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螺旋度: 湍流研究中的关键角色

于长平 胡润宁 甘润园

于长平, 胡润宁, 甘润园. 螺旋度: 湍流研究中的关键角色. 力学进展, 待出版 doi: 10.6052/1000-0992-24-018
引用本文: 于长平, 胡润宁, 甘润园. 螺旋度: 湍流研究中的关键角色. 力学进展, 待出版 doi: 10.6052/1000-0992-24-018
Yu C P, Hu R N, Gan R Y. Helicity: A key role in turbulence. Advances in Mechanics, in press doi: 10.6052/1000-0992-24-018
Citation: Yu C P, Hu R N, Gan R Y. Helicity: A key role in turbulence. Advances in Mechanics, in press doi: 10.6052/1000-0992-24-018

螺旋度: 湍流研究中的关键角色

doi: 10.6052/1000-0992-24-018
基金项目: 此研究受到国家自然科学基金项目 (12072349, 91852203, 12232018) 与国家重点研发项目 (2020YFA0711800, 2019YFA0405300) 资助.
详细信息
    作者简介:

    于长平, 中国科学院力学研究所研究员, 长期从事螺旋湍流理论与大涡模拟以及磁流体湍流等领域的研究工作. 在螺旋湍流理论方面, 提出了螺旋度级串的双通道理论, 在壁湍流中系统地研究了螺旋度输运及结构演化规律以及在磁流体湍流的研究中发现并解释了交叉螺旋度对磁螺旋度级串传输效率的影响机理. 在湍流大涡模拟建模方面, 通过理论分析提出了基于螺旋度的大涡模拟模型以及准动态多物理约束的大涡模拟模型等理论完备、工程适用性强的新模型

    通讯作者:

    cpyu@imech.ac.cn

Helicity: A key role in turbulence

More Information
  • 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.

     

  • 图  1  螺旋度的物理解释示意图

    图  2  三种基本涡线构型: (a)和(d) 扭转; (b)和(e) 链接; (c)和(f) 缠绕(Scheeler et al. 2017)

    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  4  Feynman (1955)所预测的涡环 (a)能够发生重联 (b)→(c), 形成若干较小的涡环 (d)

    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  7  能谱、螺旋度谱与能量通量、螺旋度通量示意图. (a) 能量与螺旋度均正向级串; (b) 能量反向级串, 螺旋度正向级串

    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  13  压气机流动中不同模型和实验结果等总压图对比(Sun 2023)

    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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