| Project/Area Number |
61540279
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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 |
物理学一般
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| Research Institution | Kyoto University |
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Principal Investigator |
KIDA Shigeo Research Institure for Mathematical Sciences, Kyoto University, 数理解析研究所, 助教授 (70093234)
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| Co-Investigator(Kenkyū-buntansha) |
YAMADA Michio Disaster Prevention Research Institute, Kyoto University, 防災研究所, 助教授 (90166736)
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| Project Period (FY) |
1986 – 1987
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| Project Status |
Completed (Fiscal Year 1987)
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| Budget Amount *help |
¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 1987: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1986: ¥1,000,000 (Direct Cost: ¥1,000,000)
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| Keywords | Turbulence / Numerical Simulation / High-Symmetry / Intermittency / MHD Turbulence / Dynamo / Reconnection / カオス / 特異性 |
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| Research Abstract |
The small-scale structure of turbulence was investigated by solving the Navier-Stokes equation numerically. The high-symmetry was imposed on the velocity field to save the computation time and the memory capacity. The following five subjects were mainly investigated.
(1) Small-scale structure of turbulence We realized the fully developed turbulence with the micro-scale Reynolds number <similar or equal> 200. The Kolmogorov similarity was confirmed to hold in the energy spectrum. The Kolmogorov power law of the energy spectrum in the inertial range was observed with Kolmogorov constant 1.8. The probability density distribution of the velocity derivative and the energy dissipation rate, which characterize the intermittent structure of turbulence, were found to have nuiversal forms independent of the large-scale motive c
(2) Energy decay law The power law of energy, which had been observed by experiments and preficted by statistical theories of turbulence, was confirmed quantitatively for the first time as numerical simulation.
(3) Chaos in a Navier-Stokes flow We found that the velocity field which is excited by a steady external force undergoes the following series of transitions as the Reynolds number is increased: Steady -> simply periodic -> doubly periodic ->triply periodic -> chaotic motions.
(4) MHD trubulence We found that the dynamo effect, by which the kinetic energy is converted into the magnetic energy, occurs when the Reynolds number exceeds a critical value. The kinetic and magnetic energy spectra obey power laws in the statistically equilibrium state.
(5) Reconnection of vortex tubes In order to investigate the dynamics of thehelicity, which is one of the important quantities in the theory of turbulence we made a numerical simulation of a knotted vortex tube. The helicity was found to be conserved in the inviscid limit. A new phenomenon called BRIDGING was observed in the process of vortex reconnection.
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