Examination of a critical roughness height for outer layer similarity

The existence of a critical roughness height for outer layer similarity between smooth and rough wall turbulent boundary layers is investigated. Results are presented for boundary layer measurements on flat plates covered with sandgrain and woven mesh with the ratio of the boundary layer thickness to roughness height $(\delta ∕k)$ varying from 16 to 110 at ${\mathrm{Re}}_{\theta }=7.3\times {10}^3\text{–}13\times {10}^3$ . In all cases tested, the layer directly modified by the roughness (the roughness sublayer) is confined to a region $<5k$ or $<3k_s$ from the wall (where $k_s$ is the equivalent sandgrain roughness height). In the larger roughness cases, this region of turbulence modification extends into the outer flow. However, beyond $5k$ or $3k_s$ from the wall, similarity in the turbulence quantities is observed between the smooth and rough wall boundary layers. These results indicate that a critical roughness height, where the roughness begins to affect most or all of the boundary layer, does not exist. Instead, the outer flow is only gradually modified with increasing roughness height as the roughness sublayer begins to occupy an ever increasing fraction of the outer layer.