Information and Transdisciplinary Fluid Integration
  • Place of Presentation: 宮城県仙台市
• [Presentation] Stability Analysis of Vortices with Axial Flow based on Energetics and its Application
  • Author(s): Yasuhide Fukumoto and Yuji Hattori
  • Organizer: 13th International Symposium on Advanced Fluid Information and Transdisciplinary Fluid Integration
  • Place of Presentation: 宮城県仙台市
• [Presentation] 歪み渦における局所擾乱の成長過程
  • Author(s): 服部裕司
  • Organizer: 日本物理学会第69回年次大会
  • Place of Presentation: 東海大学
• [Presentation] Evolution of localized disturbances in the elliptical flow
  • Author(s): Y. Hattori and M. S. Bin Marzuki
  • Organizer: IUTAM Symposium on Vortex Dynamics: Formation, Structure and Function
  • Place of Presentation: Fukuoka, Japan
• [Presentation] Modal and non-modal stability of two-dimensional Taylor-Green vortices
  • Author(s): Takayuki Gau, Yuji Hattori
  • Organizer: IUTAM Symposium on Vortex Dynamics: Formation, Structure and Function
  • Place of Presentation: Fukuoka, Japan
• [Presentation] 2次元テイラー-グリーン渦のモード安定性解析
  • Author(s): 我有隆行，服部裕司
  • Organizer: 日本流体力学会年会2012
  • Place of Presentation: 高知大学
• [Presentation] Modal Stability Analysis of a Helical Vortex Tube with Axial Flow
  • Author(s): Yuji Hattori and Yasuhide Fukumoto
  • Organizer: The 12th International Symposium on Advanced Fluid Information and Transdisciplinary Fluid Integration
  • Place of Presentation: Sendai, Japan
• [Presentation] A Numerical Study of the Effect of Large Deformations of a Trailing Vortex on Its Breakdown
  • Author(s): Naoya Takahashi and Yuji Hattori
  • Organizer: The 12th International Symposium on Advanced Fluid Information and Transdisciplinary Fluid Integration
  • Place of Presentation: Sendai, Japan
• [Presentation] Error Analysis of Volume Penalization Method for Two-Dimensional Navier-Stokes Equations
  • Author(s): Yuzuru Yatagai, Wakana Iwakami Nakano, Yuji Hattori
  • Organizer: The Ninth International Conference on Flow Dynamics
  • Place of Presentation: Sendai, Japan
• [Presentation] Evolution of localized disturbances in the elliptical instability
  • Author(s): Y. Hattori and M. S. Bin Marzuki
  • Organizer: The 9th European Fluid Mechanics Conference
  • Place of Presentation: Rome, Italy
• [Presentation] Effects of Axial Flow on the Curvature Instability of a Helical Vortex Tube: Modal Analysis
  • Author(s): Yuji Hattori and Yasuhide Fukumoto
  • Organizer: The 23rd International Congress of Theoretical and Applied Mechanics
  • Place of Presentation: Beijing, China
• [Presentation] Motion of axisymmetric magnetic eddies with swirl
  • Author(s): Y. Hattori and S. G. Llewellyn Smith
  • Organizer: IUTAM Symposium on Topological Fluid Dynamics
  • Place of Presentation: Cambridge, UK