Critical instability and friction scaling of fluid flows through pipes with rough inner surfaces.

It has been shown experimentally over nearly 80 years that surface fine roughness of circular pipes has a crucial effect on the natural transition to turbulence. In this Letter, a theoretical explanation is suggested for the roughness-induced instability. Once the nonlinear effect of roughness is introduced (through a pipe with fine corrugation surface), the mean velocity profile becomes unstable to three-dimensional, asymmetric, and helical traveling waves at moderate Reynolds numbers. The threshold of the aspect ratio or shape factor of the roughness element required to cause instability scales as Re-2. Inspired by the current model, a scaling form is proposed and the scaled friction factor measurements in rough pipes collapse onto a universal curve.