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Reynolds number dependence of the turbulent/non-turbulent interface in temporally developing turbulent boundary layers

Published online by Cambridge University Press:  26 May 2023

Xinxian Zhang Open the ORCID record for Xinxian Zhang [Opens in a new window] ,
Tomoaki Watanabe Open the ORCID record for Tomoaki Watanabe [Opens in a new window]  and
Koji Nagata Open the ORCID record for Koji Nagata [Opens in a new window]
Xinxian Zhang*
Affiliation:
School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, PR China Department of Aerospace Engineering, Nagoya University, Nagoya 464-8603, Japan
Tomoaki Watanabe
Affiliation:
Education and Research Center for Flight Engineering, Nagoya University, Nagoya 464-8603, Japan
Koji Nagata
Affiliation:
Department of Mechanical Engineering and Science, Kyoto University, Kyoto 615-8540, Japan
*
†Email address for correspondence: zhangxinxian@buaa.edu.cn
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Abstract

Direct numerical simulations (DNS) of temporally developing turbulent boundary layers are performed with a wide range of Reynolds numbers based on the momentum thickness $Re_{\theta } = 2000$–$13\,000$ for investigating the Reynolds number dependence of the turbulent/non-turbulent interface (TNTI) layer. The grid spacing in the DNS is determined carefully such that small-scale turbulent motions near the TNTI are well resolved. The outer edge of the TNTI layer, called the irrotational boundary, is detected with vorticity magnitude. The mean thicknesses of the TNTI layer, $\delta _{TNTI}$, turbulent sublayer, $\delta _{TSL}$, and viscous superlayer, $\delta _{VSL}$, are found to be approximately $15\eta _{TI}$, $10\eta _{TI}$ and $5\eta _{TI}$, respectively, where $\eta _{TI}$ is the Kolmogorov scale taken in the turbulent region near the TNTI layer. The mean curvature of the irrotational boundary is also characterized by $\eta _{TI}$. The shear parameter and the shear-to-vorticity ratio show that the mean shear effects near the TNTI layer are not significant for both large and small scales. The anisotropy tensors of Reynolds stress and vorticity suggest that the turbulence under the TNTI layer tends to be isotropic at high $Re_{\theta }$, for which $\eta _{TI}/\delta \sim Re_{\theta }^{-3/4}$ is valid with the boundary layer thickness $\delta$. The surface area of the irrotational boundary is consistent with the fractal analysis of the interface, where the fractal dimension $D_f$ is found to be $2.14$–$2.20$. The present results suggest that the mean entrainment rate per unit horizontal area normalized by the friction velocity varies slowly as $Re_{\theta }^{(3/4)(D_f-2)}$ for $Re_{\theta } \geq 4000$.

JFM classification

Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulence simulation Turbulent Flows: Intermittency

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JFM Papers
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Journal of Fluid Mechanics , Volume 964 , 10 June 2023 , A8
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© The Author(s), 2023. Published by Cambridge University Press

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