1994 Fiscal Year Final Research Report Summary
DYNAMICS OF SPATIALLY PERIODIC FLOWS
| Project/Area Number |
05650066
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
Engineering fundamentals
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| Research Institution | UNIVERSITY OF OSAKA PREFECTURE |
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Principal Investigator |
MURAKAMI Youichi UNIVERSITY OF OSAKA PREFECTURE,COLLEGE OF ENGINEERING,ASSOCIATE PROFESSOR, 工学部, 助教授 (90192773)
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| 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)
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| Project Period (FY) |
1993 – 1994
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| Keywords | linear stability / nonlinear stability / three-dimensional instability / secondary flow / vortex merging / periodic flow / cell flow / bifurcation |
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| 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.)
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