Turbulent swirling flows viewed from the notion of helicity

根据螺旋度（速度和涡度之间的相关性）的概念进行变分分析。结果表明，在等螺旋度的约束下，平均速度剖面能使平均流的涡度拟能最小化，其剖面与湍流旋流中观测到的剖面吻合得很好。除了螺旋度约束，我们还考虑了角动量守恒。这一处理使得轴向旋转湍流管流中的平均速度剖面可以用与湍流旋流相似的方式再现，但两者的行为却截然不同，湍流螺旋度有望成为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，关于湍流螺旋度的信息确实是缺乏的。这使得难以用采用螺旋度作为基本统计量的湍流模型适当地模拟湍流。本研究从湍流螺旋度的观点出发，对湍流旋转流的典型实验数据进行了重新检验。分析揭示了产生湍流螺旋度的主要机理，并对中心区湍流旋流的偏心率作了改进。在实验中观察到的中心区域的高度不对称的平均速度分布进行校准的物理参数，如旋转流的对称性和守恒性质的帮助。这为湍流旋流的数值模拟提供了坚实的基础。

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.