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

X. Zhang, T. Watanabe, and K. Nagata
Reynolds number dependence of the turbulent/non-turbulent interface in temporally developing turbulent boundary layers
Journal of Fluid Mechanics, 964 A8 2023

This article may be found at https://doi.org/10.1017/jfm.2023.329.

Accepted manuscript is available here. 
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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  Reθ=2000-13000 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, δTNTI, turbulent sublayer,  δTSL , and viscous superlayer, δVSL, are found to be approximately 15ηTI, 10ηTI and 5ηTI, respectively, where  ηTI is the Kolmogorov scale taken in the turbulent region near the TNTI layer. The mean curvature of the irrotational boundary is also characterized by  ηTI . 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  Reθ, for which  ηTI/δ∼Reθ^−3/4 is valid with the boundary layer thickness  δ. The surface area of the irrotational boundary is consistent with the fractal analysis of the interface, where the fractal dimension  Df 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 Reθ^(3/4)(Df−2) for Reθ≥4000.

日本語訳 (DeepL翻訳)

日本語タイトル

乱流／非乱流境界層（TNTI）のレイノルズ数依存性を調べるために、運動量厚Reθ=2000-13000に基づく幅広いレイノルズ数で、時間発展する乱流境界層の直接数値シミュレーション（DNS）を実施した。DNSの格子間隔は、TNTI付近の小規模な乱流運動がよく解像されるように注意して決定した。TNTI層の平均厚さδTNTI、乱流下層δTSL、粘性上層δVSLは、それぞれ約15ηTI、10ηTI、5ηTIであり、ηTIはTNTI層近くの乱流領域でとったコルモゴロフスケールを示していることがわかった。また、irrotational boundaryの平均曲率もηTIで特徴付けられる。レイノルズ応力と渦度の異方性テンソルから、TNTI層下の乱流は高Reθで等方的になる傾向があり、境界層の厚さδでηTI/δ〜Reθ^-3/4が成立する。 回転しない境界の表面積は界面のフラクタル解析と一致しており、フラクタル次元Dfは2.14〜2.20と判明した。本結果から、摩擦速度で規格化された単位水平面積あたりの平均巻き込み率は、Reθ≧4000の場合、Reθ^(3/4)(Df-2)として緩やかに変化することがわかった。

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