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.

本项目旨在研究谱稳定可压缩均质剪切流中湍流的维持机制。我们提出这一建议的动机是最近在研究不可压缩和可压缩剪切流湍流动力学方面取得的进展(G. Mamatsashvili等人，“均匀剪切湍流动力学：非线性横向级联在旁路概念中的关键作用”，Phys.Rev.。E, 94,2016和Hau等，等熵恒切变流中涡旋扰动产生线性和非线性气动声的数值对比分析，流体物理，27（2015）。在那里我们研究了线性瞬态增长的傅里叶谐波和非线性过程的相互作用。在这种谱稳定流中，谐波的线性增长具有瞬态性质，在谱空间上具有很强的各向异性。这反过来又导致了频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正/逆的，而是谐波在傅里叶空间中的横向/角重分布，称为非线性横向级联。本文对不可压缩均匀剪切流的非线性横向叶栅进行了详细的研究和分析。我们证明了湍流是由线性瞬态增长和非线性横向级联的相互作用维持的。结果表明，这类流动中的湍流可以用可压缩涡旋模态和声波来描述。开发了一种分离这些模式的精细程序，这也将是本项目使用的基本方法之一。产生的声场在波数平面上是各向异性的，这导致了高度定向的线性声辐射，而非线性产生的波几乎是全方位的。它的来源是由非正态性引起的线性模态耦合，在中等马赫数下变得有效。在可压缩均匀剪切流中，涡旋模和声波模是线性耦合的。这导致不可避免地产生声波模式的旋涡和一个可能的连接横向级联。因此，在这些新特性的激励下，我们建议对可压缩均匀剪切流的谱空间湍流动力学进行分析，以研究非线性横向叶栅如何在那里表现出来，因为固有的可压缩性效应可能会发挥作用，影响动力学。这将通过模拟受不同梯度和湍流马赫数影响的均匀剪切湍流来实现。