Asymptotic turbulent friction in 2D rough-walled flows

Abstract

The friction f is the property of wall-bounded flows that sets the pumping cost of a pipeline, the draining capacity of a river, and other variables of practical relevance. For highly turbulent rough-walled pipe flows, f depends solely on the roughness length scale r, and the f -- r relation may be expressed by the Strickler empirical scaling f $\propto$ r${}^{\frac{1}{3}}$. Here, we show experimentally that for soap film flows that are the two-dimensional (2D) equivalent of highly turbulent rough-walled pipe flows, f $\propto$ r and the f -- r relation is not the same in 2D as in 3D. Our findings are beyond the purview of the standard theory of friction but consistent with a competing theory in which f is linked to the turbulent spectrum via the spectral exponent $\alpha$: In 3D, $\alpha$ = 5/3 and the theory yields f $\propto$ r${}^{\frac{1}{3}}$; in 2D, $\alpha$ = 3 and the theory yields f $\propto$ r.

References in corpus (8)

• Turbulent Friction in Rough Pipes and the Energy Spectrum of the Phenomenological Theory
• Wall roughness induces asymptotic ultimate turbulence
• Macroscopic effects of the spectral structure in turbulent flows
• Experimental study of Taylor's hypothesis in a turbulent soap film
• Intermittency and rough-pipe turbulence
• The friction factor of two-dimensional rough-boundary turbulent soap film flows
• Turbulence appearance and non-appearance in thin fluid layers
• Rough-conduit flows and the existence of fully developed turbulence