Reynolds stress in turbulent boundary layers at high Reynolds number

Abstract

A two-dimensional turbulent boundary layer experiment with zero pressure gradient has been carried out over a smooth surface using two cross hot-wire probes. Wind tunnel speeds of 10 and 20 m s−1 were set up to investigate the effect of the upstream conditions and Reynolds number on the outer flow. For a given set of upstream conditions such as the wind tunnel speed, trip wire size and location, the three components of the velocity field were measured from about 14 m away from the inlet of the wind tunnel up to 30 m downstream. This experiment is unique because it achieves Reynolds numbers as high as R θ = 120 000 for which measurements of the mean velocity and the Reynolds stress profiles, ⟨u 2⟩, ⟨v 2⟩, ⟨w 2⟩ and −⟨uv⟩, are reported. It is shown that by fixing the upstream conditions, the mean velocity profiles, and the normal Reynolds stress components, particularly the ⟨u 2⟩ and ⟨v 2⟩ expressed in outer variables, tend to collapse even though the local Reynolds numbers, R θ, vary from approximately 31 000 up to 120 000. However, the spanwise component of the Reynolds stress, ⟨w 2⟩, and the Reynolds shear stress component, −⟨uv⟩, showed a dependence on the Reynolds number. Moreover, these measurements will be compared with the low Reynolds number (761≤R θ≤5321) data of Castillo and Johansson (2002 J. Turbulence 3 031). More importantly, it will be shown that the Reynolds stress is significantly influenced by the upstream conditions (i.e. flow history and wind tunnel speed).