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

*(English)*Zbl 1430.76223Summary: The transition from laminar to turbulent flows has challenged the scientific community since the seminal work of O. Reynolds [Philos. Trans. R. Soc. Lond. 174, 935-982 (1883; JFM 16.0845.02)]. 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.

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\textit{A. S. Pereira} et al., J. Fluid Mech. 877, 405--428 (2019; Zbl 1430.76223)

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