DNS of an oscillating turbulent boundary layer with an enlarged Reynolds-number range

DNS is used to examine oscillating turbulent boundary layers (TBLs) with doubly-periodic boundary conditions in which the mean pressure gradient varies sinusoidally in time (one cycle consists of the phase-angle φ= 0 to π). In the cycle, the adverse-pressure-gradient (APG) is first imposed (φ=0 to π/2), causing a reversal of the wall shear stress equivalent to separation. The favorable-pressure-gradient (FPG) is subsequently imposed (φ = π/2 to π) so that the flow which has reversed direction is attached and then momentarily exhibits a laminar-like velocity profile. As the FPG is reduced, the flow finally approaches the zero-pressure-gradient TBL (φ =0 and π). The seminal DNS study has been performed by Spalart and Baldwin (1989) at Re_δs =600 to 1200, where Re_δs denotes the Reynolds number based on the amplitude of the freestream velocity and the laminar boundary-layer thickness. Their Reynolds number includes the transitional Re range. In the current DNS, three values of the Reynolds number (Re_δs =1000, 1800 and 2600) are used to compare with the measurements of Jensen et al. (1989). The latter two Reynolds numbers are free of low Re effects. At Re_δs =1000, there appears a large peak in the wall-shear stress profile near φ =π. By contrast, the latter peak becomes insignificant for Re_δs =1800 and 2600 where the profile varies slowly with Re_δs. With increasing Re, the mean streamwise velocity exhibits a log law over a wider range of φ, while large-scale motions and their near-wall footprints become prominent with the APG.