New Development in Computational Physics of Turbulence

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。分析表明，DNS不支持湍流不稳定性的唯象理论中常用的假设。(2)本文在一个迄今为止最大的计算域中，用DNS给出了一个支持Loitsyansky假设的证据，即自由衰减湍流中大尺度统计的普遍性。2.待处理信息的约简：（1）用1-（1）的数据分析了从大尺度到小尺度的能量传递的统计，阐明了统计与粗粒化方法和尺度的依赖关系。(2)利用1-（1）的数据对湍流相干和非相干模式的统计特性进行了小波分析，结果表明，相干模式数与总模式数的比值随雷诺数的增加而减小。3.壁面湍流：提出了新的壁面湍流数值模拟格式，并与传统的数值模拟格式进行了比较。从精度和性能价格比两方面考虑，本文提出的边界层湍流数值模拟方案是可行的。本文在对槽道湍流惯性子区的物理理解的基础上，对-DNS的可行性进行了检验，结果表明，在我们的研究水平上，只有DNS才有可能实现[1]和[2]的结果，这为发展湍流理论和模型提供了坚实的基础。文[3]中的结果对于大尺度壁面湍流的DNS是有用的。它们有助于理解湍流的计算方法。

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.