Mathematical Structure of the Probability Density Function and Intermittency in Turbulence and Massive Parallel Numerical Computation.

概率密度函数的数学结构和湍流的间歇性以及大规模并行数值计算。

基本信息

批准号：
12640118
负责人：
GOTOH Toshiyuki
金额：
$ 2.3万
依托单位：
Nagoya Institute of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2002
项目状态：
已结题

项目摘要

1. Steady homogeneous isotropic turbulence at R_λ=460 was obtained by using massive parallel numerical computation with the spatial resolution N=1024^3. Various statistical data were gathered from the DNS data base and compared with turbulence theories. The inertial range of the kinetic energy with small but finite width was observed for the first time in the history of DNS of turbulence. The Kolmogorov constant was found to be 1.64 in agreement with experimental data, and various kinds of structure functions for the velocity increments were also computed. The scaling exponents of the structure functions were computed and found to be in agreement with those computed by phenomenological theories. It was also found that the scaling exponents of the transverse structure functions at the order higher than 4 are smaller than those of the longitudinal ones. These findings was read at International Workshop on Statistical Hydrodynamics at Santa Fe, March 2002. A collaboration with Prof.Bifela … More re on the SO(3) analysis for the anisotropy of the structure functions has begun since then, and been continuing by now. The results so far obtained are very positive to support our previous findings. Also new findings regarding to the anisotropy are obtained, but need theoretical analysis.2. There have been many studies which apply the Tsallis statistics to turbulence. The Tsallis statistics is nonextensitve nature for the Entropy, and expected to shed some lights on the statistical nature of the Turbulence. Scaling exponents of the velocity increments and probability density functions of the velocity increments and the Lagrangian acceleration are the objects for the theory to be applied. Dr.Kraichnan and myself have critically examined those applications. Currently our conclusion is negative to those studies because the turbulence has strong coupling among the many degrees of freedom which is inconsistent with the non-additiveness of the Tsallis statistics, and because the energy cascade, the essence of turbulence, is not properly described in the theory. This collaboration is still under way and further development will be expected.3. In order to obtain more quantitative relation among various terms of Navier-Stokes (NS) equation, we have examined the equation of higher order structure functions derived from the NS equation. It contains the pressure-velocity correlation term which needs a closure. We have studied the pressure contributions in terms of the conditional average. It was found that the conditional average is of the quadratic function in the velocity increments. A theoretical model based on the Bernoulli theorem was proposed to explain it, The implication of this theory is that some of the scaling exponents at the same order are identical, differing from the DNS observation. Further study with international collaboration is now under way. Less

1.通过空间分辨率N=1024^3的大规模并行数值计算，获得了R_λ=460的稳态均匀各向同性湍流，并从DNS数据库收集了各种统计数据，并与湍流理论进行了比较。在湍流 DNS 历史上首次观测到具有小但有限宽度的能量，发现 Kolmogorov 常数为 1.64，与此一致。还计算了速度增量的各种结构函数，并发现结构函数的标度指数与唯象理论计算的结果一致。还发现横向的标度指数。高于 4 阶的结构函数小于纵向函数。这些发现是在 2002 年 3 月于圣达菲举行的国际统计流体动力学研讨会上宣读的。与 Bifela 教授合作……更多关于从那时起，结构函数的各向异性的 SO(3) 分析就开始了，迄今为止所获得的结果非常积极地支持了我们之前的发现，而且还获得了有关各向异性的新发现，但需要理论基础。 2. 有许多研究将 Tsallis 统计应用于湍流 Tsallis 统计对于熵来说是非广延的，并且有望对湍流的统计性质有所启发。速度增量的指数和速度增量的概率密度函数以及拉格朗日加速度是该理论应用的对象，Kraichnan 博士和我本人对这些应用进行了严格的检验，因为湍流已经对这些应用产生了负面影响。多个自由度之间存在强耦合，这与 Tsallis 统计的非可加性不一致，并且因为理论中没有正确描述能量级联（湍流的本质）。合作仍在进行中，预计会有进一步的发展。 3．为了获得Navier-Stokes(NS)方程各项之间的更多定量关系，我们研究了由NS方程导出的高阶结构函数方程。需要闭包的压力-速度相关项我们研究了条件平均值的压力贡献，发现条件平均值是基于伯努利定理的二次函数。提出来解释这一点，该理论的含义是，一些相同阶的缩放指数是相同的，与 DNS 观察不同，目前正在进行较少的国际合作研究。