论文标题
局部涡流拓扑和湍流的几何形状
Local vortex line topology and geometry in turbulence
论文作者
论文摘要
Chong等人的局部流线拓扑分类方法。 （1990年）进行了调整并扩展以描述无穷小涡流线的几何形状。强制各向同性湍流的直接数值仿真（DNS）数据表明，第二个（$q_Ω$）和第三（$r_Ω$）的联合概率密度函数（PDF）的涡度梯度张力张量的归一化不变性均超过$re_λ> 200 $。在泰勒绿色涡流的分解晚期也可以看到相同的PDF形状，这表明湍流中钟形PDF形式的普遍性。此外，检查了从不同初始配置的Vortex重新连接。在所有情况下，一侧的局部拓扑和重新连接桥的几何形状都相同，另一侧具有椭圆形涡旋线，另一侧具有双曲线丝。总体而言，涡度场的拓扑表征为检查湍流和其他流体流中的涡度动态提供了有用的分析基础。
The local streamline topology classification method of Chong et al. (1990) is adapted and extended to describe the geometry of infinitesimal vortex lines. Direct numerical simulation (DNS) data of forced isotropic turbulence reveals that joint probability density function (PDF) of the second ($q_ω$) and third ($r_ω$) normalized invariants of the vorticity gradient tensor asymptotes to a self-similar bell form beyond $Re_λ> 200$. The same PDF shape is also seen at the late stages of breakdown of Taylor-Green vortex suggesting the universality of the bell-shaped pdf form in turbulent flows. Additionally, vortex reconnection from different initial configurations is examined. The local topology and geometry of the reconnection bridge is shown to be identical in all cases with elliptic vortex lines on one side and hyperbolic filaments on the other. Overall, topological characterization of vorticity field provides a useful analytical basis for examining vorticity dynamics in turbulence and other fluid flows.
