Reynolds-number scaling of turbulent channel flow

Results of an experimental study of smooth-wall, fully developed, turbulent channel flow are presented. The Reynolds number (Rem) based on the channel height and the bulk mean velocity ranged from 10 000 to 300 000. The present results indicate that the skin-friction coefficient (Cf) closely follows a power law for Rem 62 000. At higher Reynolds numbers, Cf is best described by a log law. Detailed two-component velocity measurements taken at friction Reynolds numbers of Reτ = 1000–6000 indicate that the mean flow and Reynolds shear stress display little or no Reynolds-number dependence. The streamwise Reynolds normal stress (u^{ 2 } ^ + u′2¯+), on the other hand, varies significantly with Reynolds number. The inner peak in u^{ 2 } ^ + u′2¯+ is observed to grow with Reynolds number. Growth in u^{ 2 } ^ + u′2¯+ farther from the wall is documented over the entire range of Reynolds number giving rise to a plateau in the streamwise Reynolds normal stress in the overlap region of the profile for Reτ = 6000. The wall-normal Reynolds normal stress (v^{ 2 } ^ + v′2¯+) displays no Reynolds-number dependence near the wall. Some increase in v^{ 2 } ^ + v′2¯+ in the outer layer is noted for Reτ ≤ 4000. The trends in the present Reynolds stress results agree qualitatively with recent experimental results from pipe and boundary layer flows.