An analysis of the spectral turbulent kinetic energy budget in a fully developed turbulent plane channel flow is performed. Direct numerical simulation data are evaluated at friction Reynolds numbers Re τ of 180 and 1000. The analysis is focused on the influence of the Reynolds number on the spectral cascade of energy and the corresponding energy cascade in physical space in the presence of inhomogeneity and anisotropy. The turbulent kinetic energy distribution is compared for both Reynolds numbers, and the relevant characteristics of the energy transfer process in a wall-bounded turbulent flow are described. Differences in energy cascade are noted between the Reynolds number at both low and high wavenumbers. The results of the analysis are further assessed with a comparison to an earlier study of spectral energy transfer at Re τ = 180.

The present paper provides an analysis of the statistical uncertainties associated with direct numerical simulation (DNS) results and experimental data for turbulent channel and pipe flows, showing a new physically based quantification of these errors, to improve the determination of the statistical deviations between DNSs and experiments. The analysis is carried out using a recently proposed criterion by Thompson et al. [“A methodology to evaluate statistical errors in DNS data of plane channel flows,” Comput. Fluids 130, 1–7 (2016)] for fully turbulent plane channel flows, where the mean velocity error is estimated by considering the Reynolds stress tensor, and using the balance of the mean force equation. It also presents how the residual error evolves in time for a DNS of a plane channel flow, and the influence of the Reynolds number on its convergence rate. The root mean square of the residual error is shown in order to capture a single quantitative value of the error associated with the dimensionless averaging time. The evolution in time of the error norm is compared with the final error provided by DNS data of similar Reynolds numbers available in the literature. A direct consequence of this approach is that it was possible to compare different numerical results and experimental data, providing an improved understanding of the convergence of the statistical quantities in turbulent wall-bounded flows.