The dynamics of coherent structures in developed turbulence

在发展湍流的动力学和结构方面，我主要得到了以下三个结果。在二维自由对流(FC)湍流中，熵级联控制着湍流在尺度上的传输。与三维Navier-Stokes湍流中的能量级联一样，熵级联具有间歇性。根据ESS(扩展自相似)假设，确定了温差和速度差函数的结构指数。结果表明，即使对于自由对流系统，ESS方法也能很好地进行计算，并给出了可信的结果。然而，现有的模型并不能解释观察到的间歇性。这是因为现有的模型是基于耗散率的间歇性的，并且直接处理速度差的统计。和温差。我正在试着建造一种新的模型。我从动力学的角度考察了熵级联的间歇性，重点考察了它的特征时间。结果表明，看似引起间歇性的大波动在时间和尺度上都高度相关，它们的相关时间波动很弱。另一方面，这些大的涨落，均匀的涨落，是结构的背景，包含了系统的大部分熵。它们的平均值在空间上的比例决定了间歇性或结构的特征时间。在槽流湍流中，提出了条纹的定义，用它可以很好地显示从粘性底层到对数层的整个条纹结构。研究了结构卷在粘性下层中的重要性。边界层的动力学可以用条纹的动力学来解释。在其演化过程中观察到的条纹的三维结构可以用基于构型对称性的简单论证来解释。

I obtained mainly the following three results on the dynamics and the structures in developed turbulence.1. In two-dimensional free convection (FC) turbulence, entropy cascade governs turbulent transfers in scales. Entropy cascade is intermittent like energy cascade in three dimensional Navier-Stokes turbulence. I have determined the exponents of structure of functions of temperature differences and velocity differences in terms of ESS (Extended Self-Similarity) hypothesis. As a result, it is shown that ESS method works well even for the free convection system and gives plausible results. However, the intermittency observed is not explained by the existing models. This is because the existing models are based on the intermittency of the dissipation rate and deal with directly the statistics of the velocity differences. and temperature differences. I am trying to construct a new model.2. I have examined the intermittency of entropy cascade from the dynamical perspective focusing on its character-istic times. It is shown that the large fluctuations which seem to cause the intermittency and are observed as structures, highly correlate both in time and scale and fluctuations of their correlation times are weak. These large fluctuations On the other hand, homogeneous fluctuations which are the background of the structures, contain the greater part of the entropy of the system. The scaling of their average over space determines the characteristic times of the intermittency or the structures.3. In channel flow turbulence, Iproposed the definition of streak by which whole structure of streak from the viscous sub-layr to the log-layr is well visualized. The importance of the roll of structures in the viscous sub-layr is examined. It is also shown that the dynamics of the boundary layr is explained by the dynamics of streak. The three dimensional structure of streaks observed in their evolutions is explained by the simple argument based on the symmetry of the configuration.