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Studies of Turbulence as a Nonlinear Science

Research Project

Project/Area Number 08404006
Research Category

Grant-in-Aid for Scientific Research (A)

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

Principal Investigator

KIMURA Yoshifumi  Nagoya University, Graduate School of Mathematics, Professor, 大学院・多元数理科学研究科, 教授 (70169944)

Co-Investigator(Kenkyū-buntansha) NAWA Hayato  Graduate School of Mathematics, Associate Professor, 大学院・多元数理科学研究科, 助教授 (90218066)
OBATA Nobuaki  Graduate School of Mathematics, Associate Professor, 大学院・多元数理科学研究科, 助教授 (10169360)
OHTA Hiroshi  Graduate School of Mathematics, Associate Professor, 大学院・多元数理科学研究科, 助教授 (50223839)
KIDA Shigeo  National Institute for Fusion Science, Professor, 核融合科学研究所, 教授 (70093234)
NAITO Hisashi  Graduate School of Mathematics, Associate Professor, 大学院・多元数理科学研究科, 助教授 (40211411)
熊谷 隆  名古屋大学, 大学院・多元数理化学研究科, 助教授 (90234509)
金田 行雄  名古屋大学, 大学院・多元数理科学研究科, 教授 (10107691)
長谷川 勝夫  名古屋大学, 大学院・多元数理科学研究科, 教授 (70004463)
四方 義啓  名古屋大学, 大学院・多元数理科学研究科, 教授 (50028114)
Project Period (FY) 1996 – 1999
Project Status Completed (Fiscal Year 1999)
Budget Amount *help
¥20,000,000 (Direct Cost: ¥20,000,000)
Fiscal Year 1999: ¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 1998: ¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 1997: ¥4,600,000 (Direct Cost: ¥4,600,000)
Fiscal Year 1996: ¥9,800,000 (Direct Cost: ¥9,800,000)
Keywordsturbulence / fluid mechanics / vortex motion / diffusion / geophysical flows / Navier-Strokes equations / Hamiltonian dynamics / Group theory / 自己相似性 / 特異点 / エネルギーカスケード / 渦度 / 密度成層 / ランダム現象 / シンプレクティック積分 / ランダムネス
Research Abstract

(1) Vortex Formation and Diffusion in Rotating Stratified Turbulence : Rotation and Stratification are two fundamental physical mechanisms in atmospheres and oceans. Studies of vortex formation and diffusion in such flows play a vital role in improving our understanding of geophysical and astrophysical turbulent phenomena. We examine results of direct numerical simulation of the Navier-Stokes equations with the effects of rotation and stably stratification. Both rotation and stratifications tend to make flows two dimensional (or two components), but we verified that they work in different ways in generating vertical structures. As for diffusion, we observed that stratification suppresses the particle migration in the vertical direction and so does rotation, and that the linear growth in time for single particle dispersion persists in the horizontal direction under strong rotation and/or stratification.
(2) Vortex Motion on Surfaces with Constant Curvature : Vortex motion on two- dimensi … More onal Riemannian surfaces with constant curvature is formulated. By way of the stereographic projection, the relation and difference between the vortex motion on a sphere and on a hyperbolic plane can be clearly analyzed. The Hamiltonian formalism is presented for the motion of point vortices on a sphere and a hyperbolic plane. As an example of analytic solutions, the motion of a vortex pair (dipole) is considered. It is shown that a dipole draws a geodesic curve as its trajectory on both surfaces.
(3) Evolution of decaying two-dimensional turbulence and self similarity : We examine the consequences of self-similarity of the energy spectrum of two-dimensional decaying turbulence, and conclude that traditional closures are consistent with this principle only if the regions of space contributing significantly to energy and enstrophy transfer comprise an ever diminishing region of space as time proceeds from the initial time of Gaussian chaos.
(4) Axisymmetrization process for a non-uniform elliptic vortex : The axisymmetrization of a 2D non-uniform elliptic vortex is studied in terms of the growth of palinstrophy, the squared of the vorticity gradient. First, it is pointed out that the equation for the palinstrophy growth, if written in terms of the strain rate tensor, has a similar form to that of enstrophy growth in 3D - the vortex-stretching equation. Then palinstrophy production is analyzed particularly for non-uniform elliptic vortices. It is shown analytically and verified numerically that a non-uniform elliptic vortex in general has quadrupole structure for the palinstrophy production, and that in the positive production regions, vortex filaments are ejected following the gradient enhancement process for vorticity.
(5) Pressure distribution for random Gaussian Velocities : Pressure distributions for random Gaussian velocities are studied both analytically and numerically. Arguments based on rotation symmetry allow to clarify the analytical structure of the characteristic function of pressure and to find the power of all its singularities, which in turn, allows to obtain the exact form of the PDF tail, including both exponent and power pre-exponent factors. For the narrow velocity spectrum (velocity restricted to a shell in k-space), the characteristic function is found explicitly, generating pressure cummulants of all orders. Less

Report

(5 results)
  • 1999 Annual Research Report   Final Research Report Summary
  • 1998 Annual Research Report
  • 1997 Annual Research Report
  • 1996 Annual Research Report
  • Research Products

    (22 results)

All Other

All Publications (22 results)

  • [Publications] Y. Kimura and J. R. Herring: "Diffusion in stably stratified turbulence"J. Fluid Mech.. 328. 253-269 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Y. Kimura: "Vortex Motion on surfaces with constant curvature"Proc. R. Soc. London Ser A. 455. 245-259 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Y. Kimura and J. R. Herring: "Particle dispersion in rotating stratified turbulence"Proc. Fluid Engng Div. Summer Meeting. (in press). (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] J. R. Herring, Y. Kimura and J. Chasnoy: "Evolution of decaying two-dimensional turbulence and self-similarity"Trends in Mathematics. 175-183 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Y. Kimura and O. Metais: "Vortex Formation and diffusion in rotating stratified turbulence"Development in Geophysical Turbulence. (in press). (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Y. Kimura and J. R. Herring: "Gradient enhancement and filament ejection for non-uniform elliptic vortex in 2d turbulence"J. Fluid Mech.. (in press).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Y. Kimura and J. R. Herring: "Diffusion in stably stratified turbulence"J Fluid Mech. 328. 253-269 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Y. Kimura: "Vortex motion on surfaces with constant curvature"Proc. R. Soc. London Ser A. 455. 245-259 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Y. Kimura and J. R. Herring: "Particle dispersion in rotating stratified turbulence, Proceedings of Fluid Engineering Division Summer Meeting"San Francisco. (in press). (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] J. R. Herring, Y. Kimura and J. Chasnov: "Evolution of decaying two-dimensional turbulence and similarity Trends in Mathematics"Birkhauser Verlag. 175-183 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Y. Kimura and O. Metais: "Vortex formation and diffusion in rotation stratified turbulence (R. M. Kerr & Y. Kimura ed.) Proceedings of the IUTAM/IUGG symposium on "Developments in Geophysical Turbulence""Kluwer Academic Publisher. submitted. (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Y. Kimura and J. R. Herring: "Gradient enhancement and filament ejection for non-uniform elliptic vortex in 2d turbulence"J. Fluid Mech. submitted. (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] J. R. Herring,Y. Kimura and J. Chasnoy: "Evolution of decaying two-dimensional turbulence and self-similarity"Trends in Mathematics. 175-183 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Y. Kimura and J. R. Herring: "Gradient enhancement and filament ejection for non-uniform elliptic vortex in 2d turbulence"J. Fluid Mech.. (in press).

    • Related Report
      1999 Annual Research Report
  • [Publications] Y.Kimura: "Vortex motion on surfaces with constant curvature" Proc.R.Soc.London A. 455. 245-259 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] Y.Kimura & J.R.Herring: "Particle dispersion in rotating stratified turbulence" Proc.Fluid Eng.Div.Summer Meeting 1999. (in press).

    • Related Report
      1998 Annual Research Report
  • [Publications] Yoshifumi Kimura: "Vortex motion on surfaces with constant curvature" Proc.of Royal Soc.of London,Ser.A. (in press).

    • Related Report
      1997 Annual Research Report
  • [Publications] Takashi Kumagai: "Short time asymptotic behavior and large deviations for Brownian motion on some affine nested fractals" Publ.RIMS.Kyoto Univ.33-2. 223-240 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] Hayato Nawa: "Limiting profiles of blow-up solutions of the nonlinear Schrodinger equation with critical power nonlinearity" Prod.Japan Acad.(to appear).

    • Related Report
      1997 Annual Research Report
  • [Publications] 木村芳文: "Diffusion in stably stratified turbulence" Journal of Fluid Mechanics. 328. 253-269 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 尾畑伸明: "White noise approach to quantum martingales" in ″Probability theory and mathematical statistics″. 379-386 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] 熊谷隆: "Heat kernel estimates and homogenization for asymptotically lower dimensional processes on some nested fractals" Potential Analysis. (印刷中).

    • Related Report
      1996 Annual Research Report

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Published: 1996-04-01   Modified: 2016-04-21  

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