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Developments of the mathematical research of the system of 2D point vortices

Research Project

Project/Area Number 21654014
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionNagoya University

Principal Investigator

KIMURA Yoshifumi  名古屋大学, 多元数理科学研究科, 教授 (70169944)

Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥3,270,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2009: ¥1,200,000 (Direct Cost: ¥1,200,000)
Keywords渦運動 / 乱流 / 渦衝突 / パンルベ方程式 / ソリトン方程式 / 定常配置問題 / エルミート多項式
Research Abstract

The objective of the research project was to consider and develop the mathematical aspects of the point vortex system as a model for two dimensional vortex motions. As one of the characteristics of the model, we have studied the problem of vortex collapse, and extended the 2D self-similar collapse solution into one in three dimensions. We have also studied the statistical properties of stably stratified turbulence as a middle of 2D and 3D turbulence, and investigated the difference in the dimensionality.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (29 results)

All 2012 2011 2010 2009 Other

All Journal Article (11 results) (of which Peer Reviewed: 7 results) Presentation (17 results) Remarks (1 results)

  • [Journal Article] Energy spectra of stably stratified turbulence2012

    • Author(s)
      Y. Kimura & J. R. Herring
    • Journal Title

      Journal of Fluid Mech.

      Volume: 698 Pages: 19-50

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Predictability error growth of turbulent flows2012

    • Author(s)
      Ye Zhou, C. E. Leith, J. R. Herring & Y. Kimura
    • Journal Title

      Mehcanics Research Communications

      Volume: 39 Pages: 15-17

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Energy spectra of stably stratified turbulence2012

    • Author(s)
      Y.Kimura, J.R.Herring
    • Journal Title

      Journal of Fluid Mehcanics

      Volume: (accepted)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Spectra and Distribution Funciton of Stably Stratified Turbulence2010

    • Author(s)
      J. R. Herring & Y. Kimura
    • Journal Title

      Proceedings of the IUTAM Symposium on "Turbulence in the Atmosphere and Oceans"

      Pages: 143-154

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Self-similar collapse of 2D and 3D vortex filament models2010

    • Author(s)
      Y. Kimura
    • Journal Title

      Theoretical and Computational Fluid Dynamcis

      Volume: 24 Pages: 389-394

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Spectra and Distribution Funciton of Stably Stratified Turbulence2010

    • Author(s)
      J.R.Herring, Y.Kimura
    • Journal Title

      Proceedings of the IUTAM Symposium on "Turbulence in the Atmosphere and Oceans"

      Pages: 143-154

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Self-similar collapse of 2D and 3D vortex filament models2010

    • Author(s)
      Yoshifumi Kimura
    • Journal Title

      Theoretical and Computational Fluid Dynamcis 24

      Pages: 389-394

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 2次元乱流における勾配の発展2009

    • Author(s)
      木村芳文
    • Journal Title

      第58回理論応用力学講演会講演論文集

      Pages: 527-528

    • NAID

      130004604347

    • Related Report
      2011 Final Research Report
  • [Journal Article] ナヴィエ・ストークス方程式と流体の運動2009

    • Author(s)
      木村芳文
    • Journal Title

      数理科学

      Pages: 35-39

    • Related Report
      2011 Final Research Report
  • [Journal Article] 2次元乱流における勾配の発展2009

    • Author(s)
      木村芳文
    • Journal Title

      第58回理論応用講演会講演論文集NCTAM2009

      Pages: 527-528

    • NAID

      130004604347

    • Related Report
      2009 Annual Research Report
  • [Journal Article] ナヴィエ・ストークス方程式と流体の運動2009

    • Author(s)
      木村芳文
    • Journal Title

      数理科学 6月号

      Pages: 35-39

    • Related Report
      2009 Annual Research Report
  • [Presentation] 地球流体乱流の数値解析2012

    • Author(s)
      木村芳文
    • Organizer
      平成23年度名古屋大学HPC計算科学連携研究プロジェクト成果報告シンポジウム
    • Place of Presentation
      名古屋大学情報基盤センター
    • Year and Date
      2012-05-09
    • Related Report
      2011 Final Research Report
  • [Presentation] Energy transfer for stably stratified turbulence2011

    • Author(s)
      Y. Kimura & J. R. Herring
    • Organizer
      64th Annual Meeting of APS/DFD
    • Place of Presentation
      Baltimore, Meryland, USA
    • Year and Date
      2011-11-22
    • Related Report
      2011 Final Research Report
  • [Presentation] Energy transfer for stably stratified turbulence2011

    • Author(s)
      Y.Kimura, J.R.Herring
    • Organizer
      American Physical Society Division of Fluid Dynamics. 64th Annual Meeting
    • Place of Presentation
      Baltimore, MD, USA
    • Year and Date
      2011-11-22
    • Related Report
      2011 Annual Research Report
  • [Presentation] Herring, Energy spectra of stably stratified turbulence2011

    • Author(s)
      Y. Kimura & J. R.
    • Organizer
      6th AIAA Theoretical Fluid Mechanics Conference
    • Place of Presentation
      Hawaii Convention Center, Honolulu, Hawaii
    • Year and Date
      2011-06-28
    • Related Report
      2011 Final Research Report
  • [Presentation] 地球流体乱流の数値解析2011

    • Author(s)
      木村芳文
    • Organizer
      平成22年度名古屋大学HPC計算科学連携研究プロジェクト成果報告シンポジウム
    • Place of Presentation
      名古屋大学情報基盤センター
    • Year and Date
      2011-05-11
    • Related Report
      2011 Final Research Report
  • [Presentation] Point vortex motion and complex-time singularities2011

    • Author(s)
      Y. Kimura
    • Organizer
      48th Annual Technical Conference of Society of Engineering Sciences
    • Place of Presentation
      Northwestern University, Evanston, Illinois USA
    • Related Report
      2011 Final Research Report
  • [Presentation] Energy Spectra of Stably Stratified Turbulence2010

    • Author(s)
      Kimura & J. R. Herring
    • Organizer
      62ndAnnual Meeting of APS/DFD
    • Place of Presentation
      Long Beach, California
    • Year and Date
      2010-11-23
    • Related Report
      2011 Final Research Report
  • [Presentation] Energy Spectra of Stably Stratified Turbulence2010

    • Author(s)
      Y.Kimura, J.R.Herring
    • Organizer
      63^<nd> Annual Meeting of APS/DFD
    • Place of Presentation
      Long Beach, CA, USA
    • Year and Date
      2010-11-23
    • Related Report
      2010 Annual Research Report
  • [Presentation] 成層乱流におけるエネルギースペクトル2010

    • Author(s)
      木村芳文
    • Organizer
      第2回名古屋大学計算科学セミナー
    • Place of Presentation
      名古屋大学情報基盤センター
    • Year and Date
      2010-11-10
    • Related Report
      2011 Final Research Report
  • [Presentation] Structure Formation in Stratified Turbulence2010

    • Author(s)
      Y. Kimura
    • Organizer
      Workshop on"Topics in rotating Stratified Turbulence"
    • Place of Presentation
      National Center for Atmospheric Research Atmospheric Research
    • Year and Date
      2010-08-02
    • Related Report
      2011 Final Research Report
  • [Presentation] Structure Formation in Stratified Turbulence2010

    • Author(s)
      Y.Kimura
    • Organizer
      NCAR GTP Workshop "Topics in Rotating Stratified Turbulence"
    • Place of Presentation
      Boulder, CO, USA
    • Year and Date
      2010-08-02
    • Related Report
      2010 Annual Research Report
  • [Presentation] Energy Spectra of Stably Stratified Turbulence2009

    • Author(s)
      Y. Kimura & J. R. Herring
    • Organizer
      62nd Annual Meeting of APS/DFD
    • Place of Presentation
      Minneapolis, Minesota
    • Year and Date
      2009-11-24
    • Related Report
      2011 Final Research Report
  • [Presentation] Energy Spectra of Stably Stratified Turbulence2009

    • Author(s)
      Y.Kimura, J.R.Herring
    • Organizer
      62^<nd> Annual Meeting of APS/DFD
    • Place of Presentation
      Minneapolis, MN, USA
    • Year and Date
      2009-11-24
    • Related Report
      2009 Annual Research Report
  • [Presentation] Energy Spectra of Stably Stratified Turbulence2009

    • Author(s)
      Y. Kimura & J. R. Herring
    • Organizer
      EUROMECH/European Turbulence Conference
    • Place of Presentation
      Marburg, Germany
    • Year and Date
      2009-09-09
    • Related Report
      2011 Final Research Report
  • [Presentation] Energy Spectra of Stably Stratified Turbulence32009

    • Author(s)
      Y.Kimura, J.R.Herring
    • Organizer
      EUROMECH/ European Turbulence Conference 12
    • Place of Presentation
      Marburg, Germany
    • Year and Date
      2009-09-09
    • Related Report
      2009 Annual Research Report
  • [Presentation] 2次元乱流における勾配の発展2009

    • Author(s)
      木村芳文
    • Organizer
      第58回理論応用力学講演会
    • Place of Presentation
      日本学術会議
    • Year and Date
      2009-06-11
    • Related Report
      2011 Final Research Report
  • [Presentation] 2次元乱流における勾配の発展2009

    • Author(s)
      木村芳文
    • Organizer
      第58回理論応用力学連合講演会
    • Place of Presentation
      日本学術会議
    • Year and Date
      2009-06-11
    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • URL

      http://www.math.nagoya-u.ac.jp/.kimura

    • Related Report
      2011 Final Research Report

URL: 

Published: 2009-04-01   Modified: 2016-04-21  

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