Intermittency and rough-pipe turbulence.

Recently, by analyzing the measurement data of Nikuradze [NACA Tech. Memo No. 1292 (1950)], it has been proposed [N. Goldenfeld, Phys. Rev. Lett. 96, 044503 (2006)] that the friction factor, f , of rough-pipe flow obeys a scaling law in the turbulent regime. Here, we provide a phenomenological scaling argument to explain this law and demonstrate how intermittency modifies the scaling form, thereby relating f to the intermittency exponent, eta . By statistically analyzing the measurement data of f , we infer a satisfactory estimate for eta ( approximately 0.02) , the inclusion of which is shown to improve the data-collapse curve. This provides empirical evidence for intermittency other than the direct measurement of velocity fluctuations.