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摘要: 螺旋度与湍流的拓扑结构以及动力学演化过程密切相关. 本文首先详细阐述了螺旋度与流动结构之间具体的关联关系. 随后, 本文重点探讨了螺旋度在湍流输运中的作用, 以及与其他物理效应之间的耦合关系. 由于螺旋度对流动结构的表征作用以及对湍流动力学演化的重要影响, 本文随后简要介绍了螺旋度在湍流建模中的应用. 最后, 本文对当前的研究进展进行了总结, 指出了螺旋度与湍流相关研究的未来主要发展方向.Abstract: Helicity is closely related to the topology of flow. This paper first explains the specific connection between helicity and flow structures. Subsequently, this paper focuses on elaborating the role of helicity in turbulence, as well as its coupling with other physical effects. Based on the crucial influence of helicity on flow structures and turbulent dynamics, this paper then briefly introduces the current applications of helicity in turbulence theory and simulation modeling. Finally, this paper summarizes the current research progress, outlining the overall advancement of helicity and the main directions for future studies.
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Key words:
- helicity /
- turbulent theory /
- turbulent simulation /
- helical dynamics /
- helical wave decomposition /
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图 3 三种螺旋度之间的转换. (a)一对涡环之间的链接螺旋度在涡重联后转换为单个涡环的缠绕, 经过局部放大(Scheeler et al. 2014); (b) “三叶形结”的涡重联, 链接转化为缠绕(Alexakis & Biferale 2018, Yao et al. 2021); (c) Hopf link 的涡重联, 链接转化为缠绕(Kivotides & Leonard 2021); (d) 涡的追击过程中缠绕通过涡拉伸转换为扭转(Scheeler et al. 2017)
图 5 螺旋湍流中的 (a) 涡结构与 (b) 相对螺旋度分布(Kitamura 2021)
图 6 三波交互的四种分类(Waleffe 1992, Alexakis & Biferale 2018); 箭头代表了能量输运的方向, 线条粗细代表了能量通量的大小; 蓝色代表正向级串, 红色代表反向级串
图 8 螺旋度级串的双通道对能量级串的影响(Yan et al. 2020c) (a)
$ \Pi _\Delta ^{H1} $ ; (b)$ \Pi _\Delta ^{H2} $ 
图 9 带有螺旋度的典型旋转湍流 (a) 螺旋旋转湍流(Hu et al. 2022); (b) 旋转壁湍流(Hu et al. 2024); (c) 旋转射流(Luginsland et al. 2016)
图 10 MHD 流动. (a) 日冕中的磁重联过程(Shibata & Magara 2011); (b) 霍尔 MHD 湍流中的电流密度(Ferrand 2021)
图 11 可压缩螺旋湍流中的速度散度(Yan et al. 2019)
图 12 可压缩螺旋湍流中动能与螺旋度的输运(Yan et al. 2020b)
图 14 边界层转捩中模型效果比较(Zhou et al. 2019b). DNS为直接数值模拟结果; CSM与DSM分别是常系数与动态Smagorinsky模型; CHM与DHM分别是常系数与动态螺旋度模型; WALE是壁面自适应局部涡粘模型
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