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.

该项目的目的是研究谱稳定的可压缩均匀剪切流中湍流的维持机制，我们的提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时取得的进展（G. Mamatsashvili 等人，2017）。 ，“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 等人，对等熵恒定剪切流中涡旋扰动产生的线性和非线性气动声音的比较数值分析，流体物理，27 (2015)）我们研究了傅里叶线性瞬态增长的相互作用。在这种光谱稳定流中，谐波的线性增长具有瞬态性质，并且在光谱空间中具有很强的各向异性。导致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/逆向的，而是傅里叶空间中谐波的横向/角度重新分布，在我们的研究中被称为非线性横向级联。在本文中，我们对这种新的非线性横向叶栅针对不可压缩均匀剪切流进行了详细研究和分析，证明了湍流是通过相互作用来维持的。另外还表明，这些类型的流动中的湍流可以通过可压缩涡流模式和声波来描述，这将是这些模式的分离过程之一。该项目使用的基本方法也是如此。生成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，而非线性生成的波几乎是全向的。由非正态性引起，在中等马赫数下变得有效，涡流和声波模式是线性耦合的，这导致不可避免地从涡流模式中产生声波模式，并且可能与横向叶栅有关。因此，受这些新颖性的启发，我们建议对可压缩均匀剪切流的谱空间中的湍流动力学进行分析，以研究非线性横向级联如何在其中表现出来，作为内在的。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。