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2012 Fiscal Year Final Research Report

Towards a mathematical theory of fluid turbulence via singular vortex dynamics

Research Project

  • PDF
Project/Area Number 21340017
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionHokkaido University

Principal Investigator

SAKAJO Takashi  北海道大学, 大学院・理学研究院, 教授 (10303603)

Co-Investigator(Renkei-kenkyūsha) NAWA Hayato  大阪大学, 大学院・基礎工学研究科, 教授 (90218066)
MATSUMOTO Takeshi  京都大学, 大学院・理学研究科, 助教 (20346076)
AKAHORI Takahumi  静岡大学, 大学院・数理システム工学科, 准教授 (90437187)
Project Period (FY) 2009 – 2012
Keywords乱流 / 点渦 / 渦層 / 散逸的弱解 / オイラー方程式 / オイラーα方程式
Research Abstract

It has been pointed out that dissipative weak solutions of the hydrodynamic equations plays an important role in understand the statistical theory of turbulence. But the existence of such a singular solution has not yet proven and its dynamical property is uncertain. In the present project, we successfully obtain a self-similar collapsing solution of α point vortex system. This is a dissipative weak solution of 2D Euler equation, which acquires one of the important properties observed in 2D turbulence.

  • Research Products

    (16 results)

All 2013 2012 2011 2010 2009

All Journal Article (7 results) (of which Peer Reviewed: 4 results) Presentation (9 results)

  • [Journal Article] 二次元Euler-α方程式の弱解の特異極限解とその性質2013

    • Author(s)
      坂上貴之
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1823巻 Pages: 54-71

  • [Journal Article] Anomalous enstrophy dissipation via the self-similar triple collapse of the Euler-alpha point vortices2013

    • Author(s)
      T. Sakajo
    • Journal Title

      Nankai Series in Applied Mathematics and Theoretical Physics

      Volume: vol.10 Pages: 155-169

  • [Journal Article] Instantaneous energy and enstrophy variations in Euler-alpha point vortices via triple collapse2012

    • Author(s)
      T. Sakajo
    • Journal Title

      Journal of Fluid Mechanics

      Volume: vol.702 Pages: 188-214

    • DOI

      doi:10.1017/jfm.2012.172

    • Peer Reviewed
  • [Journal Article] Sakajo, Corrigendum: Oscillatory damping in long-time evolution of the surface quasi-geostrphic equations with generalized viscosity2012

    • Author(s)
      K. Ohkitani and T
    • Journal Title

      a numerical study, Nonlinearity

      Volume: vol. 25 Pages: 2181-2202

    • DOI

      doi:10.1088/0951-7715/25/7/2181

    • Peer Reviewed
  • [Journal Article] Sakajo, Oscillatory damping in long-time evolution of the surface quasi-geostrphic equations with generalized viscosity2010

    • Author(s)
      K. Ohkitani and T
    • Journal Title

      a numerical study, Nonlinearity

      Volume: vol. 23 Pages: 3029-3051

    • Peer Reviewed
  • [Journal Article] 球面点渦相互作用の高速Tree-codeアルゴリズム2009

    • Author(s)
      坂上貴之
    • Journal Title

      京都大学数理解析研究所講究録「オイラー方程式の数理:渦運動150年」

      Volume: 1642巻 Pages: 184-196

  • [Journal Article] From generation to chaotic motion of a ring configuration of vortex structure on a sphere2009

    • Author(s)
      T. Sakajo
    • Journal Title

      Theor. Comput. Fluid Dyn.

      Volume: vol,24 Pages: 151-156

    • Peer Reviewed
  • [Presentation] Euler-α方程式の点渦衝突によるエンストロフィー散逸2012

    • Author(s)
      坂上貴之
    • Organizer
      京都大学数理解析研究所共同研究集会「流体と気体の数学解析」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2012-07-06
  • [Presentation] 二次元Euler-α流れの点渦衝突と特異エンストロフィー散逸2012

    • Author(s)
      坂上貴之
    • Organizer
      北海道大学複雑系セミナー
    • Place of Presentation
      北海道大学
    • Year and Date
      2012-06-11
  • [Presentation] α点渦系の三体衝突によるエンストロフィー散逸2012

    • Author(s)
      坂上貴之
    • Organizer
      日本数学会年会
    • Place of Presentation
      東京理科大学
    • Year and Date
      2012-03-28
  • [Presentation] Enstrophy dissipation in Euler alpha point vortices via triple collapse2012

    • Author(s)
      坂上貴之
    • Organizer
      北海道大学北東解析研究集会
    • Place of Presentation
      北海道大学
    • Year and Date
      2012-02-17
  • [Presentation] 二次元Euler-α方程式の弱解の特異極限解とその性質について2011

    • Author(s)
      坂上貴之
    • Organizer
      京都大学数理解析研究所共同研究「偏微分方程式の背後にある確率過程と解の族が示す統計力学的な現象の解析」
    • Place of Presentation
      京都大学数理奇跡研究所.
    • Year and Date
      2011-12-20
  • [Presentation] Enstrophy dissipation in Euler-alpha point vortices via triple collapse2011

    • Author(s)
      T. Sakajo
    • Organizer
      Emerging Topics on Differential Equations and their Applications- Sino-Japan Conference of Young Mathematicians
    • Place of Presentation
      Nankai University,China, Invited speaker.
    • Year and Date
      2011-12-07
  • [Presentation] 三点渦衝突によるハミルトンエネルギーの変動2011

    • Author(s)
      坂上貴之
    • Organizer
      大阪大学大学院基礎工学研究科流体科学セミナー
    • Place of Presentation
      大阪大学
    • Year and Date
      2011-08-29
  • [Presentation] Energy variations of a point-vortex dynamics via triple collapse2011

    • Author(s)
      坂上貴之
    • Organizer
      東北大学大学院情報科学研究科仙台シンポジウム
    • Place of Presentation
      東北大学
    • Year and Date
      2011-08-17
  • [Presentation] 流体方程式の特異点形成に関する数学的・数値的研究2009

    • Author(s)
      坂上貴之
    • Organizer
      東京工業大学グローバルCOE計算世界観の深化と展開シンポジウム
    • Place of Presentation
      東京工業大学
    • Year and Date
      2009-12-31

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Published: 2014-08-29  

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