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1994 Fiscal Year Final Research Report Summary

DYNAMICS OF SPATIALLY PERIODIC FLOWS

Research Project

Project/Area Number 05650066
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field Engineering fundamentals
Research InstitutionUNIVERSITY OF OSAKA PREFECTURE

Principal Investigator

MURAKAMI Youichi  UNIVERSITY OF OSAKA PREFECTURE,COLLEGE OF ENGINEERING,ASSOCIATE PROFESSOR, 工学部, 助教授 (90192773)

Co-Investigator(Kenkyū-buntansha) GOTOH Kanefusa  UNIVERSITY OF OSAKA PREFECTURE,COLLEGE OF ENGINEERING,PRINCIPAL, 校長 (40027363)
TAJIRI Masayoshi  UNIVERSITY OF OSAKA PREFECTURE,COLLEGE OF ENGINEERING,PROFESSOR, 工学部, 教授 (10081423)
Project Period (FY) 1993 – 1994
Keywordslinear stability / nonlinear stability / three-dimensional instability / secondary flow / vortex merging / periodic flow / cell flow / bifurcation
Research Abstract

(a) It is found that the large-scale mode with the negative eddy viscosity effect or the periodic mode whose periodicity is the same as the main glow gives the critil linear Reynolds number of the rectangular cell flow. The vortex merging which was observed in the experiments by Tabelin et al (1990) is explained qualitatively by superposition of the periodic mode on the main flow. (Phys.Fluids, Vol.7(No.2), pp-302-306(1995).) The truncated nolinear ODE system is derived to show that a steady secondary flow exists in the supercritical regime. (RIMS 1995.1.)
(b) In the contrast with the parallel flows, the primary instability due to the three-dimensional disturbance may take place in the non-paralled flows. We have presented explicit examples that the critical Reynolds number is actually determined by the three-dimensional disturbances. The rectangular cell flows (to appear in Plys.Rev.E(1995)) and the triangular ones with some parameter ranges belong to these cases.
(c) On the nonlinear stability of the quasi-two-dimensional flows. The effect of the bottom-friction in the thin layr is approximatety regarded as the Rayleigh friction proportional to the horizontal velocity in the two-dimesional NS equation. This procedure is often called the quasi-two-dimensional approximation. We have shown that the critical Reynolds number by the linear stability as well as the nonlinear stability by the energy method increases linearly with increasing the coefficient of the Rayleigh friction. (IUTAM Symposium Potsdam, NY,USA July 26-31.1993.in preparation.)

  • Research Products

    (12 results)

All Other

All Publications (12 results)

  • [Publications] K.Gotoh: "Instability of spatially periodic flow to three-dimensional disturbances" Fluid Dynamics Res.12. 271-279 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 村上洋一: "底の抵抗を持つコルモゴロフ流のエネルギー法による非線形安定性" 京都大学数理解析研究所講究録. 852. 52-66 (1993)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 村上洋一: "準2次元流の安定性" ながれ. 13. 115-123 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y.Murakami: "Stability of a nonparallel periodic flow with bottom friction" Nonlinear Instability of Nonparallel Flows IUTAM Symposium Potsdam,NY,USA July 26-31.1993. 320-329 (1994)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Gotoh: "Large-scale and periodic modes of rectangular cell flow" Phys.Fluids. 7. 302-306 (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Y.Murakami: "Three-dimensional negative eddy viscosity effect on the onset of instability in some planar flows(出版予定 No.4)" Phys.Rev.E. 51. (1995)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Gotoh, Y.Murakami and M.Murakami: "Instability of spatially periodic flow to three-dimensional disturbances" Fluid Dynamics Res.12. 271-279 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y.Murakami, H.Fukuta and K.Gotoh: "Nonlinear stability of the Kolmogorov flow with the the bottom-friction using the energy method" RIMS Publication. 852. 52-66 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y.Murakami: "Stability of quasi-two-dimensional flows" Nagare. 13. 115-123 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y.Murakami H.Fukuta and K.Gotoh: "Stability of a nonparallel periodic flow with bottom friction" Nonlinear Instability of Nonparallel Flows IUTAM Symposium Potsdam NY,USA. 320-329 (1994)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Gotoh, Y.Murakami and N.Matsuda: "Large-scale and periodic modes of rectangular cell flow" Phys.Fluids. 7. 302-306 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Y.Murakami, M.Murakami and K.Gotoh: "Three-dimensional negative eddy viscosity effect on the onset of instability in some planar flows" Phys.Rev.E. 51(to be published in NO.4). (1995)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 1996-04-15  

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