Time‐series and extended Karhunen–Loève analysis of turbulent drag reduction in polymer solutions

Direct numerical simulations and statistical analysis techniques are used to study the drag‐reducing effect of polymer additives on turbulent channel flow in minimal domains. Additionally, a new formulation of Karhunen–Loève decomposition for viscoelastic flows is introduced, allowing the dominant features of the polymer stress fields to be characterized. In minimal channels, there are intervals of “active” and “hibernating” turbulence that display very different structural and energetic characteristics; the present work illustrates how the statistics of these intervals evolve over the entire range of drag reduction (DR) levels. The effect of viscoelasticity on minimal channel turbulence is twofold: first, it strongly suppresses the active turbulent dynamics that predominate in Newtonian flow and second, at sufficiently high Weissenberg number it stabilizes the dynamics of hibernating turbulence, allowing it to predominate in the maximum drag reduction regime. In this regime, the stress fluctuations become delocalized from the wall region, encompassing the entire flow domain. © 2014 American Institute of Chemical Engineers AIChE J , 60: 1460–1475, 2014