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。

• 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
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640118/
• 关键词: Homogeneous Isotropic Turbulence; Massive Parallel Computation; Structure Function; Probability Density Function; Conditional Average; Tsallis Statistics; 高次モーメント; 乱流; 直接数値計算; スケーリング指数; エネルギー流束; エネルギー散逸率; マルチフラクタル; 対数正規分布; 確立密度関数; 間欠性; 圧力ス

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.采用空间分辨率为N=1024^3的大规模并行数值计算，获得了R_λ=460的稳定均匀各向同性湍流。从DNS数据库中收集了各种统计数据，并与湍流理论进行了比较。在湍流动力学数值模拟的历史上，首次观测到了小而有限宽度的动能惯性区。计算得到的Kolmogorov常数为1.64，与实验数据吻合较好，并计算了各种速度增量的结构函数。计算了结构函数的标度指数，发现与唯象理论计算的标度指数一致。此外，还发现横向结构函数的标度指数在4阶以上比纵向结构函数的标度指数小。2002年3月在圣达菲举行的统计流体动力学国际讲习班上宣读了这些研究结果。与比费拉教授合作 ...更多信息 关于结构函数各向异性的SO（3）分析从那时起就开始了，并一直持续到现在。到目前为止，所获得的结果是非常积极的，以支持我们以前的发现。在各向异性方面也有了新的发现，但尚需理论分析.有许多研究将Tsallis统计应用于湍流。Tsallis统计量是熵的非广延性质，并有望揭示湍流的统计性质。速度增量的标度指数、速度增量和拉格朗日加速度的概率密度函数是该理论的应用对象。Kraichnan博士和我本人对这些应用进行了严格的审查。目前我们的结论是否定的，因为湍流的多个自由度之间的强耦合，这是不符合的非加性的Tsallis统计，因为能量级联，湍流的本质，是没有适当的描述在理论中。这一合作仍在进行中，预计将有进一步发展。为了得到NS方程各项之间更定量的关系，我们研究了由NS方程导出的高阶结构函数方程。它包含了需要封闭的压力-速度相关项。我们已经研究了条件平均的压力贡献。结果表明，条件平均值是速度增量的二次函数。提出了一个基于Bernoulli定理的理论模型来解释它，该理论的含义是，在相同的阶数的标度指数是相同的，不同于DNS观测。目前正在与国际合作开展进一步研究。少

项目成果

R.Kerr, M Meneguzzi, and T.Gotoh: "An inertial range crossover in structure functions"Phys.Fluids. 13. 1985-1994 (2001)

R.Kerr、M Meneguzzi 和 T.Gotoh：“结构函数中的惯性范围交叉”Phys.Fluids。

T.Nakano, D.fukayama, A.Bershadskii, T.Gotoh: "Stretched lognormal distribution and extended self-similarity in 3D turbulence"J. Phys. Soc. Japan. 71. 2148-2157 (2003)

T.Nakano、D.fukayama、A.Bershadskii、T.Gotoh：“3D 湍流中的拉伸对数正态分布和扩展自相似性”J。

T.Gotoh: "Small-scale statistics of turbulence at high Reynolds numbers by massive computation"Computer Physics Comm. 147. 530-532 (2002)

T.Gotoh：“通过大量计算对高雷诺数湍流进行小规模统计”计算机物理通讯。

T.Gotoh, T.Nakano: "Role of pressure in Turbulence"J. Stati. Phys.. (To appear). (2003)

T.Gotoh，T.Nakano：“压力在湍流中的作用”J。

T.Gotoh, D.Fukayama, and T.Nakano: "Velocity field statistics in homogeneous steady turbulence obtained using a high-resolution direct numerical simulation"Phys.Fluids. 14. 1065-1081 (2002)

T.Gotoh、D.Fukayama 和 T.Nakano：“使用高分辨率直接数值模拟获得的均匀稳定湍流中的速度场统计”Phys.Fluids。