Large-eddy simulation study of the logarithmic law for second- and higher-order moments in turbulent wall-bounded flow

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 $ #1{} #1{ {#1}} ≤ = ≤ = ≥ = ≥ = {Pr} {Fr} {Re}u⁺$ 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.