Asymptotic turbulent friction in 2D rough-walled flows.

Vilquin, Alexandre; Jagielka, Julie; Djambov, Simeon; Herouard, Hugo; Fisher, Patrick; Bruneau, Charles-Henri; Chakraborty, Pinaki; Gioia, Gustavo et al. · Sci Adv · 2021

basic_science · Level V

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Abstract

The friction <i>f</i> 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, <i>f</i> depends solely on the roughness length scale <i>r</i>, and the <i>f</i> - <i>r</i> relation may be expressed by the Strickler empirical scaling <i>f</i> ∝ <i>r</i> <sup>1/3</sup> Here, we show experimentally that for soap film flows that are the two-dimensional (2D) equivalent of highly turbulent rough-walled pipe flows, <i>f</i> ∝ <i>r</i> and the <i>f</i> - <i>r</i> 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 <i>f</i> is linked to the turbulent spectrum via the spectral exponent α: In 3D, α = 5/3 and the theory yields <i>f</i> ∝ <i>r</i> <sup>1/3</sup>; in 2D, α = 3 and the theory yields <i>f</i> ∝ <i>r</i>.