Reynolds number effects in the outer layer of the turbulent flow in a channel with rough walls

Turbulent channel flow measurements for two different rough surfaces have been compared with a smooth reference case. A range of Reynolds numbers, ${\mathrm{Re}}_{\tau }∊⟨\mathrm{360,6000}⟩$ , has been investigated using hot-wire anemometry. Reynolds stresses and third-order moments are shown to be very little affected by the substantially different wall conditions outside $5k$ , where $k$ is the characteristic length scale of the roughness. In this region, a reasonably good collapse with Reynolds number is demonstrated when scaling with friction velocity is used. This contrasts some of the rough-wall investigations previously published for boundary layers and channels with only one rough wall. It is believed that the differences observed are due to the differences in boundary conditions and that symmetrically roughened channel flows and flows in rough-wall pipes may be better candidates for the Townsend’s wall similarity hypothesis than asymmetrical flows.