Roughness-Induced Critical Phenomena in a Turbulent Flow

I present empirical evidence that turbulent flows are closely analogous to critical phenomena, from a reanalysis of friction factor measurements in rough pipes. The data collapse found here corresponds to Widom scaling near critical points, and implies that a full understanding of turbulence requires explicit accounting for boundary roughness.

Figure 1

Friction factor for turbulent flow in a rough pipe, as reported by Nikuradze [11]. The data were measured at different values of $\mathrm{Re}$ and $r/D$, and extracted from Nikuradze’s tabular and graphical presentation.

Figure 2

Friction factor for turbulent flow in a rough pipe, as reported by Nikuradze [11], scaled according to the text. Inset: the same plot on a logarithmic scale.