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Theory of vortex-wave interaction by deepening the topological vorticity dynamics

Research Project

Project/Area Number 24540407
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Mathematical physics/Fundamental condensed matter physics
Research InstitutionKyushu University

Principal Investigator

FUKUMOTO Yasuhide  九州大学, 学内共同利用施設等, 教授 (30192727)

Project Period (FY) 2012-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Keywordsトポロジカル不変量 / クロスヘリシティ / ネータ―の定理 / 弱非線形安定性 / 波のエネルギー / 等磁気循環摂動 / 磁気回転不安定性 / ケプラー型回転流 / 方位磁気回転不安定性 / Hain-Lust方程式 / 非理想MHD / WKB法 / Landau-Darrieus不安定性 / 燃焼界面 / トポロジカル積分不変量 / 三波共鳴 / カシミール不変量 / トポロジー的不変量 / バロクリニック流体 / ケルヴィン波 / 渦対 / 運動速度
Outline of Final Research Achievements

By invoking the Noether theory associated with the particle-relabeling symmetry, we revealed that the topological integral invariants for barotropic and baroclinic flows, magnetohydrodynamics (MHD) and a relativistic flow are all represented in the form of the cross-helicity. By restricting disturbances to isovortical ones that keep the topology of the vorticity, we succeeded in calculating the weakly nonlinear stability of a rotating flow with elliptic streamlines. By restricting to the isomagnetovortical perturbations, we derived a general formula for waves on MHD flows. Using the Lagrangian treatment that realizes this class of perturbations, we made the three-dimensional short-wave stability analysis of the azimuthal magnetorotational instability, and showed that the Keplerian rotational flow is unstable.

Report

(4 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (45 results)

All 2015 2014 2013 2012 Other

All Journal Article (17 results) (of which Peer Reviewed: 17 results,  Acknowledgement Compliant: 7 results,  Open Access: 1 results) Presentation (24 results) (of which Invited: 4 results) Book (3 results) Remarks (1 results)

  • [Journal Article] Stability of a hydrodynamic discontinuity2015

    • Author(s)
      Snezhana I. Abarzhi, Yasuhide Fukumoto, Leo P. Kadanof
    • Journal Title

      Physica Scripta

      Volume: 90 Issue: 1 Pages: 018002-018002

    • DOI

      10.1088/0031-8949/90/1/018002

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Lagrangian approach to weakly nonlinear interaction of Kelvin waves and a symmetry-breaking bifurcation of a rotating flow2015

    • Author(s)
      Yasuhide Fukumoto, Youichi Mie
    • Journal Title

      Fluid Dynamics Research

      Volume: 47 Issue: 1 Pages: 015509-015509

    • DOI

      10.1088/0169-5983/47/1/015509

    • NAID

      120005690812

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Instabilities of rotational flows in azimuthal magnetic fields of arbitrary radial dependence2014

    • Author(s)
      Oleg N Kirillov, Frank Stefani, Yasuhide Fukumoto
    • Journal Title

      Fluid Dynamics Research

      Volume: 46 Issue: 3 Pages: 031403-031403

    • DOI

      10.1088/0169-5983/46/3/031403

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Regularity criteria for the incompressible Hall-MHD system2014

    • Author(s)
      Jishan Fan, Yasuhide Fukumoto, Gen Nakamura, Yong Zhou
    • Journal Title

      Zeitschrift fur Angewandte Mathematik und Mechanik: ZAMM

      Volume: online Issue: 11 Pages: 1156-1160

    • DOI

      10.1002/zamm.201400102

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Relabeling symmetry in relativistic fluids and plasmas2014

    • Author(s)
      Y. Kawazura, Z. Yoshida, and Y. Fukumoto
    • Journal Title

      J. Phys. A: Math. Theor.

      Volume: 47 Issue: 46 Pages: 4655011-17

    • DOI

      10.1088/1751-8113/47/46/465501

    • NAID

      130005478019

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Local instabilities in magnetized rotational flows: A short-wavelength approach2014

    • Author(s)
      Oleg N. Kirillov, Frank Stefani, Yasuhide Fukumoto
    • Journal Title

      Journal of Fluid Mechanics

      Volume: 760 Pages: 591-633

    • DOI

      10.1017/jfm.2014.614

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Local stability analysis of azimuthal magnetorotational instability of ideal MHD flows2014

    • Author(s)
      Rong Zou, Yasuhide Fukumoto
    • Journal Title

      Progress of Theoretical and Experimental Physics

      Volume: 2014 Issue: 11 Pages: 113J01-113J01

    • DOI

      10.1093/ptep/ptu139

    • NAID

      120005690813

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Modal stability analysis of a helical vortex tube with axial flow2014

    • Author(s)
      Yuji Hattori and Yasuhide Fukumoto
    • Journal Title

      Journal of Fluid Mechanics

      Volume: 738 Pages: 222-249

    • DOI

      10.1017/jfm.2013.591

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Instabilities of rotational flows in azimuthal magnetic fields of arbitrary radial dependence2014

    • Author(s)
      Oleg N Kirillov, Frank Stefani and Yasuhide Fukumoto
    • Journal Title

      Fluid Dynamics Research

      Volume: 46

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Lagrangian approach to weakly nonlinear interaction of Kelvin waves and a symmetry-breaking bifurcation of a rotating flow2014

    • Author(s)
      Yasuhide Fukumoto, Youichi Mie
    • Journal Title

      Fluid Dynamics Research

      Volume: 46

    • NAID

      120005690812

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] A unified view of topological invariants of barotropic and baroclinic fluids and their application to formal stability analysis of three-dimensional ideal gas flows2013

    • Author(s)
      Yasuhide Fukumoto, Hirofumi Sakuma
    • Journal Title

      Procedia IUTAM Vol. 7 "Topological Fluid Dynamics: Theory and Applications"

      Volume: 7 Pages: 213-222

    • DOI

      10.1016/j.piutam.2013.03.025

    • Related Report
      2013 Research-status Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Logarithmically improved regularity criteria for the generalized Navier-Stokes and related equations2013

    • Author(s)
      Jishan Fan, Yasuhide Fukumoto, Yong Zhou
    • Journal Title

      Kinetic and Related Models

      Volume: 6 Issue: 3 Pages: 545-556

    • DOI

      10.3934/krm.2013.6.545

    • Related Report
      2013 Research-status Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Hamiltonian bifurcation theory for a rotating flow subject to elliptic straining field2013

    • Author(s)
      Yasuhide Fukumoto, Youichi Mie
    • Journal Title

      Physica Scripta T

      Volume: 155 Pages: 014042-014042

    • DOI

      10.1088/0031-8949/2013/t155/014042

    • Related Report
      2013 Research-status Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] An example exempted from Thomson-Tait-Chetayev's theorem2013

    • Author(s)
      Abuduwaili Paerhati, Yasuhide Fukumoto
    • Journal Title

      J. Phys.Soc. Japan

      Volume: 82 Issue: 4 Pages: 430021-4

    • DOI

      10.7566/jpsj.82.043002

    • NAID

      40019628773

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Singular electromagnetic modes in an anisotropic medium2013

    • Author(s)
      Yasuhide Fukumoto, A. B. Samokhin
    • Journal Title

      Wave Motion

      Volume: 50 Issue: 3 Pages: 481-493

    • DOI

      10.1016/j.wavemoti.2012.11.001

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Effects of axial flow on the stability of a helical vortex tube2012

    • Author(s)
      Y. Hattori and Y. Fukumoto
    • Journal Title

      Physics of Fluids

      Volume: 24 Issue: 5

    • DOI

      10.1063/1.4717769

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] A unifying picture of helical and azimuthal MRI, and the universal significance of the Liu limit2012

    • Author(s)
      Oleg N. Kirillov, Frank Stefani, Yasuhide Fukumoto
    • Journal Title

      Astrophysical Journal Letters

      Volume: 756 Issue: 1 Pages: 83-83

    • DOI

      10.1088/0004-637x/756/1/83

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] Azimuthal magnetorotational instabilities to non-axisymmetric perturbations2014

    • Author(s)
      福本 康秀, Rong Zou
    • Organizer
      67th Annual Meeting of the APS Division of Fluid Dynamcs
    • Place of Presentation
      Moscone (West) Convention Center, San Francisco, USA
    • Year and Date
      2014-11-23
    • Related Report
      2014 Annual Research Report
  • [Presentation] Local and global analyses of azimuthal magnetorotational instability2014

    • Author(s)
      福本 康秀, Rong Zou
    • Organizer
      The 8th CREST-SBM International Conference on Mathematical Fluid Dynamics, Present and Future
    • Place of Presentation
      早稲田大学西早稲田キャンパス、東京
    • Year and Date
      2014-11-14
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Topological magnetohydrodynamics and its application to azimuthal magnetorotational instability2014

    • Author(s)
      福本 康秀, Rong Zou
    • Organizer
      The Seventh International Conference on Sciences and Mathematics Education in Developing Countries
    • Place of Presentation
      The University of Mandalay, Myanmar
    • Year and Date
      2014-11-07
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 方位磁気回転不安定性のモード解析2014

    • Author(s)
      福本 康秀, Rong Zou
    • Organizer
      日本流体力学会年会2014
    • Place of Presentation
      東北大学川内北キャンパス、仙台市
    • Year and Date
      2014-09-15
    • Related Report
      2014 Annual Research Report
  • [Presentation] Short-wavelength analysis of azimuthal magnetorotational instability2014

    • Author(s)
      福本 康秀, Rong Zou
    • Organizer
      日本物理学会2014年秋季大会
    • Place of Presentation
      中部大学春日井キャンパス、春日井市
    • Year and Date
      2014-09-07
    • Related Report
      2014 Annual Research Report
  • [Presentation] Azimuthal and helical magnetorotational instabilities to non-axisymmetric perturbations2014

    • Author(s)
      福本 康秀, Rong Zou
    • Organizer
      International Conference on Turbulent Mixing and Beyond Workshop: Mixing in Rapidly Changing Environment - Probing Matter at the Extremes
    • Place of Presentation
      The Abdus Salam International Centre for Theoretical Physics (ICTP) Trieste, Italy
    • Year and Date
      2014-08-05
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Three-dimensional formal stability of stratified shear flows of an ideal gas

    • Author(s)
      uhide Fukumoto, Hirofumi Sakuma
    • Organizer
      International Conference "FLUXES AND STRUCTURES IN FLUIDS"
    • Place of Presentation
      Russian State Hydrometeorological Universitym, St.-Petersburg, Russia
    • Related Report
      2013 Research-status Report
  • [Presentation] Energy, pseudomomentum and Stokes drift of inertial waves and their application to stability of a columnar vortex

    • Author(s)
      Yasuhide Fukumoto
    • Organizer
      The 6th Pacific RIM Conference on Mathematics 2013
    • Place of Presentation
      札幌コンベンションセンター
    • Related Report
      2013 Research-status Report
  • [Presentation] Motion of a vortex ring and a vortex pair in a viscous fluid

    • Author(s)
      Yasuhide Fukumoto
    • Organizer
      2nd International Retreat on Vortex Dynamics and Vorticity Aerodynamics (IRVDVA)
    • Place of Presentation
      Shanghai Sun Island Resort, Shanghai, China
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Energy, pseudomomentum and Stokes drift of inertial waves and their application to stability of a columnar vortex

    • Author(s)
      Yasuhide Fukumoto
    • Organizer
      A mini-Conference "Topological Vorticity Dynamics and Magnetohydrodynamics"
    • Place of Presentation
      Exeter University, Exeter, UK
    • Related Report
      2013 Research-status Report
  • [Presentation] Are all the topological invariants representable as cross helicities?

    • Author(s)
      Yasuhide Fukumoto
    • Organizer
      JSPS/UK Meeting "Topological Vorticity Dynamics in the Physical Sciences"
    • Place of Presentation
      Isaac Newton Institute for Mathematical Sciences, Cambridge, UK
    • Related Report
      2013 Research-status Report
  • [Presentation] 有限太さの渦の2次元相互作用

    • Author(s)
      福本 康秀
    • 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
    • Related Report
      2013 Research-status Report
  • [Presentation] 有限太さの渦の2次元相互作用

    • Author(s)
      福本 康秀
    • Organizer
      日本物理学会 2013年秋季大会
    • Place of Presentation
      徳島大学常三島キャンパス
    • Related Report
      2013 Research-status Report
  • [Presentation] MHD回転流のスペクトルと不安定性

    • Author(s)
      福本 康秀
    • 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
      核融合科学研究所, 土岐市
    • Related Report
      2013 Research-status Report
  • [Presentation] Lagrangian approach to weakly nonlinear stability of a columnar vortex

    • Author(s)
      Yasuhide Fukumoto
    • Organizer
      Workshop on Lagrangian Coherent Structures and Dynamical Systems
    • Place of Presentation
      北海道大学
    • Related Report
      2013 Research-status Report
  • [Presentation] 回転MHD流に立つ波のエネルギー

    • Author(s)
      福本 康秀, Rong Zou
    • Organizer
      日本物理学会 第69回年次大会
    • Place of Presentation
      東海大学湘南キャンパス, 平塚市
    • Related Report
      2013 Research-status Report
  • [Presentation] A unified view of topological invariants of barotropic and baroclinic fluids and their application to formal stability analysis of three-dimensional ideal gas flows

    • Author(s)
      Yasuhide Fukumoto, Hirofumi Sakuma
    • Organizer
      IUTAM symposium "Topological Fluid Dynamics"
    • Place of Presentation
      Isaac Newton Institute for Mathematical Sciences, Cambridge, UK
    • Related Report
      2012 Research-status Report
  • [Presentation] Effects of axial flow on the curvature instability of a helical vortex tube: Modal analysis

    • Author(s)
      Yuji Hattori, Yasuhide Fukumoto
    • Organizer
      23rd International Congress of Theoretical and Applied Mechanics (ICTAM 2012)
    • Place of Presentation
      China National Convention Center (CNCC), Beijing, China
    • Related Report
      2012 Research-status Report
  • [Presentation] Lagrangian and Eulerian hybrid method for weakly nonlinear stability of a rotating flow in a cylinder of elliptic cross-section

    • Author(s)
      Yasuhide Fukumoto, Youichi Mie
    • Organizer
      23rd International Congress of Theoretical and Applied Mechanics (ICTAM 2012
    • Place of Presentation
      China National Convention Center (CNCC), Beijing, China
    • Related Report
      2012 Research-status Report
  • [Presentation] 河川における降雨流出解析

    • Author(s)
      杉本 尚子, 福本 康秀
    • Organizer
      日本流体力学会年会2012
    • Place of Presentation
      高知大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Energy, Pseudomomentum and Stokes Drift of Kelvin Waves and Their Application to Weakly Nonlinear Stability of an Elliptic Vortex

    • Author(s)
      Yasuhide Fukumoto
    • Organizer
      Vortex Theory Now--Frontiers of Mathematical Physics
    • Place of Presentation
      大阪大学豊中キャンパス
    • Related Report
      2012 Research-status Report
  • [Presentation] Lagrangian and Eulerian hybrid method for symmetric breaking bifurcation of a rotating flow

    • Author(s)
      Yasuhide Fukumoto, Makoto Hirota, Youichi Mie
    • Organizer
      BIRS Workshop "Spectral Analysis, Stability and Bifurcation in Modern Nonlinear Physical Systems"
    • Place of Presentation
      Banff International Research Station for Mathematical Innovation and Discovery (BIRS), Banff, Canada
    • Related Report
      2012 Research-status Report
  • [Presentation] Lagrangian approach to weakly nonlinear interaction of Kelvin waves and a symmetry-breaking bifurcation of a rotating flow

    • Author(s)
      Yasuhide Fukumoto, Youichi Mie
    • Organizer
      IUTAM Symposium on Vortex Dynamics: Formation, Structure and Function
    • Place of Presentation
      九州大学医学部百年講堂
    • Related Report
      2012 Research-status Report
  • [Presentation] バロクリニック流体のカシミール不変量のクロス・ヘリシティ表現

    • Author(s)
      福本 康秀, 佐久間 弘文
    • Organizer
      日本物理学会 第68回年次大会
    • Place of Presentation
      広島大学東広島キャンパス
    • Related Report
      2012 Research-status Report
  • [Book] A Mathematical Approach to Research Problems of Science and Technology、Series: Mathematics for Industry Vol. 52014

    • Author(s)
      Yasuhide Fukumoto
    • Total Pages
      14
    • Publisher
      Springer
    • Related Report
      2014 Annual Research Report
  • [Book] Note on representation of wave energy of a rotating flow in terms of dispersion relation, In Nonlinear physical systems: Spectral Analysis, Stability and Bifurcations2014

    • Author(s)
      Yasuhide Fukumoto, Makoto Hirota, Youichi Mie
    • Total Pages
      15
    • Publisher
      ISTE and John Wiley& Sons
    • Related Report
      2013 Research-status Report
  • [Book] Modeling of fluid flows by nonlinear Schroedinger equation, In Mathematical Approach to Research Problems of Science and Technology -Theoretical basis and developments in mathematical modelling -2014

    • Author(s)
      Yasuhide Fukumoto
    • Total Pages
      13
    • Publisher
      Springer-Verlag
    • Related Report
      2013 Research-status Report
  • [Remarks] 九州大学研究者情報 福本康秀

    • URL

      http://hyoka.ofc.kyushu-u.ac.jp/search/details/K000449/index.html

    • Related Report
      2012 Research-status Report

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Published: 2013-05-31   Modified: 2019-07-29  

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