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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 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 A(1) approximate to 1.25. The LES also yields approximate
logarithmic laws for the higher-order moments of the streamwise
velocity. Good agreement is found between A(p), 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 z(0), the LES grid scale Delta, and subgrid scale
mixing length C-s Delta are examined. We also present LES results on
moments of spanwise and wall-normal fluctuations of velocity.