Self-Sustaining Process of Townsend’s Attached Eddies in High-Reynolds-Number Wall Turbulence

在过去的十年里，对壁面湍流中的相干结构的理解已经取得了重大进展，尤其是在两个方面。一个是发现了Navier-Stokes方程的非平凡精确解，即所谓的精确相干结构，这使得用动力系统方法处理低雷诺数湍流成为可能。另一种是由高雷诺数的新的相干结构的发现引发的，这是支持汤森的附着涡假说的新证据，该假说认为所有的附着涡的大小从内到外都是自相似的，并形成一个分级组织。最近，我们的研究小组计算了分级组织中的单个涡实体，称为附着涡，为附着涡的存在提供了令人信服的证据。结果发现，计算得到的附着涡的物理特征与精确相干结构的物理特征非常相似。因此，这项研究的目的是在高雷诺数壁面湍流中汤森附加旋涡和精确的相干结构之间建立理论联系。为此，提出了两个工作包，一个是研究单个附加涡旋(特别是条纹不稳定性)的详细物理过程，另一个是直接计算与给定附加涡旋相关的精确相干结构。该研究将是在大范围雷诺数范围内(特别是旁路转变)到完全发展的湍流区域内相干结构的统计和动力学特征的一致理论描述的重要一步。这对理解和控制高雷诺数下的壁面湍流也具有很大的潜力，这对下一代航空和机械工程设备的发展至关重要。

Over the past decade, significant progress on understanding the coherent structures in wall turbulence has been made, especially in twofold. One is discovery of the non-trivial exact solutions of the Navier-Stokes equation, known as exact coherent structures, which has allowed for tackling low-Reynolds-number turbulence with dynamical system approaches. The other, initiated by discovery of new coherent structures emerging much further from wall at high Reynolds numbers, is the emerging evidence supporting Townsend's attached eddy hypothesis, which views that all the coherent structures, the size of which varies from the inner to outer length scale, are self-similar and form a hierarchial organisation.Recently, the single eddy entity in the hierarchial organisation, called attached eddy, has been computed by our group, providing compelling evidence on the existence of the attached eddy. It has been found that the computed attached eddies exhibit the physical features highly reminiscent of those of the exact coherent structures. The goal of the proposed research is therefore to establish a theoretical link between the Townsend's attached eddies and the exact coherent structures in high-Reynolds-number wall turbulence. To achieve this, two work packages are proposed, one of which is to examine the detailed physical processes of a single attached eddy (especially streak instability) and the other is to directly compute the exact coherent structures associated with the given attached eddy.The proposed research will be an important step towards a consistent theoretical description of statistical and dynamical features of the coherent structures in a wide range of the Reynolds numbers, covering from transitional (especially bypass transition) to fully-developed turbulent regime. It will also have a great potential to contribute to understanding and controlling wall turbulence at high Reynolds numbers, crucial for development of next generation aeronautical and mechanical engineering devices.