Turbulent swirling flows viewed from the notion of helicity

基于螺旋度(速度和涡度之间的关系)的概念进行了变分分析。结果表明，在恒螺旋度的约束下，实现了使平均流拟合度最小的平均速度分布，其分布与在湍流旋流中观察到的相应分布相吻合。除了螺旋度约束外，我们还考虑了角动量守恒。这种处理使得能够以类似于湍流旋流的方式再现轴向旋转湍流中的平均速度分布，两者的行为似乎完全不同。湍流螺旋度被认为是描述管状流中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。这使得采用螺旋度作为基本统计量的湍流模型难以恰当地模拟湍流流动。在本研究中，从湍流螺旋度的角度重新考察了具有代表性的湍流旋流实验数据。分析表明，产生湍流螺旋度的主要机制是什么，与中心区域湍流旋流的偏心程度有关。利用旋流的对称性和守恒性等物理参数，对实验中观察到的中心区域高度不对称的平均速度分布进行了标定。可望为湍流旋流的数值模拟奠定坚实的基础。

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.