Non-dimensional energy dissipation rate near the turbulent/non-turbulent interfacial layer in free shear flows and shear free turbulence

T. Watanabe, C. B. da Silva, K. Nagata
Non-dimensional energy dissipation rate near the turbulent/non-turbulent interfacial layer in free shear flows and shear free turbulence
Journal of Fluid Mechanics, 875 321-344 2019

This article may be found at https://doi.org/10.1017/jfm.2019.462.

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Accepted manuscript is available here
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Abstract

The non-dimensional dissipation rate Cε=εL/u′3, where ε, L and u′ are the viscous energy dissipation rate, integral length scale of turbulence and root-mean-square of the velocity fluctuations, respectively, is computed and analysed within the turbulent/non-turbulent interfacial (TNTI) layer using direct numerical simulations of a planar jet, mixing layer and shear free turbulence. The TNTI layer that separates the turbulent and non-turbulent regions exists at the edge of free shear turbulent flows and turbulent boundary layers, and comprises both the viscous superlayer and turbulent sublayer regions. The computation of Cε is made possible by the introduction of an original procedure, based on local volume averages within spheres of radius r, combined with conditional sampling as a function of the location with respect to the TNTI layer. The new procedure allows for a detailed investigation of the scale dependence of several turbulent quantities near the TNTI layer. An important achievement of this procedure consists in permitting the computation of the turbulent integral scale within the TNTI layer, which is shown to be approximately constant. Both the non-dimensional dissipation rate and turbulent Reynolds number Reλ vary in space within the TNTI layer, where two relations are observed: Cε∼Re−1λ and Cε∼Re−2λ. Specifically, whereas the viscous superlayer and part of the turbulent sublayer display Cε∼Re−2λ, the remaining of the turbulent sublayer exhibits Cε∼Re−1λ, which is consistent with non-equilibrium turbulence (Vassilicos, Annu. Rev. Fluid Mech. vol. 47, 2015, pp. 95–114).

日本語訳 (DeepL翻訳)

自由剪断乱流および無剪断乱流における乱流・非乱流界面層近傍の無次元エネルギー散逸率

平面噴流,混合層,無剪断乱流の直接数値シミュレーションにより,無次元散逸率Cε=εL/u′3(ε,L,u′はそれぞれ粘性エネルギー散逸率,乱流の積分長スケール,速度変動の二乗平均)を求め,乱流/非乱流界面(TNTI)層内での解析を行った.乱流領域と非乱流領域を分けるTNTI層は、自由せん断乱流と乱流境界層の端に存在し、粘性超層と乱流下層の両方の領域から構成されている。Cεの計算は、半径rの球内の局所的な体積平均と、TNTI層に対する位置の関数としての条件付きサンプリングに基づく、独自の手順の導入により可能となった。この新しい手順により、TNTI層近傍のいくつかの乱流量のスケール依存性を詳細に調べることができる。この手法の重要な成果は、TNTI層内の乱流積分スケールを計算できるようになったことであり、このスケールはほぼ一定であることが示された。無次元散逸率と乱流レイノルズ数Reλは、TNTI層内で空間的に変化し、2つの関係が観測された。Cε∼Re-1λ と Cε∼Re-2λ の2つの関係が見られる。具体的には、粘性超層と乱流下層の一部がCε∼Re-2λを示すのに対し、乱流下層の残りはCε∼Re-1λを示し、非平衡乱流と一致する(Vassilicos, Annu. Rev. Fluid Mech. vol. 47, 2015, pp.95-114 )。

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