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On the effectiveness of local vortex identification criteria in the vortex representation of wall-bounded turbulence

旋涡识别准则在壁湍流涡表征方面的有效性比较

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Abstract

Compressing complex flows into a tangle of vortex filaments is the basic implication of the classical vortex-representation notion. This work focuses on the effectiveness of the local identification criteria in the vortex representation of wall-bounded turbulence. Basically, five local identification criteria regarding vortex strength and three criteria for vortex axis are considered. Instead of separately evaluating the two classes of criteria, the current work defines vortex vectors by arbitrarily combining the vortex strength and vortex axis expressed by various criteria, and attempts to figure out the most effective one regarding the vortex representation. The effectiveness of these vortex vectors is evaluated based on two aspects: first, the alignment of the vortex axis and vortex iso-surface should be well established, which benefits the simplification of the vortex filaments; second, vortices could be viewed as the “gene code” of turbulent flows, which means reconstructing the velocity fields based on them should be effective. For the first aspect, the differential geometry method is employed to describe the vortex isosurface-axis alignment property quantitatively. For the second aspect, the Biot-Savart law is employed to accomplish the vortex-to-velocity reconstruction. Results of this work provide some reference for the applications of vortex identification criteria in wall-bounded turbulence.

摘要

将复杂、多尺度的流动表示为丝状旋涡结构的诱导作用是经典旋涡表征观点的基本内容. 本文主要研究不同旋涡识别准则在 壁湍流旋涡表征方面的有效性. 主要考察五个关于旋涡强度的识别准则以及三个关于涡轴方向的识别准则, 通过任意组合这两类旋涡 识别准则定义不同版本的旋涡矢量, 然后从两个方面对这些旋涡矢量的有效性进行了评估. 首先, 涡轴方向与旋涡等值面伸展的方向 应具有一致性, 这是丝状旋涡结构的特点;其次, 旋涡是湍流的“基因密码”, 这意味着基于它们重建速度场是有效的. 对于第一个方 面, 采用微分几何方法定量地描述涡轴与旋涡等值面的关联性. 对于第二个方面, 采用毕奥-萨伐尔定律来实现旋涡到速度场的重建. 本文的研究结果对壁湍流旋涡识别和表征方面的工作具有一定的参考意义.

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Funding

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11902371 and 91852204), and China Postdoctoral Science Foundation (Grant No. 2019M653172).

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Authors and Affiliations

  1. School of Science, Nanjing University of Science and Technology, Nanjing, 210094, China

    Chengyue Wang  (王成跃)

  2. State Key Laboratory of Fluid Power and Mechatronic System, Department of Mechanics, School of Aeronautics and Astronautics, Zhejiang University, Hangzhou, 310027, China

    Qi Gao  (高琪)

  3. Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-sen University, Zhuhai, 519082, China

    Tianle Chen  (陈添乐) & Biao Wang  (王彪)

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  1. Chengyue Wang  (王成跃)
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  2. Qi Gao  (高琪)
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  3. Tianle Chen  (陈添乐)
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Correspondence to Qi Gao  (高琪).

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Wang, C., Gao, Q., Chen, T. et al. On the effectiveness of local vortex identification criteria in the vortex representation of wall-bounded turbulence. Acta Mech. Sin. 38, 321463 (2022). https://doi.org/10.1007/s10409-021-09085-x

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