English

Asymptotic turbulent friction in 2D rough-walled flows

Fluid Dynamics 2021-02-03 v1

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 r13^{\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 α\alpha: In 3D, α\alpha = 5/3 and the theory yields f \propto r13^{\frac{1}{3}}; in 2D, α\alpha = 3 and the theory yields f \propto r.

Keywords

Cite

@article{arxiv.2102.00734,
  title  = {Asymptotic turbulent friction in 2D rough-walled flows},
  author = {Alexandre Vilquin and Julie Jagielka and Simeon Djambov and Hugo Herouard and Patrick Fisher and Charles-Henri Bruneau and Pinaki Chakraborty and Gustavo Gioia and Hamid Kellay},
  journal= {arXiv preprint arXiv:2102.00734},
  year   = {2021}
}