论文标题
壁构成的湍流中流速速度的活动和不活跃的成分
Active and inactive components of the streamwise velocity in wall-bounded turbulence
论文作者
论文摘要
汤森（Townsend，1961）介绍了壁挂式湍流的主动和不活跃运动的概念，在该流动的湍流中，主动运动完全负责产生雷诺剪切应力，这是这些流中的关键动量传输术语。虽然速度的壁正常成分仅与活动运动仅相关，但速度的壁平行成分与活动性运动和非活性运动均相关。在本文中，我们提出了一种方法来隔离流向速度的2-D能量光谱的活性和不活动成分，从而使我们能够测试前者的自相似性特征，这对于壁渗透的理论模型至关重要。该方法基于分析包含两点流速度信号以及基于光谱线性随机估计（SLSE）过程的数据集。所考虑的数据跨越摩擦reynolds编号范围$re_τ$ \ sim $ $ {\ mathcal {o}} $（$ 10^3 $） - $ {\ Mathcal {o}} $（$ 10^4 $）。该过程将完整的2-D光谱（$φ$）线性分解为两个组件，分别包括$φ_{ia} $和$φ__{a} $，分别包括来自非活动和活跃运动的贡献。对于流向和跨度波长的$φ__{a} $证实了这一点，与文献中报道的reynolds剪切应力COSPECTRA很好地对应。 $φ_{a} $和$φ_{ia} $都可以描绘出靠近墙壁附近的惯性主导的区域中的显着自相似特征，这表明汤森（Townsend）附带的涡流的贡献。附着的涡流的不活动贡献揭示了纯$ k^{ - 1} $ - 相关的1-d光谱（其中$ k $是流向/跨度的波数），对Perry＆Chong（1982）附带的涡流模型进行经验支持。
Townsend (1961) introduced the concept of active and inactive motions for wall-bounded turbulent flows, where the active motions are solely responsible for producing the Reynolds shear stress, the key momentum transport term in these flows. While the wall-normal component of velocity is associated exclusively with the active motions, the wall-parallel components of velocity are associated with both active and inactive motions. In this paper, we propose a method to segregate the active and inactive components of the 2-D energy spectrum of the streamwise velocity, thereby allowing us to test the self-similarity characteristics of the former which are central to theoretical models for wall-turbulence. The approach is based on analyzing datasets comprising two-point streamwise velocity signals coupled with a spectral linear stochastic estimation (SLSE) based procedure. The data considered span a friction Reynolds number range $Re_τ$ $\sim$ ${\mathcal{O}}$($10^3$) -- ${\mathcal{O}}$($10^4$). The procedure linearly decomposes the full 2-D spectrum ($Φ$) into two components, $Φ_{ia}$ and $Φ_{a}$, comprising contributions predominantly from the inactive and active motions, respectively. This is confirmed by $Φ_{a}$ exhibiting wall-scaling, for both streamwise and spanwise wavelengths, corresponding well with the Reynolds shear stress cospectra reported in the literature. Both $Φ_{a}$ and $Φ_{ia}$ are found to depict prominent self-similar characteristics in the inertially dominated region close to the wall, suggestive of contributions from Townsend's attached eddies. Inactive contributions from the attached eddies reveal pure $k^{-1}$-scaling for the associated 1-D spectra (where $k$ is the streamwise/spanwise wavenumber), lending empirical support to the attached eddy model of Perry & Chong (1982).
