title: Critical instability and friction scaling of fluid flows through pipes with rough inner surfaces.
abstract: 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.
authors.affiliation: State Key Laboratory of Turbulence and Complex Systems, CAPT, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China. jjtao@pku.edu.cn
authors.forename: Jianjun
authors.initials: J
authors.lastname: Tao