1998 Fiscal Year Final Research Report Summary
Numerical simulations of nonlinear dynamical systems with large degree of freedom and turbulence
| Project/Area Number |
09640487
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
物理学一般
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| Research Institution | KYOTO UNIVERSITY (1998)
Kyushu University (1997) |
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Principal Investigator |
FUJISAKA Hirokazu Kyoto University, Graguate School of Informatics, Professor, 情報学研究科, 教授 (40156849)
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| Co-Investigator(Kenkyū-buntansha) |
IWAYAMA Takahiro Faculty of Science, Associate Professor, 理学部, 助教授 (10284598)
YAMADA Tomoji Kyushu Institute of Technology, Faculty of Engineering, Professor, 工学部, 教授 (80037928)
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| Project Period (FY) |
1997 – 1998
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| Keywords | two-dimensional turbulence / Charney-Hasegawa-Mima equation / drift wave turbulence / decay turbulence / nonlinear media / coupled map / on-off intermittency / on-off diffusion |
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| Research Abstract |
Theoretical and numerical study of two-dimensional turbulence
In the Charney-Hasegawa-Mima turbulence, energy flows into a small wavenumber region in the wavenumber space in the process of the development of turbulence. We observed that a quasi-crystal structure is formed in this inverse cascade process, and that the structure function of the vorticity field obeys the dynamic scaling law. In the decaying turbulence we showed that the total energy is asymptotically conserved, and that there exists a dynamical scaling law for the vorticity spectrum and developed a phenomenological theory. Furthermore the exponent characterizing the decaying process of the vortix ensemble is phenomenologically determined by utilizing the Hamiltonian dynamics characteristics of the ensemble of vortices.
Nonlinear dynamical systems with large degrees of freedom
A new model for nonlinear media with a strong dissipation in high-wavenumber dynamics is proposed, and three models with chaotic elements, including the proposed one were numerically solved. When the systems size is less than the critical size Lc, the spatially uniform chaotic oscillation is stable. On the other hand, when the system size is larger than Lc, it becomes unstable. In the latter case, we observed an intermittency, whose statitics turned out to be identical to those of on-off intermittency. Furthemore, we found the following new characteristics of on-off intermittency : (1) We found a new diffusion generated via on-off intermittency. It was termed as on-off diffusion. (2) A new dynamical scaling law for the Fourier spectrum of on-off variable is proposed. (3) A new statistical law of transient process before the onset of on-off intermittency is found.
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Research Products
(7 results)
