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Numerical studies on the regularity properties of the fluid dynamical equations

Research Project

Project/Area Number 16540103
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

OHKITANI Koji  KYOTO UNIVERSITY, Research Institute for Mathematical Sciences, Associate Professor, 数理解析研究所, 助教授 (70211787)

Project Period (FY) 2004 – 2005
Project Status Completed (Fiscal Year 2005)
Budget Amount *help
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2005: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2004: ¥2,300,000 (Direct Cost: ¥2,300,000)
KeywordsNavier-Stokes equations / regularity of solutions / megneto-hydrodynamics / Euler-Lagrange formalism / magnetic reconnection / 乱流 / オイラーラグランジュ定式化 / 特異点 / 特異摂動
Research Abstract

In order to clarify fast reconnection phenomena in magnetohydrodynamics, we performed numerical experiments on the basis of the Eulerian-Lagrangian formalism.
In 2004, we extended the Eulerian-Lagrangian formalism for the Navier-Stokes equations to magnetohydrodynamical equations. There are two Weber transforms corresponding to conservation of two kinds of helicities. For the case of unit Prandtl number, we have shown that one connection tensor is sufficient to reformulate the magnetohydrodynamical system. By using it, direct numerical simulations of 2D Orszag-Tang were done and it was found that correspondence between diffusive labels A and spatial positions x becomes non-invertible (resetting phenomena). We showed that it is related with magnetic reconnection. Furthermore, numerical simulations were done with initial conditions of 3D generalized O-T vortices and orthogonally offset magnetic flux tubes. Resetting phenomena also take place for these cases.
In 2005, more practical numerical simulations with twisted magnetic flux tubes were performed. Parallel/anti-parallel flux tubes and linked flux rings were used as initial conditions. It was confirmed that magnetic reconnections are associated with resetting phenomena. The time scales defined by the resetting intervals are smaller that those estimated by global characteristics and are closer to time-scales of fast reconnections. In this sense we showed that this method can quantify fast reconnections. We also found by visualizations that a spatial correspondence between reconnecting magnetic fields and the resetting phenomena.
A regularity criterion for ideal magnetohydrodynamical equations is known to be given in terms of the vorticity and the current density fields A simple argument respecting helicity invariants shows that if the magnetic field is smooth, then so is the velocity field, thereby suggesting some room for improving the above criterion.

Report

(3 results)
  • 2005 Annual Research Report   Final Research Report Summary
  • 2004 Annual Research Report
  • Research Products

    (16 results)

All 2006 2005

All Journal Article (16 results)

  • [Journal Article] 理想磁気流体力学方程式の解の正則性条件について2006

    • Author(s)
      大木谷 耕司
    • Journal Title

      第55回理論応用力学講演会 講演論文集

      Pages: 459-460

    • NAID

      130005020378

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Annual Research Report 2005 Final Research Report Summary
  • [Journal Article] A note on regularity conditions on ideal MHD equations2006

    • Author(s)
      K.Ohkitani
    • Journal Title

      J. Plasma Phys. (to appear)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Invariants, Diffusion and Topological Change2006

    • Author(s)
      P.Constantin, K.Ohkitani
    • Journal Title

      Proceedings for the IUTAM symposium on Elementary vortices and coherent structures (to appear)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Annual Research Report 2005 Final Research Report Summary
  • [Journal Article] On regularity conditions on ideal magnetohydrodynamical equations2006

    • Author(s)
      Ohkitani, Koji
    • Journal Title

      Proceedings of NCTAM 2006

      Pages: 459-460

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] A note on regularity conditions on ideal MHD equations2006

    • Author(s)
      Ohkitani, Koji
    • Journal Title

      J.Plasma Physics (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Invariants, Diffusion and Topological Change2006

    • Author(s)
      Constantin, Peter, Ohkitani, Koji
    • Journal Title

      Proceedings for the IUTAM symposium on Elementary vortices and coherent structures (to appear)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] A note on regularity conditions on ideal MHD equations2006

    • Author(s)
      K.Ohkitani
    • Journal Title

      J.Plasma Phys. (to appear)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Euler-Lagrange定式化による磁気流体力学方程式の解析2005

    • Author(s)
      大木谷耕司, P.Constantin
    • Journal Title

      京都大学数理解析研究所講究録 1434

      Pages: 116-129

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Annual Research Report 2005 Final Research Report Summary
  • [Journal Article] Burgers-Donaldson-Sullivan の軸対称流のクラス-定常解と非定常解の爆発問題-2005

    • Author(s)
      大木谷 耕司
    • Journal Title

      九州大学応用力学研究所 研究集会報告 17ME-S3

      Pages: 87-97

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] On the Role of the Convection Term in the Equations of Motion of Incompressible Fluid2005

    • Author(s)
      H.Okamoto, K.Ohkitani
    • Journal Title

      J. Phys. Soc. Jpn. 74

      Pages: 2737-2742

    • NAID

      110002250644

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Eulerian-Lagrangian analyses of MHD equations2005

    • Author(s)
      Ohkitani, Koji, Constantin, Peter
    • Journal Title

      RIMS, Kokyuroku 1434

      Pages: 116-129

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] On the Role of the Convection Term in the Equations of Motion of Incompressible Fluid2005

    • Author(s)
      Okamoto, Hisashi, Ohkitani, Koji
    • Journal Title

      J.Phys.Soc.Jpn. 74

      Pages: 2737-2742

    • NAID

      110002250644

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Burgers-Donaldson-Sullivan class of axisymmetric flows -stationary solutions and vlow-up of nonstationary solutions-2005

    • Author(s)
      Ohkitani, Koji
    • Journal Title

      Reports of RIAM Symposium 17ME-S3

      Pages: 87-97

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Burgers-Donaldson-Sullivanの軸対称流のクラス-定常解と非定常解の爆発問題-2005

    • Author(s)
      大木谷 耕司
    • Journal Title

      九州大学応用力学研究所 研究集会報告 17ME-S3

      Pages: 87-97

    • Related Report
      2005 Annual Research Report
  • [Journal Article] On the Role of the Convection Term in the Equations of Motion of In-compressible Fluid2005

    • Author(s)
      H.Okamoto, K.Ohkitani
    • Journal Title

      J.Phys.Soc.Jpn. 74

      Pages: 2737-2742

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Euler-Lagrange定式化による磁気流体力学方程式の解析2005

    • Author(s)
      K.Ohkitani, P.Constantin
    • Journal Title

      数理解析研究所講究録 乱流現象と力学系的縮約 (in press)

    • Related Report
      2004 Annual Research Report

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Published: 2004-04-01   Modified: 2016-04-21  

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