New Development in Computational Physics of Turbulence

本课题取得的成果包括：1.湍流统计的普遍性：(1)利用世界上最高分辨率的DNS资料，研究了湍流的小尺度统计特性。分析表明，该模型不支持现象学理论中常用的湍流间歇性假设。(2)在迄今为止DNSS中最大的计算域中，该模型提供了支持洛伊琴斯基自由衰减湍流大尺度统计普适性假设的证据。2.需要处理的信息归纳：(1)利用1-(1)的数据分析了能量从大到小尺度传递的统计量。(1)阐明了统计量对粗粒化方法和尺度的依赖。-(2)小波分析用1-(1)的数据对湍流的相干模式和非相干模式进行了统计，结果表明，相干模式的数目与总模式的数目之比随着雷诺数的增加而减小。3.壁面湍流：提出了壁面边界湍流数值模拟的新格式，并与传统方法进行了比较。从边界层湍流数值模拟的精度和性价比的角度来看，这是一种很有前途的方案。在对物理理解的基础上，对槽道湍流中的惯性子程进行了数值模拟，1和2的结果只有在我们研究的水平上才有可能，为湍流理论和数值模拟的发展提供了良好的基础。文3中的结果对于壁面边界湍流的超大规模数值模拟具有一定的参考价值。它们有助于通过计算方法理解湍流。

The achievements of this project include the following.1.Universality in the Statistics of Turbulence :(1) We studied the small scale statistics of turbulence by using the data of DNS with the world's highest resolution. The analysis showed that the DNS does not support assumptions commonly used in phenomenological theories of intermittency of turbulence.(2) An evidence supporting the Loitsyansky hypothesis on universality of large scale statistics in freely decaying turbulence was presented by DNS in a computation domain which is the largest in the DNSs so far made.2.Reduction of Information to be treated :(1) The analysis of the statistics of the energy transfer from large to small scales by using the data of 1-(1)clarified the dependence of the statistics on the method and scale of the coarse graining.-(2) The wavelet-analysis of the statistics of the coherent and incoherent modes of turbulence by using the data of 1-(1)showed that the ratio of the numbers of the coherent modes to that of the total modes decreases with the Reynolds number.3.Wall bounded turbulence :New numerical schemes for DNS of wall bounded turbulence were proposed, and compared with conventional ones. A scheme was shown to be promising in view of the accuracy and cost performance for DNS of boundary layer turbulence. The feasibility of -DNS of the inertial subrange in a turbulent channel flow was examined on the basis of our understanding of the physics.The achievements of 1 and 2 were possible only by DNS at the level of our study, and provide us with sound basis for developing turbulence theory and modeling. The finding in 3 should be useful for very large scale DNS of wall bounded turbulence. They contribute to the understanding of turbulence by computational approaches.