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Chin. Phys. B, 2020, Vol. 29(11): 114702    DOI: 10.1088/1674-1056/abbbdc
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The role of velocity derivative skewness in understanding non-equilibrium turbulence

Feng Liu(刘锋)1,2, †, Le Fang(方乐)2, and Liang Shao(邵亮)3$
1 School of Energy and Power Engineering, North University of China, Taiyuan 030051, China
2 Laboratory of Mathematics and Physics, Ecole Centrale de Pékin, Beihang University, Beijing 100191, China
3 Laboratoire de Mécaniques des Fluides et d’Acoustique, Ecole Centrale de Lyon–Université de Lyon, Ecully 69134, France
Abstract  

The turbulence governed by the Navier–Stokes equation is paramount in many physical processes. However, it has been considered as a challenging problem due to its inherent nonlinearity, non-equilibrium, and complexity. Herein, we review the connections between the velocity derivative skewness Sk and the non-equilibrium properties of turbulence. Sk, a reasonable candidate for describing the non-equilibrium turbulence, which varies during the non-equilibrium procedure. A lot of experimental or numerical evidences have shown that the perturbation of energy spectrum, which associated with the excitation of large scales, results in an obvious variation of Sk, and Sk is a negative value in this rapid energy decay process. The variation of positive Sk is closely related to the perturbation of transfer spectrum, and this corresponds to the backward energy transfer process. In addition, the skewness characterizes the production (or reduction) rate of enstrophy due to vortex stretching (or compression). Using the transport equation of turbulent energy dissipation rate and enstrophy, it is possible to establish a theoretical connection between skewness and the non-equilibrium turbulence. It is expected that this work could trigger the rapid advancement of the future studies of non-equilibrium turbulence, and also the improvement of turbulence models.

Keywords:  velocity derivative skewness      non-equilibrium turbulence      turbulence model  
Received:  10 August 2020      Revised:  20 September 2020      Accepted manuscript online:  28 September 2020
Fund: the National Natural Science Foundation of China (Grant No. 11772032) and the Science Foundation of North University of China (Grant No. 11026829).
Corresponding Authors:  Corresponding author. E-mail: feng.liu@nuc.edu.cn   

Cite this article: 

Feng Liu(刘锋), Le Fang(方乐), and Liang Shao(邵亮)$ The role of velocity derivative skewness in understanding non-equilibrium turbulence 2020 Chin. Phys. B 29 114702

Fig. 1.  

Streamwise evolution of Sk in fractal-generated grid turbulence. Different symbols correspond to different transverse locations. Sk reaches an approximately constant at x/M ≈ 20. Reproduced from Ref. [4], copyright 2015, with permission of AIP Publishing.

Fig. 2.  

Cε versus Reλ for NN and RR cases. NN: normally decaying case (equilibrium); RR: non-equilibrium decaying case, which is produced by reversing all velocities at time 0. Stages I, II, III, and IV represent different time-evolution stages, among which I denotes the ${C}_{\epsilon }\sim R{e}_{\lambda }^{-2}$ stage, IV denotes the non-equilibrium stage. Reproduced from Ref. [35], copyright 2019, with permission of American Physical Society.

Fig. 3.  

Temporal evolution of Sk for NN and RR cases. The inset is the short-time evolution of Sk. Reproduced from Ref. [35], copyright 2019, with permission of American Physical Society.

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