Project/Area Number  09440076 
Research Category 
GrantinAid for Scientific Research (B)

Section  一般 
Research Field 
General mathematics (including Probability theory/Statistical mathematics)

Research Institution  Nagoya University 
Principal Investigator 
KANEDA Yukio Graduate School of Engineering, Nagoya University, Prof., 工学研究科, 教授 (10107691)

CoInvestigator(Kenkyūbuntansha) 
GOTOH Toshiyuki Nnagoya Institute of Technology, Department of System Engineering, Assoc.Prof., 工学部, 助教授 (70162154)
ISHIHARA Takashi Graduate School of Engineering, Assistant, 工学研究科, 助手 (10262495)
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)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥7,700,000 (Direct Cost : ¥7,700,000)
Fiscal Year 1998 : ¥2,300,000 (Direct Cost : ¥2,300,000)
Fiscal Year 1997 : ¥5,400,000 (Direct Cost : ¥5,400,000)

Keywords  Statistical theory of turbulence / Turbulent diffusion in stably stratified turbulence / Anomalous diffusion in shear flow turbulence / Lagrangian renormalized approximation (LRA) / Energy spectrum in twodimensional turbulence / Betaplane turbulence / Phase shift due to waveturbulence interaction / Pade approximation for Lagrangian twotime correlation / 乱流の統計理論 / 安定成層乱流中の乱流拡散 / 剪断乱流中の異常拡散 / ラグランジュ的繰り込み近似(LRA) / 次元乱流のエネルギースペクトル / ベータ面乱流 / 波と乱流の相互作用による位相変調 / ラグランジュ的2時刻相 / 乱流のラグランジュ的統計理論 / β面乱流 / 一様剪断乱流中の拡散 / 乱流拡散の統計理論 / ラグランジュ的2時刻相関関数 / バデ近似 / 直接数値シミュレーション(DNS) / 渦層の微細構造の解析 / 2次元乱流のスペクトル / 安定成層乱流 / 鉛直拡散の抑制 / ハデ近似 
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 twodimensional turbulence may exist, which is not explained by the theory of KraichnanBatchelorLeith (KBL) , but still exhibits the k^3 spectrum as predicted by KBL.By constructing a Lagrangian statistical theory for the betaplane 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 twotime 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 twoparticle correlation, and not only for isotropic but also anisotropic axisymmetric turbulence.
