2014/05/31 by Richard J. A. M. Stevens, Richard J. A. M. Stevens, Michael Wilczek +1 · 116 citations
Engineering · Environmental Science · Physics and Astronomy · #Boundary (topology) #Combustion and flame dynamics #Constant (computer programming) #Flow (mathematics) #Fluid Dynamics and Turbulent Flows #Logarithm #Open-channel flow #Second moment of area #Turbulence #Variance (accounting) #Wind and Air Flow Studies #physics.flu-dyn
paper · pdf · doi:10.1017/jfm.2014.510
published in Journal of Fluid Mechanics 757, 888-907 (Cambridge University Press) · 20 pages, 16 figures, J. Fluid Mech. (2014)
arxiv created 2014/09/03 · openalex publication_date 2014/09/29 · arxiv updated 2014/12/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Abstract The logarithmic law for the mean velocity in turbulent boundary layers has long provided a valuable and robust reference for comparison with theories, models and large-eddy simulations (LES) of wall-bounded turbulence. More recently, analysis of high-Reynolds-number experimental boundary-layer data has shown that also the variance and higher-order moments of the streamwise velocity fluctuations \def \xmlpi #1\def \mathsfbi #1\boldsymbol \mathsf #1\let ≤ =\leqslant \let ≤ =\leqslant \let ≥ =\geqslant \let ≥ =\geqslant \def Pr \mathit Pr\def \Fr \mathit Fr\def \Rey \mathit Reu′ + display logarithmic laws. Such experimental observations motivate the question whether LES can accurately reproduce the variance and the higher-order moments, in particular their logarithmic dependency on distance to the wall. In this study we perform LES of very high-Reynolds-number wall-modelled channel flow and focus on profiles of variance and higher-order moments of the streamwise velocity fluctuations. In agreement with the experimental data, we observe an approximately logarithmic law for the variance in the LES, with a ‘Townsend–Perry’ constant of A1≈ 1.25 . The LES also yields approximate logarithmic laws for the higher-order moments of the streamwise velocity. Good agreement is found between Ap , the generalized ‘Townsend–Perry’ constants for moments of order 2p , from experiments and simulations. Both are indicative of sub-Gaussian behaviour of the streamwise velocity fluctuations. The near-wall behaviour of the variance, the ranges of validity of the logarithmic law and in particular possible dependencies on characteristic length scales such as the roughness length z0 , the LES grid scale Δ , and subgrid scale mixing length CsΔ are examined. We also present LES results on moments of spanwise and wall-normal fluctuations of velocity.