Application of power laws to low Reynolds number boundary layers on smoothand rough surfaces

Scaling laws for the overlap region of near-wall turbulent flows are of par ticular interest to turbulence researchers and engineers. For the mean flow at sufficiently high Reynolds numbers, the classical boundary layer theory proposes a logarithmic law for the overlap region. On the other hand, at l ow Reynolds numbers, refined measurements and direct numerical simulation r esults indicate that the log law region becomes negligibly small. Instead, power laws have received increasing attention as an alternative formulation for the overlap region at low Reynolds numbers. In the present study, we u se open channel flow measurements to assess the ability of the power laws p roposed by Barenblatt [J. Fluid Mech. 248, 513 (1993)] and George and Casti llo [Appl. Mech. Rev. 50, 689 (1997)] to describe the overlap region in low Reynolds number boundary layers on smooth and rough surfaces. The skin fri ction laws derived from the power laws are also used to estimate the fricti on velocity, which values are then compared to measurements obtained by oth er reliable techniques. The results indicate that at low Reynolds numbers t he power law formulations can model a wider extent of the flow than the cla ssical logarithmic profile. Both Barenblatt's and George and Castillo's pow er laws give an excellent prediction of the friction velocities for flows o ver a smooth surface, but only the skin friction law proposed by George and Castillo gives good prediction for the rough wall data. (C) 2001 American Institute of Physics.