剪切湍流中的尺度分布及其关联行为研究

Turbulent flows are typical nonlinear complex dynamical system, in which abundant scale-dependent structures are involved. The complex property of turbulent flows come from a large range of scale turbulent motions (eddies) and interaction among them. Therefore, one of the fundamental questions is how these different size of structures distribute and how they interact with each other and what is the memory effect in both spatial and temporal domains. In this study,the classical turbulent shear flows will be investigated experimentally by meaning of particle image velocimetry (PIV) and planar laser induced fluorescence (PLIF). The Hilbert spectral analysis methodology will be applied and furhter developed to characterize the motion of different size of turbulent structures. The distrubtion and interaction of turbulent scales will be studied both in spatial and temporal domains. The energy transfer between different turbulent structures and the memory effect will be studied by using a correlation analysis in both spatial and temporal domains. Special attention will be paid to the interaction between typical large scale structures,e.g.,ramp-cliff structure, etc., and other turbulent structures. Thoeretical study will provide the mathematical and physical models for scale distribution, two scale interaction, energy transfer and memory effect. This research will enrich our knowledge of turbulent theory and will provide useful information for turbulent modeling.

湍流作为一种复杂的非线性力学系统，包含大量各种尺度的湍流结构(涡旋)。不同尺度湍流结构的运动及其相互作用构成了湍流所特有的复杂性。为此，研究各种尺度湍流结构的时空分布、相互作用规律以及时空记忆效应成为认识湍流本质的核心之一。本研究拟以实验为基础，使用PIV、PLIF等测量手段，以典型的剪切湍流为研究对象，利用并改进Hilbert谱分析方法，研究各种尺度湍流结构的运动规律；分析剪切湍流运动中不同尺度湍流结构的时空分布及其相互作用；通过相关函数法确定能量在不同湍流结构间的传递，并刻画不同湍流结构的时空记忆效应；着重分析大尺度结构，如由剪切效应诱导的Ramp-Cliff结构等与其它尺度间的相互作用规律；通过相应的理论分析，给出尺度分布、双尺度相互作用、能量在不同湍流结构间的传递以及不同尺度湍流结构的时空记忆效应的数学、物理模型，为现有湍流模式理论的完善提供一定理论依据。

湍流问题是经典物理学中一直没有得到很好解决的难题。湍流问题的关键是不同尺度漩涡间相互作用的规律的研究，如时空尺度的分布，能量传递等。本项目以实验数据与直接数值模拟数据为主，对湍流中的尺度分布、不同尺度间的相互作用等基本问题进行了研究，给出不同尺度间相互作用满足的统计规律。在国家自然基金的支持下，我们还对拉格朗日湍流的间歇性及其来源、二维湍流的间歇性、湍流热对流中的温度逆梯度输运、二维瑞利-泰勒湍流中的级串过程等问题进行了探索。项目执行期间共计发表学术论文13篇，出版专著1部。