Direct numerical simulation of a turbulent boundary layer up to Reθ = 2500

Abstract Direct numerical simulations (DNSs) of a turbulent boundary layer (TBL) with Reθ = 570–2560 were performed to investigate the spatial development of its turbulence characteristics. The inflow simulation was conducted in the range Reθ = 570–1600 by using Lund’s method. To resolve the numerical periodicity induced by the recycling method, we adopted a sufficiently long streamwise domain of x/θin,i = 1000 (=125δ0,i), where θin,i is the inlet momentum thickness and δ0,i is the inlet boundary layer thickness in the inflow simulation. Furthermore, the main simulation with a length greater than 50δ0 was carried out independently by using the inflow data, where δ0 is the inlet boundary layer thickness of the main simulation. The integral quantities and the first-, second- and higher-order turbulence statistics were compared with those of previous data, and good agreement was found. The present study provides a useful database for the turbulence statistics of TBLs. In addition, instantaneous field and two-point correlation of the streamwise velocity fluctuations displayed the existence of the very large-scale motions (VLSMs) with the characteristic widths of 0.1–0.2δ and that the flow structure for a length of approximately ∼6δ fully occupies the streamwise domain statistically.