Outer-layer turbulence intensities in smooth- and rough-wall boundary layers

Abstract

AbstractClear differences in turbulence intensity profiles in smooth, transitional and fully rough zero-pressure-gradient boundary layers are demonstrated, using the diagnostic plot introduced by Alfredsson, Segalini & Örlü (Phys. Fluids, vol. 23, 2011, p. 041702) – ${u}^{\prime } / U$ versus $U/ {U}_{e} $, where ${u}^{\prime } $ and $U$ are the local (root mean square) fluctuating and mean velocities and ${U}_{e} $ is the free stream velocity. A wide range of published data are considered and all zero-pressure-gradient boundary layers yield outer flow ${u}^{\prime } / U$ values that are roughly linearly related to $U/ {U}_{e} $, just as for smooth walls, but with a significantly higher slope which is completely independent of the roughness morphology. The difference in slope is due largely to the influence of the roughness parameter ($ \mathrm{\Delta} {U}^{+ } $ in the usual notation) and all the data can be fitted empirically by using a modified form of the scaling, dependent only on $ \mathrm{\Delta} U/ {U}_{e} $. The turbulence intensity, at a location in the outer layer where $U/ {U}_{e} $ is fixed, rises monotonically with increasing $ \mathrm{\Delta} U/ {U}_{e} $ which, however, remains of $O(1)$ for all possible zero-pressure-gradient rough-wall boundary layers even at the highest Reynolds numbers. A measurement of intensity at a point in the outer region of the boundary layer can provide an indication of whether the surface is aerodynamically fully rough, without having to determine the surface stress or effective roughness height. Discussion of the implication for smooth/rough flow universality of differences in outer-layer mean velocity wake strength is included.