Intermittency and rough-pipe turbulence

TL;DR

This paper explains the scaling law of the friction factor in rough pipe turbulence using a phenomenological approach, incorporating intermittency effects, and provides empirical evidence for intermittency through data analysis.

Contribution

It introduces a phenomenological scaling argument that accounts for intermittency in rough pipe turbulence, linking the friction factor to the intermittency exponent and improving data collapse.

Findings

Estimated intermittency exponent $\\eta \\approx 0.02$ from data analysis

Intermittency improves the collapse of the friction factor data

Provides empirical evidence for intermittency beyond velocity fluctuation measurements

Abstract

Recently, by analyzing the measurement data of Nikuradze, it has been proposed (N. Goldenfeld, Phys. Rev. Lett. {\bf{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 $\eta$ ($\approx 0.02$), 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.