Mamatsashvili G, Khujadze G, Chagelishvili G, Dong S, Jiménez J, Foysi H
Helmholtz-Zentrum Dresden-Rossendorf, P.O. Box 510119, D-01314 Dresden, Germany.
Department of Physics, Faculty of Exact and Natural Sciences, Tbilisi State University, Tbilisi 0179, Georgia.
Phys Rev E. 2016 Aug;94(2-1):023111. doi: 10.1103/PhysRevE.94.023111. Epub 2016 Aug 22.
To understand the mechanism of the self-sustenance of subcritical turbulence in spectrally stable (constant) shear flows, we performed direct numerical simulations of homogeneous shear turbulence for different aspect ratios of the flow domain with subsequent analysis of the dynamical processes in spectral or Fourier space. There are no exponentially growing modes in such flows and the turbulence is energetically supported only by the linear growth of Fourier harmonics of perturbations due to the shear flow non-normality. This non-normality-induced growth, also known as nonmodal growth, is anisotropic in spectral space, which, in turn, leads to anisotropy of nonlinear processes in this space. As a result, a transverse (angular) redistribution of harmonics in Fourier space is the main nonlinear process in these flows, rather than direct or inverse cascades. We refer to this type of nonlinear redistribution as the nonlinear transverse cascade. It is demonstrated that the turbulence is sustained by a subtle interplay between the linear nonmodal growth and the nonlinear transverse cascade. This course of events reliably exemplifies a well-known bypass scenario of subcritical turbulence in spectrally stable shear flows. These two basic processes mainly operate at large length scales, comparable to the domain size. Therefore, this central, small wave number area of Fourier space is crucial in the self-sustenance; we defined its size and labeled it as the vital area of turbulence. Outside the vital area, the nonmodal growth and the transverse cascade are of secondary importance: Fourier harmonics are transferred to dissipative scales by the nonlinear direct cascade. Although the cascades and the self-sustaining process of turbulence are qualitatively the same at different aspect ratios, the number of harmonics actively participating in this process (i.e., the harmonics whose energies grow more than 10% of the maximum spectral energy at least once during evolution) varies, but always remains quite large (equal to 36, 86, and 209) in the considered here three aspect ratios. This implies that the self-sustenance of subcritical turbulence cannot be described by low-order models.
为了理解谱稳定（恒定）剪切流中亚临界湍流自我维持的机制，我们对不同长宽比的流动区域进行了均匀剪切湍流的直接数值模拟，并随后在谱空间或傅里叶空间中分析了动力学过程。在这种流动中不存在指数增长模式，并且湍流仅通过剪切流非正态性引起的扰动傅里叶谐波的线性增长来获得能量支持。这种由非正态性引起的增长，也称为非模态增长，在谱空间中是各向异性的，这反过来又导致了该空间中非线性过程的各向异性。因此，傅里叶空间中谐波的横向（角向）重新分布是这些流动中的主要非线性过程，而不是直接或反向级联。我们将这种类型的非线性重新分布称为非线性横向级联。结果表明，湍流是由线性非模态增长和非线性横向级联之间的微妙相互作用维持的。这一系列事件可靠地例证了谱稳定剪切流中亚临界湍流的一个众所周知的旁路情景。这两个基本过程主要在与区域大小相当的大长度尺度上起作用。因此，傅里叶空间的这个中心、小波数区域在自我维持中至关重要；我们定义了它的大小并将其标记为湍流的关键区域。在关键区域之外，非模态增长和横向级联的重要性次之：傅里叶谐波通过非线性直接级联转移到耗散尺度。尽管在不同长宽比下，湍流的级联和自我维持过程在定性上是相同的，但积极参与此过程的谐波数量（即在演化过程中其能量至少有一次增长超过最大谱能量的10%的谐波）会有所不同，但在这里考虑的三个长宽比中始终相当大（分别为36、86和209）。这意味着亚临界湍流的自我维持不能用低阶模型来描述。
