One-point statistics for turbulent wall-bounded flows at Reynolds numbers up to δ+ ≈ 2000

TLDR

We performed direct numerical simulations of zero‑pressure‑gradient turbulent boundary layers at Reθ = 2780–6680 (δ+ ≈ 1000–2000), extending the Reynolds‑number and wall‑distance range to over a decade and providing one‑point statistics. The simulations reveal that eddy‑turnover length better predicts recovery of large scales than Reynolds number, that integral parameters, mean velocities, Reynolds stresses, and pressure fluctuations agree with data yet differ from internal flows in wall units—especially in the outer layer—and that logarithmic intensity profiles for spanwise velocity and pressure, as well as a logarithmic increase of peak streamwise velocity and pressure fluctuations with Reynolds number, are confirmed, while streamwise velocity fluctuations require higher Reynolds numbers to develop a clear logarithmic profile, suggesting a mesolayer for fluctuations. The statistics of the new simulation are available on our website.

Abstract

One-point statistics are presented for new direct simulations of the zero-pressure-gradient turbulent boundary layer in the range Reθ = 2780–6680, matching channels and pipes at δ+ ≈ 1000–2000. For tripped boundary layers, it is found that the eddy-turnover length is a better criterion than the Reynolds number for the recovery of the largest flow scales after an artificial inflow. Beyond that limit, the integral parameters, mean velocities, Reynolds stresses, and pressure fluctuations of the new simulations agree very well with the available numerical and experimental data, but show clear differences with internal flows when expressed in wall units at the same wall distance and Reynolds number. Those differences are largest in the outer layer, independent of the Reynolds number, and apply to the three velocity components. The logarithmic increase with the Reynolds number of the maximum of the streamwise velocity and pressure fluctuations is confirmed to apply to experimental and numerical internal and external flows. The new simulations also extend to a wider range of Reynolds numbers, and to more than a decade in wall distance, the evidence for logarithmic intensity profiles of the spanwise velocity and of the pressure intensities. Streamwise velocity fluctuations appear to require higher Reynolds numbers to develop a clear logarithmic profile, but it is argued that the comparison of the available near-wall data with fluctuation profiles experimentally obtained by other groups at higher Reynolds numbers can only be explained by assuming the existence of a mesolayer for the fluctuations. The statistics of the new simulation are available in our website.