Large - eddy simulation of the zero - pressure - gradient turbulent boundary layer up to Re θ = O ( 10 12 )

A near-wall subgrid-scale (SGS) model is used to perform large-eddy simulation (LES) of the developing, smooth-wall, zero-pressure-gradient flat-plate turbulent boundary layer. In this model, the stretched-vortex, SGS closure is utilized in conjunction with a tailored, near-wall model designed to incorporate anisotropic vorticity scales in the presence of the wall. Large-eddy simulations of the turbulent boundary layer are reported at Reynolds numbers Reθ based on the free-stream velocity and the momentum thickness in the range Reθ = 103–1012. Results include the inverse squareroot skin-friction coefficient, √ 2/Cf , velocity profiles, the shape factor H, the von Kármán ‘constant’ and the Coles wake factor as functions of Reθ . Comparisons with some direct numerical simulation (DNS) and experiment are made including turbulent intensity data from atmospheric-layer measurements at Reθ = O(106). At extremely large Reθ , the empirical Coles–Fernholz relation for skin-friction coefficient provides a reasonable representation of the LES predictions. While the present LES methodology cannot probe the structure of the near-wall region, the present results show turbulence intensities that scale on the wall-friction velocity and on the Clauser length scale over almost all of the outer boundary layer. It is argued that LES is suggestive of the asymptotic, infinite Reynolds number limit for the smooth-wall turbulent boundary layer and different ways in which this limit can be approached are discussed. The maximum Reθ of the present simulations appears to be limited by machine precision and it is speculated, but not demonstrated, that even larger Reθ could be achieved with quador higher-precision arithmetic.