1998 Fiscal Year Final Research Report Summary
Development and verification of analytical and statistical theory of turbulence
| Project/Area Number |
09440076
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Nagoya University |
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Principal Investigator |
KANEDA Yukio Graduate School of Engineering, Nagoya University, Prof., 工学研究科, 教授 (10107691)
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| Co-Investigator(Kenkyū-buntansha) |
ISHIHARA Takashi Graduate School of Engineering, Assistant, 工学研究科, 助手 (10262495)
GOTOH Toshiyuki Nnagoya Institute of Technology, Department of System Engineering, Assoc.Prof., 工学部, 助教授 (70162154)
KOZONO Hideo Graduate School of Mathematics, Assoc.Prof., 多元数理科学研究科, 助教授 (00195728)
ISHII Katsuya Graduate School of Engineering, Assoc.Prof., 工学研究科, 助教授 (60134441)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Statistical theory of turbulence / Turbulent diffusion in stably stratified turbulence / Anomalous diffusion in shear flow turbulence / Lagrangian renormalized approximation (LRA) / Energy spectrum in two-dimensional turbulence / Beta-plane turbulence / Phase shift due to wave-turbulence interaction / Pade approximation for Lagrangian two-time correlation |
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| Research Abstract |
The purpose of this study is to develop analytical and statistical theories of turbulence that are practically applicable not only to isotropic, but also to anisotropic turbulence, and to verify them by numerical simulations.
The results of the study include the followings :
(1) An analytical and statistical theory is developed for turbulent diffusion in strongly stratified turbulence. It is based on a linearized approximation (Rapid Distortion Theory) and Corrsin's conjecture, and clarifies an mechanism of suppression of vertical turbulent diffusion by strong stratification. It is also shown that an anomalous turbulent diffusion that could not be explained by existing turbulence models, may occur in turbulence with a mean flow of simple shearing motion. These theoretical results were confirmed by numerical simulations.
(2) By applying the Lagrangian Renormalized Approximation (LRA) , it is shown that a new kind of energy spectrum in two-dimensional turbulence may exist, which is not explained by the theory of Kraichnan-Batchelor-Leith (KBL) , but still exhibits the k^3 spectrum as predicted by KBL.By constructing a Lagrangian statistical theory for the beta-plane turbulence, which is a well known model for the fluid motion on a rotating sphere such as a planet, an analysis is made of the phase shift due to the interaction between waves and turbulence. The theoretical results were shown to be in good agreement with direct numerical simulations (DNS).
(3) A new computational method is proposed for efficiently estimating Lagrangian two-time correlations that play the key roles in the study of mass and heat transfer in turbulence. The method uses Taylor expansions in powers of time and corresponding Pade approximations. It is shown thet the method works well and its results are in good agreement with DNS, not only for single but also two-particle correlation, and not only for isotropic but also anisotropic axisymmetric turbulence.
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