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On hairpin vortex generation from near-wall streamwise vortices

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Abstract

The generation of a hairpin vortex from near-wall streamwise vortices is studied via the direct numerical simulation (DNS) of the streak transient growth in the minimal channel flow at \(Re_\tau =400\). The streak profile is obtained by conditionally averaging the DNS data of the fully developed turbulent channel flow at the same Reynolds number. The near-wall streamwise vortices are produced by the transient growth of the streak which is initially subjected to the sinuous perturbation of the spanwise velocity. It is shown that the arch head of the hairpin vortex first grows from the downstream end of the stronger streamwise vortex and then connects with the weaker, opposite-signed streamwise vortex in their overlap region, forming a complete individual hairpin structure. The vorticity transport along the vortex lines indicates that the strength increase and the spatial expansion of the arch head are due to the stretching and the turning of the vorticity vector, respectively. The hairpin packets could be further produced from the generated individual hairpin vortex following the parent-offspring process.

Graphical Abstract

Generation of hairpin vortex from a pair of counter-rotating streamwise vortices due to stretching and turning effects. (a1)(b1)(c1) perspective view of vortex and strain vectors; (a2)(b2)(c2) distribution of stretching and turning terms along the vortex line projected to y - z plane. Meshed surface: \(\lambda _{ci} = 10\); black vector: strain vector; red solid line: vortex line; dashed line: turning; dash-dotted line: stretching.

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Acknowledgments

This project was supported by the National Natural Science Foundation of China (Grants 11490551, 11472154, 11132005, and 11322221).

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Authors and Affiliations

  1. AML, Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, China

    Yinshan Wang, Weixi Huang & Chunxiao Xu

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  1. Yinshan Wang
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  2. Weixi Huang
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  3. Chunxiao Xu
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Correspondence to Chunxiao Xu.

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Wang, Y., Huang, W. & Xu, C. On hairpin vortex generation from near-wall streamwise vortices. Acta Mech Sin 31, 139–152 (2015). https://doi.org/10.1007/s10409-015-0415-8

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  • DOI: https://doi.org/10.1007/s10409-015-0415-8

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