Numerical and Experimental Elucidation of Statistical Laws and Spatial Structures for Large-Scale Motion in Turbulence

虽然湍流，这是无处不在的我们周围，已经研究了多年，在小尺度上的统计规律是普遍的动力学一直是主要的目标。在本研究中，我们着重于大尺度动力学，并得到以下结果。(1)我们提出了大尺度下动能涨落的理论框架。(2)我们已经证明，统计规律可以通过用它们的相关长度归一化来普适地描述。(3)通过对流体方程和随机过程方程的数值模拟，再现了大尺度下的对数正态性。(4)我们证明了在某些波动-湍流系统中，两种具有不同统计规律的湍流状态共存。

Although turbulence, which is ubiquitous around us, has been studied through the ages, the dynamics at small scales where the statistical law is universal has been the main target. In this study, we focus on the large-scale dynamics and obtain following results. (1) We have proposed the theoretical framework for the fluctuation of kinetic energy at large scales. (2) We have shown that statistical laws can be described universally by normalizing them with their correlation length. (3) We have reproduced the log-normality at large scales by numerically simulating the fluid equation and the stochastic process equation. (4) We have shown that in some wave-turbulence system, two turbulence states which have different statistical laws coexist.