Asymptotic turbulent friction in 2D rough-walled flows

Comportement asymptotique du coefficient de friction dans les écoulements turbulents bi-dimensionnels

Alexandre Vilquin (1) , Julie Jagielka (1) , Simeon Djambov (1) , Hugo Herouard (1) , Patrick Fischer (2) , Charles-Henri Bruneau (2) , Pinaki Chakraborty (3) , Gustavo Gioia (4) , Hamid Kellay (1)

1 LOMA - Laboratoire Ondes et Matière d'Aquitaine
2 IMB - Institut de Mathématiques de Bordeaux
3 Fluid Mechanics Unit
4 Continuum Physics Unit

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 ∝ r1/3. Here, we show experimentally that for soap film flows that are the two-dimensional (2D) equivalent of highly turbulent rough-walled pipe flows, f ∝ 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: In 3D, α = 5/3 and the theory yields f ∝ r1/3; in 2D, α = 3 and the theory yields f ∝ r.

Mots clés: Turbulent flows; Friction; rough walls

Domaines: Mécanique des fluides [physics.class-ph]

Alexandre Vilquin, Julie Jagielka, Simeon Djambov, Hugo Herouard, Patrick Fischer, et al.. Asymptotic turbulent friction in 2D rough-walled flows. Science Advances , 2021, 7 (5), ⟨10.1126/sciadv.abc6234⟩. ⟨hal-03125925v2⟩