The nature of turbulence in compressible homentropic constant shear flows: its vortex and wave contents and self-sustenance.

可压缩垂直恒定剪切流中湍流的本质：其涡流和波内容以及自维持。

• 批准号: 438287556
• 负责人: Professor Dr.-Ing. Holger Foysi
• 金额: --
• 依托单位: Lehrstuhl für Strömungsmechanik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2020
• 资助国家: 德国
• 起止时间: 2019-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/438287556?language=en
• 关键词: nature; turbulence; compressible; homentropic; constant

he aim of this project is to investigate the mechanism of sustenance of turbulence in spectrally stable compressible homogeneous shear flow. The motivation of our proposal is the progress achieved recently when studying the dynamics of incompressible and compressible shear flow turbulence (G. Mamatsashvili et al., “Dynamics of homogeneous shear turbulence: A key role of the nonlinear transverse cascade in the bypass concept”, Phys.Rev.E, 94, 2016 and Hau et al., A comparative numerical analysis of linear and nonlinear aerodynamic sound generation by vortex disturbances in homentropic constant shear flows, Physics of Fluids, 27 (2015)). There we examined the interplay of linear transient growth of Fourier harmonics and nonlinear processes. In this spectrally stable flow the linear growth of the harmonics has a transient nature and is strongly anisotropic in spectral space. This, in turn, leads to anisotropy of nonlinear processes in spectral space and, as a result, the main nonlinear process appears to be not a direct/inverse, but rather a transverse/angular redistribution of harmonics in Fourier space referred to as the nonlinear transverse cascade. In our paper, this new nonlinear transverse cascade was studied and analysed in detail for incompressible homogeneous shear flow. We demonstrated, that the turbulence is sustained by the interplay of the linear transient growth and the nonlinear transverse cascade. It was shown additionally, that turbulence in these type of flows be described by compressible vortex modes and acoustic waves. A refined procedure of separation of these modes was developed, which will be one of the basic methodologies used for this project, too. The generated acoustic field is anisotropic in the wavenumber plane, which results in highly directional linear sound radiation, whereas the nonlinearly generated waves are almost omni-directional. Its source is the linear mode-coupling induced by non-normality, which becomes efficient at moderate Mach numbers. In compressible homogeneous shear flows vortex and acoustic wave modes are linearly coupled. This leads to the inevitable generation of acoustic wave modes from the vortex ones and a likely connection to the transverse cascade. Thus, motivated by these novelties, we propose to perform the analysis of the turbulence dynamics in spectral space for compressible homogeneous shear flow to investigate how the nonlinear transverse cascade manifests itself there, as intrinsic compressibility effects could come into play, influencing the dynamics. This will be achieved by simulating homogeneous shear turbulence subject to varying gradient and turbulent Mach numbers.

他的目的是研究在光谱稳定的均匀剪切流中湍流的维持机理。提案的动机是在研究不可压缩和兼容的剪切流动湍流动态时取得的进步（G. Mamatsashvili等人，“均质剪切湍流的动力学：非线性横向cascade在旁路概念中的关键作用，在旁路概念中”涡流紊乱的空气动力学发电量产生恒定常数剪切流中的涡流障碍，流体物理学，27（2015））。在那里，我们检查了傅立叶谐波和非线性过程的线性瞬态生长的相互作用。在这种光谱稳定的流中，谐波的线性生长具有短暂的性质，并且在光谱空间中具有强烈的各向异性。反过来，这导致了光谱空间中非线性过程的各向异性，因此，主要的非线性过程似乎不是直接/逆的，而是傅立叶空间中谐波的横向/角度重新分布，称为非线性横向级联。在我们的论文中，研究了这种新的非线性横向级联反应，并详细分析了不可压缩的均匀剪切流。我们证明了湍流是由线性瞬态生长和非线性横向级联反应的相互作用所维持的。另外，这些类型的流中的湍流通过兼容的涡流模式和声波描述。开发了分离这些模式的定义过程，这也将是该项目使用的基本方法之一。生成的声场是波数平面中各向异性的，这会导致高度定向的线性声音辐射，而非线性产生的波则几乎是全向方向的。它的来源是由非正态性引起的线性模式耦合，在中等马赫数下变得有效。在兼容的均匀剪切流中，涡流和声波模式是线性耦合的。这导致不可避免地从涡旋形式产生了声波模式，并可能与横向级联反应有可能的联系。在这些新颖性的推动下，我们建议对光谱空间中的湍流动力学进行分析，以兼容均匀的剪切流，以研究非线性横向级联反应如何在那里表现出来，因为内在能力效应可能会发挥作用，从而影响动力学。这将通过模拟均匀的剪切湍流来实现。