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Common features between the Newtonian laminar–turbulent transition and the viscoelastic drag-reducing turbulence

Published online by Cambridge University Press:  27 August 2019

Anselmo S. Pereira
MINES ParisTech, PSL Research University, Centre for Material Forming (CEMEF), CNRS UMR 7635, CS 10207 rue Claude Daunesse, 06904 Sophia-Antipolis CEDEX, France
Roney L. Thompson*
COPPE, Department of Mechanical Engineering, Universidade Federal do Rio de Janeiro, Centro de Tecnologia, Ilha do Fundão, 21945-970, Rio de Janeiro, RJ, Brazil
Gilmar Mompean
Université de Lille, Polytech’Lille, and Unité de Mécanique de Lille, UML EA 7512, Cité Scientifique, 59655 Villeneuve d’Ascq, France
Email address for correspondence:


The transition from laminar to turbulent flows has challenged the scientific community since the seminal work of Reynolds (Phil. Trans. R. Soc. Lond. A, vol. 174, 1883, pp. 935–982). Recently, experimental and numerical investigations on this matter have demonstrated that the spatio-temporal dynamics that are associated with transitional flows belong to the directed percolation class. In the present work, we explore the analysis of laminar–turbulent transition from the perspective of the recent theoretical development that concerns viscoelastic turbulence, i.e. the drag-reducing turbulent flow obtained from adding polymers to a Newtonian fluid. We found remarkable fingerprints of the variety of states that are present in both types of flows, as captured by a series of features that are known to be present in drag-reducing viscoelastic turbulence. In particular, when compared to a Newtonian fully turbulent flow, the universal nature of these flows includes: (i) the statistical dynamics of the alternation between active and hibernating turbulence; (ii) the weakening of elliptical and hyperbolic structures; (iii) the existence of high and low drag reduction regimes with the same boundary; (iv) the relative enhancement of the streamwise-normal stress; and (v) the slope of the energy spectrum decay with respect to the wavenumber. The maximum drag reduction profile was attained in a Newtonian flow with a Reynolds number near the boundary of the laminar regime and in a hibernating state. It is generally conjectured that, as the Reynolds number increases, the dynamics of the intermittency that characterises transitional flows migrate from a situation where heteroclinic connections between the upper and the lower branches of solutions are more frequent to another where homoclinic orbits around the upper solution become the general rule.

JFM Papers
© 2019 Cambridge University Press 

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