论文标题
规范壁湍流中自相似结构的统计行为
Statistical behaviour of self-similar structures in canonical wall turbulence
论文作者
论文摘要
汤森（Townsend）的附带涡流假说（AEH）提供了对数区域中湍流统计的理论描述，这些统计数据与壁正常距离（y）是自相似的一致运动。在这里，我们显示了使用直接的数值模拟数据集，湍流式仿真数据集，通道和管道流，通道和管流（$re_τ\ 1000 $），鉴定的结构的物理尺寸在较高的情况下，均与脉动相关性，均与湍流相关的是，均等的湍流是在湍流的三个物理尺寸上，均与高度相关的颠覆性相关的颠覆性，遵循的湍流是在湍流中，并且在壁速速度波动的隔离速度波动中所包含的湍流动作的自相似行为在流。此外，在大规模范围内（$ 12Y <λ_x<$ 3--4 $δ$），沿流向和跨度波长之间的线性关系（分别$λ_x$和$λ_x$和$λ_x$和$λ_z$）对齐相应的二维能谱。因此，通过在自相似范围内整合二维光谱获得的一维光谱显示了一些自相似缩放级别的证据，$λ_x\simλ_z$以及$ k_x^{ - 1} $和$ k_z^{ - 1} $和$ k_z^{-1} $缩放区域中的可能存在。目前的结果表明，可以通过在低雷诺数流中识别自相似的相似性结构来获得渐近行为。
Townsend's attached-eddy hypothesis (AEH) provides a theoretical description of turbulence statistics in the logarithmic region in terms of coherent motions that are self-similar with the wall-normal distance (y). Here, we show the self-similar behaviour of turbulence motions contained within wall-attached structures of streamwise velocity fluctuations using the direct numerical simulation dataset of turbulent boundary layer, channel, and pipe flows ($Re_τ\approx 1000$) The physical sizes of the identified structures are geometrically self-similar in terms of height, and the associated turbulence intensity follows the logarithmic variation in all three flows. Moreover, the corresponding two-dimensional energy spectra are aligned along a linear relationship between the streamwise and spanwise wavelengths ($λ_x$ and $λ_z$, respectively) in the large-scale range ($12y < λ_x <$ 3--4$δ$), which is reminiscent of self-similarity. Consequently, one-dimensional spectra obtained by integrating the two-dimensional spectra over the self-similar range show some evidence for self-similar scaling $λ_x \sim λ_z$ and the possible existence of $k_x^{-1}$ and $k_z^{-1}$ scaling regions in a similar subrange. The present results reveal that the asymptotic behaviours can be obtained by identifying the self-similar coherent structures in canonical wall turbulence, albeit in low Reynolds number flows.
