Turbulent swirling flows viewed from the notion of helicity

基于螺旋度（速度与涡度之间的关系）的概念进行了变分分析。结果表明，在螺旋度不变的条件下，可以得到使平均流熵最小的平均速度分布，其分布与旋涡湍流中观测到的平均速度分布吻合较好。除了螺旋度约束外，我们还考虑了角动量守恒。这种处理方法使得在轴向旋转湍流管道流动中以类似于湍流旋涡流动的方式再现平均速度分布成为可能，但其行为似乎完全不同。紊流螺旋度是描述湍流大尺度结构的重要湍流量之一。然而，在湍流的研究中确实缺乏关于湍流螺旋度的信息。这使得以螺旋度为基本统计量的湍流模型难以恰当地模拟湍流。本文从紊流螺旋度的角度重新考察了具有代表性的紊流旋流实验数据。分析揭示了产生湍流螺旋度的主要机制。另一个改进是关于中心区域湍流旋流的偏心。实验中观察到的中心区域高度不对称的平均速度分布借助旋流的对称性和守恒性等物理参数进行了校准。期望该标定剖面为紊流旋流的数值模拟提供坚实的基础。

A variational analysis based on the notion of the helicity (correlation between the velocity and the vorticity) was performed. It was shown that the mean-velocity profiles that minimize the enstrophy of the mean flow under the constraint of the constant helicity is realized, whose profiles are in good agreement with the counterpart observed in a turbulent swirling flow. In addition to the helicity constraint, we took the angular-momentum conservation into consideration. This treatment made it possible to reproduce the mean-velocity profiles in an axially rotating turbulent pipe flow in a manner similar to the case in a turbulent swirling flow, whose behaviors appeared to be totally different from each other.The turbulent helicity has been expected to be one of the important turbulent quantities in describing the large-scale structures in tubulent flows. It is, however, true that information on turbulent helicity has been lacking in the study of turbulence. This made it difficult to appropriately simulate turbulent flows with a turbulence model adopting the helicity as a basic statistical quantity. In this research, data of the representative experiment of turbulent swirling flows were re-examined from the viewpoint of the turbulent helicity. The analysis revealed what mechanism is dominant in producing the turbulent helicity.Another improvement is attained in relation to the eccentricity of the turbulent swirling flow in the center region. The highly asymmetric mean-velocity profiles in the center region observed in the experiments were calibrated with the aid of physical arguments such as the symmetry and conservation properties of the swirling flow. It is expected that this calibrated profiles provide a firm basis for the numerical simulation of the turbulent swirling flow.