A uniform momentum zone–vortical fissure model of the turbulent boundary layer
A uniform momentum zone–vortical fissure model of the turbulent boundary layer
复制标题
DOI：
10.1017/jfm.2018.769
复制
发表时间：
2018-11
影响因子：
3.7
通讯作者：
J. Bautista;A. Ebadi;C. White;G. Chini;J. Klewicki
中科院分区：
文献类型：
--
作者：
J. Bautista;A. Ebadi;C. White;G. Chini;J. Klewicki
最近的研究表明，在大摩擦雷诺数$\unicode[STIX]{x1D6FF}^{+}$时，湍流边界层的惯性主导区域是由由集中涡度的狭窄裂缝分隔的动量几乎均匀的大尺度区域组成的。实验表明，当按边界层厚度缩放时，裂缝厚度为$\mathit{O}(1/\sqrt{\unicode[STIX]{x1D6FF}^{+}})$，而通过每个裂缝的流向速度的维度跳跃与摩擦速度$u_{\unicode[STIX]{x1D70F}}$成比例。本文开发了一个简单的模型，利用了湍流边界层结构的这些基本元素$\unicode[STIX]{x1D6FF}^{+}$。首先，通过在边界层上放置离散数量的裂缝来构造流向速度的主墙-法向剖面。裂缝的数量和它们的壁法向位置遵循由平均动量方程分析得到的标度。然后，裂缝在墙法方向上随机位移，在移动时交换动量，以创建瞬时速度剖面。这个过程被重复以产生沿流速度剖面的集合，并由此计算统计矩。模拟的统计剖面与大范围湍流通道流动的直接数值模拟结果非常吻合$\unicode[STIX]{x1D6FF}^{+}$。特别是，该模型在很大的输入参数范围内稳健地再现了经验观察到的偏度和峰度分布的亚高斯行为。
Recent studies reveal that at large friction Reynolds number $\unicode[STIX]{x1D6FF}^{+}$ the inertially dominated region of the turbulent boundary layer is composed of large-scale zones of nearly uniform momentum segregated by narrow fissures of concentrated vorticity. Experiments show that, when scaled by the boundary-layer thickness, the fissure thickness is $\mathit{O}(1/\sqrt{\unicode[STIX]{x1D6FF}^{+}})$ , while the dimensional jump in streamwise velocity across each fissure scales in proportion to the friction velocity $u_{\unicode[STIX]{x1D70F}}$ . A simple model that exploits these essential elements of the turbulent boundary-layer structure at large $\unicode[STIX]{x1D6FF}^{+}$ is developed. First, a master wall-normal profile of streamwise velocity is constructed by placing a discrete number of fissures across the boundary layer. The number of fissures and their wall-normal locations follow scalings informed by analysis of the mean momentum equation. The fissures are then randomly displaced in the wall-normal direction, exchanging momentum as they move, to create an instantaneous velocity profile. This process is repeated to generate ensembles of streamwise velocity profiles from which statistical moments are computed. The modelled statistical profiles are shown to agree remarkably well with those acquired from direct numerical simulations of turbulent channel flow at large $\unicode[STIX]{x1D6FF}^{+}$ . In particular, the model robustly reproduces the empirically observed sub-Gaussian behaviour for the skewness and kurtosis profiles over a large range of input parameters.