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A Liutex based definition and identification of vortex core center lines

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Abstract

Six core issues for vortex definition and identification concern with (1) the absolute strength, (2) the relative strength, (3) the rotational axis, (4) the vortex core center, (5) the vortex core size, and (6) the vortex boundary (Liu C. 2019). However, most of the currently popular vortex identification methods, including the Q criterion, the λ2 criterion and the λci criterion et al, are Eulerian local region-type vortex identification criteria and can only approximately identify the vortex boundary by somewhat arbitrary threshold. On the other hand, the existing Eulerian local line-type methods, which seek to extract line-type features such as vortex core line, are not entirely satisfactory since most of these methods are based on vorticity or pressure minimum that will fail in many cases. The key issue is the lack of a reasonable mathematical definition for vortex core center. To address this issue, a Liutex (previously named Rortex) based definition of vortex core center is proposed in this paper. The vortex core center, also called vortex rotation axis line here, is defined as a line where the Liutex magnitude gradient vector is aligned with the Liutex vector, which mathematically implies that the cross product of the Liutex magnitude gradient vector and the Liutex vector on the line is equal to zero. Based on this definition, a novel three-step method for extracting vortex rotation axis lines is presented. Two test cases, namely the Burgers vortex and hairpin vortices, are examined to justify the proposed method. The results demonstrate that the proposed method can successfully identify vortex rotation axis lines without any user-specified threshold, so that the proposed method is very straightforward, robust and efficient.

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Acknowledgements

This work was supported by the Department of Mathematics at University of Texas at Arlington and AFOSR (Grant No. MURI FA9559-16-1-0364), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 18KJA110001) and the Visiting Scholar Scholarship of the China Scholarship Council (Grant No. 201808320079). The authors are grateful to Texas Advanced Computational Center (TACC) for providing computation hours. This work is accomplished by using code DNSUTA developed by Dr. Chaoqun Liu at the University of Texas at Arlington.

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Authors and Affiliations

  1. Department of Mathematics, University of Texas at Arlington, Arlington, Texas, 76019, USA

    Yi-sheng Gao, Jian-ming Liu, Yi-fei Yu & Chaoqun Liu

  2. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, China

    Jian-ming Liu

Authors
  1. Yi-sheng Gao
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  2. Jian-ming Liu
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  3. Yi-fei Yu
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  4. Chaoqun Liu
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Correspondence to Chaoqun Liu.

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Project supported by the National Natural Science Foundation of China (Grant No. 91530325).

Biography: Yi-sheng Gao (1984-), Male, Ph. D.

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Gao, Ys., Liu, Jm., Yu, Yf. et al. A Liutex based definition and identification of vortex core center lines. J Hydrodyn 31, 445–454 (2019). https://doi.org/10.1007/s42241-019-0048-7

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  • DOI: https://doi.org/10.1007/s42241-019-0048-7

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