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arXiv · 1604.08257

Analytic prediction for planar turbulent boundary layers

Xi Chen·Zhen-Su She
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Abstract

Analytic predictions of mean velocity profile (MVP) and streamwise ($x$) development of related integral quantities are presented for flows in channel and turbulent boundary layer (TBL), based on a symmetry analysis of eddy length and total stress. Specific predictions are the friction velocity $u_τ$: ${ U_e/u_τ}\approx 2.22\ln Re_x+2.86-3.83\ln(\ln Re_x)$; the boundary layer thickness $δ_e$: $x/δ_e \approx 7.27\ln Re_x-5.18-12.52\ln(\ln Re_x)$; the momentum thickness Reynolds number: $Re_x/Re_θ=4.94[{(\ln {{\mathop{\rm Re}\nolimits} _θ } + 1.88)^2} + 1]$, all in good agreement with empirical data.

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Xi Chen, Zhen-Su She. 2016-05-23. Analytic prediction for planar turbulent boundary layers. https://arxiv.org/abs/1604.08257

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