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Analysis of Universal Structure and Development of Statistical Theory of Inhomogeneous Anisotropic Turbulence

非均匀各向异性湍流普遍结构分析及统计理论发展

基本信息

批准号：
14340033
负责人：
KANEDA Yukio
金额：
$ 7.04万
依托单位：
Nagoya University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2004
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-14340033/
关键词：
Inhomogeneous Anisotropic Turbulence Direct Numerical Simulation(DNS)Universal Structure of Turbulence Statistical Theory of Turbulence Reynolds Number Dependence Large Eddy Simulation Plane Poiseuille Turbulence Stratified Turbulence 非一様

项目摘要

The aim of this study is to understand the universal structure of turbulence, which is indispensable for developing statistical theory of inhomogeneous anisotropic turbulence. On the basis of the method of statistical theory of turbulence and large scale Direct Numerical Simulation(DNS), the study has clarified the followings :(A)DNS of Turbulence and Data-Analysis :By analyzing the data of the world largest DNS of turbulence with the number of grid points up to 4096^3, more than 10^11 degrees of freedom and 10^22 nonlinear interactions, we clarified some of (i)Reynolds(Re)-dependence of various statistics, and (ii)asymptotic universality in the high Re-limit. We also performed quantitative examination of (iii)Kolmogorov's similarity hypotheses, and (iv)the eddy-viscosity hypothesis in Large Eddy Simulation, at high Re.(B)Universal Structure and Modeling of Anisotropic Turbulence :We derived an expression for the anisotropic spectrum at small scales of homogeneous turbulent shear flow on the basis of the analysis of a Lagrangian spectral closure equation. We also derived a general expression for the anisotropic spectrum in stratified turbulence, confirmed its form by DNS, and showed the validity of an idea similar to that of the linear responses theory for non-equilibrium system.(C)DNS of Wall Bounded Turbulence and Data-Analysis :Plane Poiseuille turbulence is one of the most basic turbulences among boundary layer turbulences or turbulences with solid wall. In order to perform the DNS, we made codes based on the Chebyshev-tau method and a Combined Compact Scheme, respectively, and validated their performance. By the DNS, we clarified the dependence on the wall normal distance and Re of eddy-scale distribution, by analyzing the wall-normal velocity correlation spectrum.

这项研究的目的是了解湍流的普遍结构，这对于发展非均匀各向异性湍流的统计理论是必不可少的。在湍流统计理论和大尺度直接数值模拟方法的基础上，研究了以下内容：(A)湍流直接数值模拟和数据分析：通过分析世界上最大的湍流直接数值模拟数据，分析了网格点数高达4096^3、10^11个自由度和10^22个非线性相互作用的湍流直接数值模拟数据，阐明了各种统计量的雷诺(Re)相关性和(Ii)高Re极限下的渐近普适性。我们还对(Iii)Kolmogorov的相似假设和(Iv)大涡模拟中的涡粘性假设进行了定量检验。(B)各向异性湍流的普遍结构和模拟：我们在分析拉格朗日谱闭合方程的基础上，导出了均匀切变湍流小尺度各向异性谱的表达式。给出了层状湍流各向异性谱的一般表达式，并用数值模拟方法对其形式进行了验证，验证了非平衡系统线性响应理论的正确性。(3)壁面湍流数值模拟及数据分析：平面Poiseuille湍流是边界层湍流或固体壁面湍流中最基本的湍流之一。为了实现域名系统，我们分别基于Chebyshev-tau方法和组合紧致格式编写了代码，并验证了它们的性能。通过对壁法向速度相关谱的分析，阐明了壁法向距离与涡度分布的Re之间的关系。