Junghwa Seo

Inner and Outer Scalings in Rough Surface Turbulent Boundary Layers

The incompressible, zero-pressure-gradient turbulent boundary layer is investigated in light of the effect of the Reynolds number and surface roughness. The experimental data from various researchers has been collected and analyzed in order to study the effect of the roughness on the inner and outer flow. The scalings of George and Castillo (GC) (1997) for the mean velocity profiles and Reynolds stresses are used for the analysis and compared with the results of the classical scalings. Moreover, the true asymptotic profile (self-preserving) solution for the velocity deficit profiles is found when the profiles are normalized by the Zagarola/Smits (1998) scaling, U∞δ /δ. This scaling successfully removes the effects of the Reynolds number, the upstream conditions, and the roughness from the outer flow. Similarly, the classical scaling, uτ , tends to remove the effects from the outer flow but not in the inner region. However, it will be shown that as the roughness parameter, k, increases beyond k ≈ 28 or less, the Reynolds stresses and velocity profiles are influenced in the outer flow by roughness. This limit corresponds to the lower limit of the outer region of a boundary layer, thus the outer flow is affected by roughness beyond this limit. However, for the inner layer, the Reynolds stresses are sensitive to values of the roughness parameter, k ≈ 0.4 while the velocity profiles are affected for values of about k ≈ 17.