Turbulent superstructures in the turbulent cascade of Reynolds stresses

不同特征长度尺度的涡结构在壁面湍流中共存并相互作用。它们的范围从远离墙壁的大型结构到墙壁附近的小型漩涡。这种大规模的运动被称为湍流上层结构（下文将介绍TSS），其长度尺度比近壁涡旋大得多。TSS在湍流动力学中起着重要的作用，它们会引起强烈的速度波动，其特征长度尺度是流动最大长度尺度的许多倍，例如湍流边界层的厚度。通过对雷诺数剪切应力的贡献，TSS对总湍流动能和壁面摩擦阻力的增加负有很大的责任。目前，对TSS的动态，特别是与其他尺度的相互作用，还没有统一的描述。虽然文献中已经记录了TSS对壁面小型结构的影响，但关于相反方向的影响，即小型结构对TSS的影响，有截然相反的证据。特别是，尚不清楚小尺度结构是否在TSS的起源中起决定性作用。了解TSS和流动的其他尺度的相互影响不仅从理论的角度来看是非常重要的，而且因为它极大地影响了我们模拟和控制湍流的能力。在本提案中，我们研究了TSS与其他较小尺度流结构之间的相互作用。我们应用了一个新的理论框架，即各向异性广义Kolmogorov方程，以描述湍流中不同长度尺度的结构和物理空间中雷诺兹应力张量的分离分量是如何产生、耗散和传输的。在这个框架中，尺度之间相互作用的结果是雷诺兹应力在尺度和空间上的可测量传递，这构成了所谓的雷诺兹应力的湍流级联。我们发展了一系列的数值实验，在这些实验中，通道中湍流的物理特性被自然地或有意地改变，以突出或熄灭TSS的某些方面。通过分析雷诺数应力在不同尺度上的传递，我们可以突出TSS与湍流其他结构之间的关系。

Vortical structures with different characteristic length scales coexist and interact reciprocally in wall-bounded turbulence. They range from very large-scale structures away from the wall to small-scale eddies in the wall vicinity. The large-scale motions are called turbulent superstructures - TSS in the following – and have length scales much larger than those of the near-wall vortices. TSS play an important role in the dynamics of turbulent flows, where they cause strong velocity fluctuations with a characteristic length scale of many times the largest length scale of the flow, for instance the thickness of a turbulent boundary layer. TSS are responsible for a significant fraction of total turbulent kinetic energy and increased friction drag at the wall, through their contribution to the Reynolds shear stress. Presently, no agreed-upon description of the dynamics of TSS exists, especially concerning their mutual interaction with other scales. While the effect of TSS on the small scale structures at the wall has been documented in literature, there is contrasting evidence regarding an influence in the opposite direction, i.e. an influence of the small scale structures onto the TSS. In particular, it is still unclear whether the small scale structures play a determinant role in the origin of TSS. Understanding the mutual influence of TSS and the other scales of the flow is of great importance not only from a theoretical point of view, but also because it greatly affect our ability to model and control a turbulent flow.In the present proposal we investigate the interaction between TSS and the other smaller scale structures of the flow. We apply a new theoretical framework, the Anisotropic Generalized Kolmogorov Equations, in order to describe how the separate component of the Reynolds stress tensor are produced, dissipated and transported through structures at different length scales and across physical space in the turbulent flow. In this framework, the result of the interaction between scales is a measurable transport of Reynolds stresses across scales and space, that constitutes the so-called turbulent cascade of Reynolds stresses.We develop a series of numerical experiments, in which the physics of turbulent flows in channels is let develop naturally or purposely altered, in order to highlight or quench some aspects of TSS. Through an analysis of how Reynolds stresses are transported through different scales, we can highlight the relationship between TSS and other structures of the turbulent flow.