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

Abstract

Scaling laws for the overlap region of near-wall turbulent flows are of particular 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 low Reynolds numbers, refined measurements and direct numerical simulation results 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 use open channel flow measurements to assess the ability of the power laws proposed by Barenblatt [J. Fluid Mech. 248, 513 (1993)] and George and Castillo [Appl. Mech. Rev. 50, 689 (1997)] to describe the overlap region in low Reynolds number boundary layers on smooth and rough surfaces. The skin friction laws derived from the power laws are also used to estimate the friction velocity, which values are then compared to measurements obtained by other reliable techniques. The results indicate that at low Reynolds numbers the power law formulations can model a wider extent of the flow than the classical logarithmic profile. Both Barenblatt’s and George and Castillo’s power laws give an excellent prediction of the friction velocities for flows over a smooth surface, but only the skin friction law proposed by George and Castillo gives good prediction for the rough wall data.